{"id":16240,"date":"2023-12-21T06:11:44","date_gmt":"2023-12-21T00:41:44","guid":{"rendered":"https:\/\/envisionmathanswerkey.com\/?p=16240"},"modified":"2023-12-22T12:49:33","modified_gmt":"2023-12-22T07:19:33","slug":"envision-math-common-core-grade-6-answer-key-topic-6","status":"publish","type":"post","link":"https:\/\/envisionmathanswerkey.com\/envision-math-common-core-grade-6-answer-key-topic-6\/","title":{"rendered":"enVision Math Common Core Grade 6 Answer Key Topic 6 Understand And Use Percent"},"content":{"rendered":"

Go through the\u00a0enVision Math Common Core Grade 6 Answer Key<\/a>\u00a0Topic 6 Understand And Use Percent<\/strong>\u00a0regularly and improve your accuracy in solving questions.<\/p>\n

enVision Math Common Core 6th Grade Answers Key Topic 6 Understand And Use Percent<\/h2>\n

Topic 6 Essential Question<\/h3>\n

What is the meaning of percent? How can percent be estimated and found?<\/p>\n

Answer:
\nA percent is a rate that compares a part to a whole.
\nThe percent can be estimated to be 100.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nA percent is a rate that compares a part to a whole.
\nthe percent can be estimated to be 100.
\nthe whole is 100%.<\/p>\n

3-ACT MATH<\/strong><\/p>\n

\"Envision<\/p>\n

Ace the Test<\/strong>
\nNumbers, percents, letters-teachers use grades as a language to help explain language to help explain how you are doing in class. When you know how your grade is determined, it is easier to understand your teacher’s expectations. Think about this during the 3-Act Mathematical Modeling lesson.
\n\"Envision<\/p>\n

Topic 6 enVision STEM Project<\/h3>\n

Did You Know?
\nExtinction normally occurs at a rate of about one to five species per year. The earth is now losing species at 1,000 to 10,000 times that rate, with dozens going extinct every day.
\n\"Envision
\nThere are 1,373 species of birds identified as threatened.
\n\"Envision
\nPolar Bears need ice floes to rest when they travel long distances to find food or migrate. Due to melting ice, the population will likely decrease by more than 30% in the next three generations.<\/p>\n

\"Envision
\nScientists estimate that the population of nearly 17,000 eastern lowland gorillas has declined by more than 50%.<\/p>\n

\"Envision
\nConservation efforts helped the total number of black rhinos to grow from 2,410 to 4,880 in 15 years.
\nAccording to the Chinese government, the population of wild giant pandas has reached 1,864, up from 1,596 at last count.<\/p>\n

In 100 years, the number of the world’s tigers declined from 100,000 to 3,200.
\n\"Envision<\/p>\n

Your Task: Engineering to Prevent Extinction
\nEngineers help to prevent extinction with both direct and indirect solutions. Materials engineers develop wood alternatives. Mechanical and chemical engineers produce clean energy. You and your classmates will research threatened species and identify ways that engineers can help to prevent the extinction of these species.
\n\"Envision<\/p>\n

Topic 6 Get Ready!<\/h3>\n

Review What You Know!<\/strong><\/p>\n

Vocabulary<\/strong>
\nChoose the best term from the box to complete each definition.<\/p>\n

    \n
  • decimal<\/li>\n
  • fraction<\/li>\n
  • ratio<\/li>\n
  • term<\/li>\n<\/ul>\n

    Question 1.
    \nA _________ can be written as x to y, x:y, or \\(\\frac{x}{y}\\).<\/p>\n

    Answer:
    \nA ratio can be written as x to y, x:y, or \\(\\frac{x}{y}\\).<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nA ratio can be written as x to y, x:y, or \\(\\frac{x}{y}\\).
    \nfor example:
    \nA ratio is a comparison of two numbers by division.
    \nthe ratio of x to y can be written as x to y.
    \nx: y, x\/y.<\/p>\n

    \"Understand<\/p>\n

    Question 2.
    \nThe number 2.25 is a ________<\/p>\n

    Answer:
    \nThe number 2.25 is a decimal.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe number 2.25 is a decimal.
    \nfor example:
    \n17.591 in this 1 is in the tens place, 7 is in one’s places.<\/p>\n

    Question 3.
    \nA number that can be used to describe a part of a whole is a ________.<\/p>\n

    Answer:
    \nA number that can be used to describe a part of a whole is a fraction.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nA number that can be used to describe a part of a whole is a fraction.
    \nfor example:
    \n1\/6 is one-sixth.<\/p>\n

    Rates<\/strong><\/p>\n

    Write an equivalent rate.
    \nQuestion 4.
    \n\"Envision<\/p>\n

    Answer:
    \nThe equivalent rate is 12 miles.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n1 hr = 60 miles.
    \n5 hours = 12 miles.
    \n12 x 5 = 60.
    \nso the equivalent rate is 12 miles.
    \n\"Envision-Math-Common-Core-6th-Grade-Answers-Key-Topic-6-Understand<\/p>\n

    Question 5.
    \n\"Envision<\/p>\n

    Answer:
    \nThe missing number of days is 14.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nThe missing number of days is 14.
    \n2 x 4 = 8.
    \n1 x 14 = 28.
    \n\"Envision-Math-Common-Core-6th-Grade-Answers-Key-Topic-6-Understand<\/p>\n

    Question 6.
    \n\"Envision<\/p>\n

    Answer:
    \nThe missing number of bags = 2.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe number of missing bags = 2.
    \n2 x 8 = 16.
    \n5 x 8 = 40.
    \nso the number of missing bags = 2.
    \n\"Envision-Math-Common-Core-6th-Grade-Answers-Key-Topic-6-Understand<\/p>\n

    Question 7.
    \n\"Envision<\/p>\n

    Answer:
    \nThe number of missing cups = 54.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe missing number of cups is 54.
    \n4 x 6 = 24.
    \n9 x 6 = 54.
    \nso the number of missing cups = 54.
    \n\"Envision-Math-Common-Core-6th-Grade-Answers-Key-Topic-6-Understand<\/p>\n

    Question 8.
    \n\"Envision<\/p>\n

    Answer:
    \nThe number of missing seconds = 27 m.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n15 x 9 = 135.
    \n3 x 9 = 27.
    \nso the missing number of seconds = 27 m.
    \n\"Envision-Math-Common-Core-6th-Grade-Answers-Key-Topic-6-Understand<\/p>\n

    Question 9.
    \n\"Envision<\/p>\n

    Answer:
    \nThe missing number of dollars = $24.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n36 lb = 9 lb.
    \n9 x 4 = 36lb.
    \n6 x 4 = 24$.
    \nso the missing number of dollars = $24.<\/p>\n

    Decimal Computation<\/strong><\/p>\n

    Find each product or quotient.
    \nQuestion 10.
    \n21 \u00f7 0.05<\/p>\n

    Answer:
    \nThe quotient is 420.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe two numbers are 21 and 0.05.
    \ndivide the numbers.
    \n21 \/ 0.05 = 420.
    \nSo the quotient is 420.<\/p>\n

    Question 11.
    \n18 \u00d7 1.25<\/p>\n

    Answer:
    \nThe product is 22.5.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe two numbers are 21 and 0.05.
    \nmultiply the numbers.
    \n18 x 1.25 = 22.5.
    \nSo the product is 22.5.<\/p>\n

    Question 12.
    \n10.2 \u00f7 1.2<\/p>\n

    Answer:
    \nThe quotient is 8.5.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe two numbers are 10.2 and 1.2.
    \ndivide the numbers.
    \n10.2 \/ 1.2 = 8.5.
    \nSo the quotient is 8.5.<\/p>\n

    Question 13.
    \n150 \u00d7 0.625<\/p>\n

    Answer:
    \nThe product is 93.75.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe two numbers are 150 and 0.625.
    \nmultiply the numbers.
    \n150 x 0.625 = 93.75.
    \nSo the product is 93.75.<\/p>\n

    Question 14.
    \n4 \u00f7 100<\/p>\n

    Answer:
    \nThe quotient is 0.04.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe two numbers are 4 and 100.
    \ndivide the numbers.
    \n4 \/ 100 = 0.04.
    \nSo the quotient is 0.04.<\/p>\n

    Question 15.
    \n0.25 \u00d7 0.1<\/p>\n

    Answer:
    \nThe product is 0.025.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe two numbers are 0.25 and 0.1.
    \nmultiply the numbers.
    \n0.25 x 0.1 = 0.025.
    \nSo the product is 0.025.<\/p>\n

    Equivalent Ratios<\/strong><\/p>\n

    Write three equivalent ratios for each ratio.
    \nQuestion 16.
    \n\\(\\frac{8}{12}\\)<\/p>\n

    Answer:
    \nThe three equivalent ratios are 4\/6, and 2\/3.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe ratio is 8\/12.
    \n8\/12 = 4\/6.
    \n4\/6 = 2\/3.
    \nso the equivalent ratios are 4\/6, and 2\/3.<\/p>\n

    Question 17.
    \n\\(\\frac{15}{35}\\)<\/p>\n

    Answer:
    \nThe equivalent ratio is 3\/7.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe ratio is 15\/35.
    \n15\/35 = 3\/7.
    \nso the equivalent ratio is 3\/7.<\/p>\n

    Question 18.
    \n\\(\\frac{30}{48}\\)<\/p>\n

    Answer:
    \nThe three equivalent ratios are 10\/18, and 5\/9.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe ratio is 30\/48.
    \n30\/48 = 10\/18.
    \n10\/18 = 5\/9.
    \nso the equivalent ratios are 10\/18, and 5\/9.<\/p>\n

    \"Understand<\/p>\n

    Question 19.
    \nWhat are two ways to find an equivalent ratio for \\(\\frac{10}{25}\\)?<\/p>\n

    Answer:
    \nThe two ways are 5 x 2 = 10, 2 x 5 = 10, and 5 x 5 = 25.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe two ways to find an equivalent ratio is 10\/25.
    \n10\/25 = 2\/5.
    \n5 x 2 = 10.
    \n5 x 5 = 25.<\/p>\n

    Language Development<\/strong>
    \nFill in the cluster diagram using key phrases, sentences, illustrations, or examples related to percents.
    \n\"Envision<\/p>\n

    Pick A Project<\/strong><\/p>\n

    PROJECT 6A
    \nHow would you describe your favorite work of art?
    \nPROJECT: BUILD A MOSAIC
    \n\"Envision<\/p>\n

    PROJECT 6B
    \nIf you had a jar of coins, what could you buy?
    \nPROJECT: ESTIMATE PERCENTS
    \n\"Envision<\/p>\n

    PROJECT 6C
    \nHow does advertising make you want to buy something?
    \nPROJECT: DESIGN FLYERS
    \n\"Envision<\/p>\n

    PROJECT 6D
    \nWhich do you think grows faster-a koala or a panda bear?
    \nPROJECT: MAKE A GROWTH CHART
    \n\"Envision<\/p>\n

    Lesson 6.1 Understand Percent<\/h3>\n

    Explain It!<\/strong>
    \nTom made a vegetable pizza and a pepperoni pizza. He cut the vegetable pizza into 5 equal slices and the pepperoni pizza into 10 equal slices. Tom’s friends ate 2 slices of vegetable pizza and 4 slices of pepperoni pizza.<\/p>\n

    I can… represent and find the percent of a whole.
    \n\"Envision<\/p>\n

    A. Draw lines on each rectangle to represent the equal slices into which each pizza was cut.
    \n\"Envision<\/p>\n

    Answer:
    \nThe number of lines on vegetable pizza is 5.
    \nthe number of lines on pepperoni pizza is 10.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nTom made a vegetable pizza and a pepperoni pizza.
    \nHe cut the vegetable pizza into 5 equal slices and the pepperoni pizza into 10 equal slices.
    \n5\/10 = 1\/2.
    \nso the number of lines on vegetable pizza is 5.
    \nthe number of lines on pepperoni pizza is 10.
    \n\"Envision-Math-Common-Core-6th-Grade-Answers-Key-Topic-6-Understand<\/p>\n

    B. Construct Arguments Tom says his friends ate the same amount of vegetable pizza as pepperoni pizza. How could that be true?<\/p>\n

    Answer:
    \nYes, Tom was correct.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nTom made a vegetable pizza and a pepperoni pizza.
    \nHe cut the vegetable pizza into 5 equal slices and the pepperoni pizza into 10 equal slices.
    \n5\/10 = 1\/2.
    \nso the number of lines on vegetable pizza is 5.
    \nthe number of lines on pepperoni pizza is 10.
    \nso Tom was correct.<\/p>\n

    Focus on math practices
    \nModel with Math What if Tom’s friends ate 6 of the pepperoni pizza? How could you use the rectangles above to find an equal amount of vegetable pizza?<\/p>\n

    Answer:
    \nThe equal amount of vegetable pizza = 3.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nTom’s friends ate 6 of the pepperoni pizza.
    \nvegetable pizza and pepperoni pizza are in the ratio is 1: 2.
    \nso the equal amount of vegetable pizza = 3.<\/p>\n

    KEY CONCEPT<\/strong>
    \nA percent is a rate that compares a part to a whole. The second term in the rate is always 100. The whole is 100%.
    \n\"Envision<\/p>\n

    Do You Understand?<\/strong>
    \nQuestion 1.
    \nEssential Question<\/strong> How can you represent a rate with 100 as the whole?<\/p>\n

    Answer:
    \nI will represent the whole as 100%.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nA percent is a rate that compares a part to a whole.
    \nThe second term in the rate is always 100.
    \nthe whole is 100%.<\/p>\n

    Question 2.
    \nWhen writing a percent as a fraction, what number do you write as the whole, or denominator?<\/p>\n

    Answer:
    \nThe percentage can be converted into a fraction by removing the %symbol and then writing the value in the form of a fraction with a 100 in the denominator.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nThe percent to a fraction is the conversion of percentage values to a fraction.
    \nAs per the percent to fraction steps, the percentage can be converted into a fraction by removing the % symbol and then writing the value in the form of a fraction with a 100 in the denominator.<\/p>\n

    Question 3.
    \nWhy are tenths, fifths, fourths, and halves easy to express as percents?<\/p>\n

    Answer:
    \n1\/10 = 0.1.
    \n1\/5 = 0.2.
    \n1\/4 = 0.25.
    \n1\/2 = 0.5.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \ntenths, fifths, fourths, and halves express as percents.
    \ntenths = 1\/10 = 0.1.
    \nfifths = 1\/5 = 0.2.
    \nfourths = 1\/4 = 0.25.
    \nhalves = 1\/2 = 0.5.<\/p>\n

    Question 4.
    \nWhy is the grid in Example 1 a good way to represent a percent?
    \nAnswer:<\/p>\n

    Question 5.
    \nLook for Relationships If CD in Example 3 represents 100%, is the length of a line segment that is 300% longer or shorter than 4 inches? Explain.
    \nAnswer:<\/p>\n

    Do You Know How?<\/strong>
    \nIn 6 and 7, write the percent of each figure that is shaded.
    \nQuestion 6.
    \n\"Envision<\/p>\n

    Answer:
    \nThe percent of the figure = 40%.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe above figure is divided into 10 equal parts.
    \nout of 10 parts 4 parts are shaded.
    \n4\/10 = 0.4%.
    \nso the percent of the figure = 40%.<\/p>\n

    Question 7.
    \n\"Envision
    \nAnswer:
    \nThe percent of the figure = 7%.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe above figure is divided into 100 equal parts.
    \nout of 100 parts 7 parts are shaded.
    \n7\/100 = 0.07.
    \nso the percent of the figure = 7%.<\/p>\n

    In 8-10, find the percent.<\/p>\n

    \"Understand
    \nQuestion 8.
    \n\"Envision<\/p>\n

    Answer:
    \nThe percent is 5%.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n1 x 20 = 20.
    \n5 x 4 = 20.
    \n20 \/ 4 = 5.
    \nso the percent is 5%.
    \n\"Envision-Math-Common-Core-6th-Grade-Answers-Key-Topic-6-Understand<\/p>\n

    Question 9.
    \n\"Envision<\/p>\n

    Answer:
    \nThe percent is 1%.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n3 x 10 = 30.
    \n10 x 3 = 30.
    \n30\/30 = 1%.
    \nso the percent is 1%.
    \n\"Envision-Math-Common-Core-6th-Grade-Answers-Key-Topic-6-Understand<\/p>\n

    Question 10.
    \n\"Envision<\/p>\n

    Answer:
    \nThe percent is 55.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n11 x 5 = 55.
    \n20 x 4 = 100.
    \n55\/100 = 55%.
    \n\"Envision-Math-Common-Core-6th-Grade-Answers-Key-Topic-6-Understand<\/p>\n

    Question 11.
    \nFind the percent of the line segment that point D represents in Example 2.<\/p>\n

    Answer:<\/p>\n

    Practice & Problem Solving<\/strong><\/p>\n

    In 12 and 13, shade each model to represent the percent.
    \nQuestion 12.
    \n14%
    \n\"Envision<\/p>\n

    Answer:
    \nThe percent is 14%.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe 14 percent.
    \nthe above figure is divided into 100 parts.
    \nso we have to shade the 14 boxes.<\/p>\n

    Question 13.
    \n20%
    \n\"Envision<\/p>\n

    Answer:
    \nThe percent is 20%.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthere are 5 boxes.
    \n20% of the boxes are filled.
    \none box is shaded.<\/p>\n

    In 14 and 15, use \\(\\overline{A B}\\).
    \n\"Envision
    \nQuestion 14.
    \nIf \\(\\overline{A B}\\) represents 50%, what is the length of a line segment that is 100%?<\/p>\n

    Answer:
    \nThe length of the line segment that is 100% is 6 in.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe length of the segment is 3 in if it is 50%.
    \nthe length of the segment is 6 in if it is 100%.
    \n3 + 3 = 6.
    \nso the length of the line segment that is 100% is 6 in.<\/p>\n

    Question 15.
    \nIf \\(\\overline{A B}\\) is 300%, what is the length of a line segment that is 100%?<\/p>\n

    Answer:
    \nThe length of a line segment that is 100% is 1in.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n\\(\\overline{A B}\\) is 300%.
    \nthe total length of the line segment is 3 in.
    \nso the length of a line segment that is 100% is 1 in.<\/p>\n

    Question 16.
    \nYour friend shows you a coin collection. In it, \\(\\frac{45}{50}\\) of the coins are quarters. What percent of the coins are quarters?<\/p>\n

    Answer:
    \nThe percent of the coins are quarters is 0.25.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n\\(\\frac{45}{50}\\) of the coins are quarters.
    \n45\/50 = 9\/10.
    \nso the percent of the coins are quarters is 0.25.<\/p>\n

    Question 17.
    \nUse Structure In a race, 19 out of 50 runners finished in fewer than 30 minutes. What percent of the runners finished in fewer than 30 minutes? Write an equivalent fraction to find the percent.<\/p>\n

    Answer:
    \nThe equivalent fraction is 9.5%.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n19 out of 50 runners finished in fewer than 30 minutes.
    \n19\/50 = 9.5.
    \nso the equivalent fraction is 9.5%.<\/p>\n

    Question 18.
    \nA basketball player made 63 out of 100 attempted free throws. What percent of free throws did the player make?<\/p>\n

    Answer:
    \nThe percent of free throws did the player make = 63%.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nA basketball player made 63 out of 100 attempted free throws.
    \n63\/100 = 63%.
    \nso the percent of free throws did the player make = 63%.<\/p>\n

    Question 19.
    \nHarry kept a weather journal for September. The sun was shining on 4 out of every 5 days. On what percent of the days was the sun not shining?
    \n\"Envision<\/p>\n

    Answer:
    \nThe number of days was the sun not shining = 8%.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nHarry kept a weather journal for September.
    \nThe sun was shining on 4 out of every 5 days.
    \n4\/5 = 0.8.
    \n8\/100 = 0.08.
    \nso the number of days was the sun not shining = 8%.<\/p>\n

    In 20 and 21, use the line segment.
    \n\"Envision
    \nQuestion 20.
    \nWhat percent of the line segment is 6 inches long?<\/p>\n

    Answer:
    \nThe line segment is 6 inches long is 100%.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe line segment is divided into 6 parts.
    \none part is equal to 1 inch.
    \n6 parts = 6 inches.
    \nso the line segment is 6 inches long is 100%.<\/p>\n

    Question 21.
    \nWhat percent of the line segment does point C represent?<\/p>\n

    Answer:
    \nThe percent of the line segment does point C represents is 50%.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe line segment is divided into 6 parts.
    \none part is equal to 1 inch.
    \n6 parts = 6 inches.
    \nso the percent of the line segment does point C represents is 50%.<\/p>\n

    \"Understand<\/p>\n

    Question 22.
    \nCritique Reasoning<\/strong> Kyle solved 18 of 24 puzzles in a puzzle book. He says that he can use an equivalent fraction to find the percent of puzzles in the book that he solved. How can he do that? What is the percent?<\/p>\n

    Answer:
    \nThe equivalent fractions are 3\/4 and 6\/8.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nKyle solved 18 of 24 puzzles in a puzzle book.
    \n18\/24 = 3\/4.
    \n18\/24 = 6\/8.
    \nso the equivalent fractions are 3\/4 and 6\/8.<\/p>\n

    Question 23.
    \nReasoning<\/strong> Twenty of the students in Hannah’s class, or 80% of the class, voted to have pizza for lunch every Wednesday. How many students are in Hannah’s class?<\/p>\n

    Answer:
    \nThe number of students is in Hannah’s class = 25 students.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nTwenty of the students in Hannah’s class, or 80% of the class, voted to have pizza for lunch every Wednesday.
    \n20\/100 = 1\/5.
    \nso the number of students is in Hannah’s class = 25 students.<\/p>\n

    Question 24.
    \nAccording to a survey of workers, \\(\\frac{2}{20}\\) of the workers walk to work, \\(\\frac{1}{20}\\) bike, \\(\\frac{4}{20}\\) carpool, and \\(\\frac{13}{20}\\) drive alone. What percent of the workers walk or bike to work?<\/p>\n

    Answer:
    \nThe percent of the workers walk or bike to work = 30 %.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nAccording to a survey of workers, \\(\\frac{2}{20}\\) of the workers walk to work,
    \n\\(\\frac{1}{20}\\) bike,
    \n\\(\\frac{4}{20}\\) carpool,
    \n\\(\\frac{13}{20}\\) drive alone.
    \n2\/20 = 1\/10.
    \n1\/20 + 1\/10 = 1\/30.<\/p>\n

    Question 25.
    \nHigher Order Thinking<\/strong> From Monday through Friday, James works in the library on 2 days and in the cafeteria on another day. On Saturday and Sunday, James washes cars 50% of the days. How many days does James work in a week? What percent of the days from Monday through Friday does he work?<\/p>\n

    Answer:
    \nThe percent of the days from Monday through Friday does he work = 80%.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nFrom Monday through Friday, James works in the library on 2 days and in the cafeteria on another day.
    \nOn Saturday and Sunday, James washes cars 50% of the day.
    \n2 + 1 = 3.
    \n3 + 2 = 5.
    \nso the percent of the days from Monday through Friday does he work = 80%.<\/p>\n

    Assessment Practice<\/strong><\/p>\n

    Question 26.
    \nSelect all the figures that are shaded to represent 20% of the whole.
    \n\"Envision<\/p>\n

    Answer:
    \nOptions 1, 3, and 5 are correct.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe figures that are shaded to 20% as a whole is:
    \nin the 1st figure, the circle is divided into 10 parts.
    \n20% of the figure is shaded.
    \nin the 3rd figure, there are 5 boxes.
    \n1 box is filled is 20%.
    \nso options 1, 3, and 5 are correct.
    \n\"Envision-Math-Common-Core-6th-Grade-Answers-Key-Topic-6-Understand<\/p>\n

    Lesson 6.2 Relate Fractions, Decimals, and Percents<\/h3>\n

    Solve & Discuss It!<\/strong>
    \nThe grid is shaded with blue, orange, and yellow. What part of the grid is shaded blue? What part is shaded orange? What part of the grid is shaded?<\/p>\n

    I can… write equivalent values as fractions, decimals, or percents.
    \n\"Envision<\/p>\n

    Use Structure
    \nLook for patterns in the grid to help count parts that are shaded in blue and in orange.<\/p>\n

    Focus on math practices
    \nReasoning Write the part of the grid that is shaded yellow as a decimal and a percent. How are the decimal and the percent alike and how are they different?<\/p>\n

    Essential Question<\/strong>
    \nHow are fractions, decimals, and percents related?<\/p>\n

    Try It!<\/strong><\/p>\n

    Ana spends 0.45 of her homework time reading. What is 0.45 as a percent? Explain.<\/p>\n

    Answer:
    \nThe percent is 45.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nAna spends 0.45 of her homework time reading.
    \n0.45 can be written as a percent is 45.
    \nso the percent is 45.<\/p>\n

    Convince Me! What relationship do you see when comparing the equivalent fraction and percent?<\/p>\n

    Try It!<\/strong><\/p>\n

    Isabel spends \\(\\frac{3}{8}\\) of her homework time on reading. What is \\(\\frac{3}{8}\\) as a decimal and as a percent?<\/p>\n

    Answer:
    \n3\/8 = 0.375 and 0.00375%<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nIsabel spends \\(\\frac{3}{8}\\) of her homework time on reading..
    \n3\/8 = 0.375.
    \n3\/8 = 0.00375%.<\/p>\n

    KEY CONCEPT<\/strong>
    \nYou can use division and equivalent ratios to express fractions, decimals, and percents in equivalent forms.
    \n\"Envision<\/p>\n

    Do You Understand?<\/strong>
    \nQuestion 1.
    \nEssential Question<\/strong> How are fractions, decimals, and percents related?<\/p>\n

    Answer:
    \nFractions, decimals, and percents are related.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n0.75 = 75\/100.
    \n75\/100 = 75%.
    \n0.75 = 75\/100 = 75%.
    \nso the fractions, decimals, and percents are related.<\/p>\n

    Question 2.
    \nWhy do you use a denominator of 100 when you write a percent as a fraction?<\/p>\n

    Answer:
    \nWe can use a denominator of 100 when we write a percent as a fraction.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nwe can use a denominator of 100 when we write a percent as a fraction.
    \nfor example:
    \n75\/100 = 0.75.
    \n0.75 = 75%.<\/p>\n

    Question 3.
    \nLook for Relationships How do you use the digits in a hundredths decimal to write a percent?
    \nAnswer:<\/p>\n

    Question 4.
    \nHow do you write a fraction with a denominator of 20 as a decimal?<\/p>\n

    Answer:
    \nThe fraction with a denominator of 20 as a decimal is 0.05.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n5\/100 = 20.
    \n5\/100 = 0.05.
    \nso the fraction with a denominator of 20 as a decimal is 0.05.<\/p>\n

    Do You Know How?<\/strong>
    \nIn 5-7, write each number in equivalent forms using the two other forms of notation: fraction, decimal, or percent.
    \nQuestion 5.
    \n27%<\/p>\n

    Answer:
    \nFraction = 27\/100.
    \ndecimal = 0.27.
    \npercent = 27%.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe decimal is 0.27.
    \nThe fraction is 27\/100.
    \nthe percent is 27%.<\/p>\n

    Question 6.
    \n0.91<\/p>\n

    Answer:
    \nFraction = 91\/100.
    \ndecimal = 0.91.
    \npercent = 91%.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe decimal is 0.91.
    \nThe fraction is 91\/100.
    \nthe percent is 91%.<\/p>\n

    Question 7.
    \n\\(\\frac{6}{100}\\)<\/p>\n

    Answer:
    \nFraction = 6\/100.
    \ndecimal = 0.06.
    \npercent = 6%.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe decimal is 0.06.
    \nThe fraction is 6\/100.
    \nthe percent is 6%.<\/p>\n

    Question 8.
    \nGreek yogurt has 25% of the calcium that most people need in a day. What is 25% as a decimal?
    \n\"Envision<\/p>\n

    Answer:
    \nThe decimal is 0.25.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nGreek yogurt has 25% of the calcium that most people need in a day.
    \n25%.
    \nso the decimal is 0.25.<\/p>\n

    Question 9.
    \nLinda received \\(\\frac{4}{5}\\) of the votes in the election for student council president. What percent of the votes did Linda receive?<\/p>\n

    Answer:
    \nThe percent of the votes did Linda receive = 80%.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nLinda received \\(\\frac{4}{5}\\) of the votes in the election for student council president.
    \n4\/5 = 0.8.
    \n80% = 80\/100.
    \n8\/10 = 0.8.
    \nso the percent of the votes did Linda receive = 80%.<\/p>\n

    Practice & Problem Solving<\/strong><\/p>\n

    Leveled Practice in 10-15, write each number in equivalent forms using the two other forms of notation: fraction, decimal, or percent.
    \nQuestion 10.
    \n0.25
    \n\"Envision<\/p>\n

    Answer:
    \n0.25 = 25\/100 = 25%.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n0.25 = 25\/100.
    \n25\/100 = 25%.
    \n25\/25 = 1.
    \n100\/25 = 4.
    \n\"Envision-Math-Common-Core-6th-Grade-Answers-Key-Topic-6-Understand<\/p>\n

    Question 11.
    \n\"Envision<\/p>\n

    Answer:
    \n2\/2 = 2 x 50\/ 2 x 50 = 100\/100 = 1%.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n2\/2 = 2x 50 = 100.
    \n100\/100 = 1%.
    \n2\/2 = 2\/1 = 2%.
    \n\"Envision-Math-Common-Core-6th-Grade-Answers-Key-Topic-6-Understand<\/p>\n

    Question 12.
    \n7%
    \n\"Envision<\/p>\n

    Answer:
    \n7% = 7\/100.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n7 percent = 7%.
    \n7% = 7\/100.
    \n7\/100 = 0.07.
    \n\"Envision-Math-Common-Core-6th-Grade-Answers-Key-Topic-6-Understand<\/p>\n

    Question 13.
    \n38%<\/p>\n

    Answer:
    \n38% = 0.38.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n38 percent = 38%.
    \n38% = 38\/100.
    \n38\/100 = 0.38.<\/p>\n

    Question 14.
    \n\\(\\frac{7}{8}\\)<\/p>\n

    Answer:
    \n7\/8 = 0.875.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n7\/8 = 0.875.
    \n0.875 = 875\/100.
    \n875\/100 = 87.5.<\/p>\n

    Question 15.
    \n0.04<\/p>\n

    Answer:
    \n0.04 = 4%.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n0.04 = 4%.
    \n4% = 4\/100.
    \n4\/100 = 0.04.<\/p>\n

    Question 16.
    \nDevon answered 23 out of 25 problems on a math test correctly. What percent of the problems did Devon answer correctly?
    \n\"Envision<\/p>\n

    Answer:
    \nThe percent of the problems did Devon answer = 92%.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nDevon answered 23 out of 25 problems on a math test correctly.
    \n23\/25 = 0.92.
    \n92\/100 = 0.92.
    \n0.92 = 92%.<\/p>\n

    Question 17.
    \nReasoning<\/strong> How could you write \\(\\frac{4}{8}\\) as a percent without dividing?<\/p>\n

    Answer:
    \n4\/8 = 0.5.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n4\/8 = 0.5.
    \n5\/10 = 0.5.
    \n5\/100 = 0.05.
    \n4\/8 = 0.5%.<\/p>\n

    In 18-21, use the circle graph.
    \n\"Envision
    \nQuestion 18.
    \nMany chemical elements, can be found in Earth’s atmosphere. What fraction of Earth’s atmosphere is made up of nitrogen?<\/p>\n

    Answer:
    \nNitrogen is made up of 78%.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nMany chemical elements, can be found in Earth’s atmosphere.
    \nnitrogen is made up of 78%.
    \noxygen is made up of 21%.
    \nother gases are made up of 1%.<\/p>\n

    Question 19.
    \nHow much of Earth’s atmosphere is made up of oxygen? Write the part as a decimal.<\/p>\n

    Answer:
    \nThe Earth’s atmosphere is made up of oxygen is 0.21.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nThe Earth’s atmosphere is made up of oxygen.
    \n21% = 21\/100.
    \n21\/100 = 0.21.
    \nso the Earth’s atmosphere is made up of oxygen is 0.21.<\/p>\n

    Question 20.
    \nWhat percent of gases in Earth’s atmosphere does the whole circle graph represent?<\/p>\n

    Answer:
    \nThe percent of gases in Earth’s atmosphere does the whole circle graph represents is 1%.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nNitrogen gas = 78%.
    \noxygen gas = 21%.
    \nthe percent of gases in Earth’s atmosphere does the whole circle graph represents is 1%.<\/p>\n

    Question 21.
    \nWhat fraction of the gases in Earth’s atmosphere are gases other than nitrogen and oxygen?<\/p>\n

    Answer:
    \nThe fraction of the gases in the Earth’s atmosphere is gases other than nitrogen and oxygen = 1\/100.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nMany chemical elements, can be found in Earth’s atmosphere.
    \nnitrogen is made up of 78%.
    \noxygen is made up of 21%.
    \nthe fraction of the gases in the earth’s atmosphere = 1\/100.
    \n1\/100 = 0.01.<\/p>\n

    Question 22.
    \nLook for Relationships All T-shirts in a store are on sale as shown. Is this markdown greater than or less than a markdown of off the original price? Explain.
    \n\"Envision<\/p>\n

    Answer:
    \nThe original price = 25%.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nAll T-shirts in a store are on sale as shown.
    \n100 – 25 = 75%.
    \nso the original price = 25%.<\/p>\n

    Question 23.
    \nCritique Reasoning<\/strong> Enrollment at Jacksonville Middle School increased by 3% this year. Sofia says that the increase, written as a decimal, is 0.3. Is Sofia correct? Explain.<\/p>\n

    Answer:
    \nNo, Sofia is correct.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nEnrollment at Jacksonville Middle School increased by 3% this year.
    \n3% = 3\/100.
    \n3\/100 = 0.03.
    \nso Sofia is correct.<\/p>\n

    Question 24.
    \nGeneralize<\/strong> What are the attributes of fractions that are equivalent to 100%?<\/p>\n

    Answer:
    \nThe attributes of fractions that are equivalent to 100% = 1000\/100.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe fractions are 1000\/100.
    \n1000\/100 = 100.
    \nso the attributes of fractions that are equivalent to 100% = 100.<\/p>\n

    Question 25.
    \nThe cost of building a new library is 0.85 of the cost of remodeling the old library. What is the cost as a percent?<\/p>\n

    Answer:
    \nThe cost as a percent = 85%.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nThe cost of building a new library is 0.85 of the cost of remodeling the old library.
    \n0.85 = 85\/100.
    \n85\/100 = 85%.
    \nso the cost as a percent = 85%.<\/p>\n

    Question 26.
    \nNine out of every 20 people walking out of a movie theater say that they would recommend the movie to a friend. What percent of the people would recommend the movie to a friend?<\/p>\n

    Answer:
    \nThe percent of the people who would recommend the movie to a friend = 45%.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nNine out of every 20 people walking out of a movie theater say that they would recommend the movie to a friend.
    \n9\/20 = 0.45.
    \n45\/100 = 0.45.
    \nso the percent of the people who would recommend the movie to a friend = 45%.<\/p>\n

    Question 27.
    \nHigher Order Thinking<\/strong> Ms. Rose bought a package of sea life stickers. Out of every 10 stickers, 4 are starfish. If there are 60 stickers in the package, what fraction of the stickers are starfish? What percent of the stickers in the package are starfish?
    \n\"Envision<\/p>\n

    Answer:
    \nThe percent of the stickers in the package is starfish = 24%.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nMs. Rose bought a package of sea life stickers.
    \nOut of every 10 stickers, 4 are starfish.
    \n10\/4 = 5\/2.
    \nfor 60 there are 24 starfish.
    \nso the percent of the stickers in the package is starfish = 24%.<\/p>\n

    Assessment Practice<\/strong><\/p>\n

    Question 28.
    \n\\(\\frac{3}{4}\\) can be represented as a percent. Select all the fractions and decimals that are also equivalent to this percent.
    \n\u2610 \\(\\frac{51}{68}\\)
    \n\u2610 0.34
    \n\u2610 \\(\\frac{36}{50}\\)
    \n\u2610 0.75
    \n\u2610 \\(\\frac{39}{52}\\)<\/p>\n

    Answer:
    \nOptions A, D, and E are correct.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n3\/4 = 0.75.
    \n51\/68 = 0.75.
    \n39\/52 = 0.75.
    \nso options A, D, and E are correct.<\/p>\n

    Question 29.
    \nThere are 110 sixth-grade students in a Florida middle school. 40% of the students enjoy playing video games on the weekends. Using the percent as a rate per 100, how many students enjoy playing video games?<\/p>\n

    Answer:
    \nThe number of students who enjoy playing video games = 4%.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nThere are 110 sixth-grade students in a Florida middle school.
    \n40% of the students enjoy playing video games on the weekends.
    \n40\/100 = 0.4.
    \nso the number of students who enjoy playing video games = 4%.<\/p>\n

    Lesson 6.3 Represent Percents Greater Than 100 or Less Than 1<\/h3>\n

    Solve & Discuss It!<\/strong>
    \nMarci, Bobby, and Max began their homework at the same time. Marci finished her homework in 60 minutes. Bobby finished his homework in 50% of the time it took Marci to finish. Max finished his homework in 150% of Marci’s time. How long did each of them work?
    \nI can… write percents that are greater than 100 or less than 1.
    \n\"Envision<\/p>\n

    Model with Math
    \nHow can you use a model to represent a part that is greater than a whole?<\/p>\n

    Focus on math practices
    \nReasoning Did Max spend more time or less time on his homework than Marci? Explain.<\/p>\n

    Essential Question<\/strong>
    \nHow can you write a percent greater than 100 or less than 1 as a fraction and as a decimal?<\/p>\n

    Try It!<\/strong><\/p>\n

    The area of a new movie theater is 225% of the area of the old theater. What is 225% as a fraction and as a decimal?<\/p>\n

    Answer:
    \nFraction = 225\/100.
    \nDecimal = 2.25.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe area of a new movie theater is 225% of the area of the old theater.
    \n225% = 225\/100.
    \n225\/100 = 2.25.
    \nso fraction = 225\/100.
    \ndecimal = 2.25.<\/p>\n

    Convince Me! How would you write 1.75 as a percent? Give an example in which you would use a percent that is greater than 100.<\/p>\n

    Answer:
    \nPercent = 175\/100.
    \nThe percent that is greater than 100 is 175.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n175\/100 = 1.75.
    \n175 is greater than 100.<\/p>\n

    Try It!<\/strong><\/p>\n

    Write each percent as a fraction and as a decimal.
    \na. \\(\\frac{2}{5}\\)%<\/p>\n

    Answer:
    \n2\/5 = 0.4.
    \n0.4% = 0.004.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n2\/5 % = 0.4%.
    \n0.4% = 0.004.<\/p>\n

    b. 0.3%<\/p>\n

    Answer:
    \n0.003.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n0.3% = 3\/100.
    \n3\/100 = 0.003.<\/p>\n

    KEY CONCEPT<\/strong>
    \nYou can express percents greater than 100 or less than 1 in equivalent forms.
    \n\"Envision<\/p>\n

    Do You Understand?<\/strong>
    \nQuestion 1.
    \nEssential Question<\/strong> How can you write a percent greater than 100 or less than 1 as a fraction and as a decimal?<\/p>\n

    Answer:
    \nThe percent greater than 100 or less than 1 is 275%.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nThe percent greater than 100 or less than 1 is 275%.
    \n275% = 275\/100.
    \n275\/100 = 11\/4.
    \n275% = 11\/4 = 2.75.
    \nso the percent greater than 100 or less than 1 is 275%.<\/p>\n

    Question 2.
    \nReasoning Explain why \\(\\frac{3}{4}\\) is less than 100%.<\/p>\n

    Answer:
    \n3\/4 = 0.75.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n3\/4 = 0.75.
    \n75\/100 = 0.75.
    \n75% is less than 100%.
    \nso 3\/4 is less than 100%.<\/p>\n

    Question 3.
    \nReasoning<\/strong> Why is the numerator greater than the denominator in a fraction that is equivalent to a percent greater than 100?<\/p>\n

    Answer:<\/p>\n

    Question 4.
    \nExplain the difference between \\(\\frac{1}{2}\\) and \\(\\frac{1}{2}\\)%.<\/p>\n

    Answer:
    \nThe difference between 1\/2 and 1\/2% is 0.5.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \n+given that,
    \n1\/2 = 0.5.
    \n1\/2 = 0.5%.
    \n0.5\/100 = 0.005.
    \n0.5 is greater than 0.005.<\/p>\n

    Do You Know How?<\/strong>
    \nIn 5\u20137, write each percent as a fraction and as a decimal.
    \nQuestion 5.
    \n150%<\/p>\n

    Answer:
    \nFraction = 150\/100.
    \ndecimal = 1.5.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe percent is 150%.
    \nfraction = 150\/100.
    \n150\/100 = 1.5.
    \ndecimal = 1.5.<\/p>\n

    Question 6.
    \n\\(\\frac{3}{10}\\)%<\/p>\n

    Answer:
    \n3\/10% = 0.003.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe percent is 3\/10%.
    \n3\/10 = 0.3.
    \n0.3% = 0.3\/100.
    \n0.3\/100 = 0.003.<\/p>\n

    Question 7.
    \n0.24%<\/p>\n

    Answer:
    \nFraction = 24\/100.
    \nDecimal = 0.24.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe percent is 0.24%.
    \nfraction is 24\/100.
    \nDecimal = 0.24.<\/p>\n

    Question 8.
    \nKelly saved \\(\\frac{4}{5}\\)% of her allowance. What is this percent expressed as a fraction and as a decimal?<\/p>\n

    Answer:
    \nThe percent expressed as a fraction and as a decimal = 0.8\/100 and 0.008.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nKelly saved \\(\\frac{4}{5}\\)% of her allowance.
    \nthe percent is 4\/5%.
    \n4\/5% = 0.8%.
    \n0.8% = 0.8\/100.
    \n0.8\/100 = 0.008.<\/p>\n

    Question 9.
    \nMrs. Sanchez sold her house for 250% of the amount she paid for it. What is this percent expressed as a fraction and as a decimal?<\/p>\n

    Answer:
    \nThe percent expressed as a fraction and as a decimal is 250\/100 and 2.5.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nMrs. Sanchez sold her house for 250% of the amount she paid for it.
    \n250\/100 = 25\/10.
    \n25\/10 = 2.5.
    \nso the percent expressed as a fraction and as a decimal is 250\/100 and 2.5.<\/p>\n

    Practice & Problem Solving<\/strong><\/p>\n

    Leveled Practice in 10-15, write each percent as a fraction and as a decimal.
    \nQuestion 10.
    \n\"Envision<\/p>\n

    Answer:
    \n3\/5% = 0.006.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n3\/5% = 3\/5 \/ 100.
    \n3\/5 x 1\/100.
    \n3\/500 = 0.006.
    \n\"Envision-Math-Common-Core-6th-Grade-Answers-Key-Topic-6-Understand<\/p>\n

    Question 11.
    \n\"Envision<\/p>\n

    Answer:
    \n3\/4% = 0.75%.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n3\/4% = 3\/4 \/ 100.
    \n0.75\/100 = 0.0075.
    \n3\/4% = 0.0075.
    \n\"Envision-Math-Common-Core-6th-Grade-Answers-Key-Topic-6-Understand<\/p>\n

    Question 12.
    \n0.1% = 0.1 \u00f7 100
    \n\"Envision<\/p>\n

    Answer:
    \n0.1% = 0.1 \/ 100.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n0.1% = 0.1 \/ 100.
    \n0.1 \/ 100 = 0.001.
    \n1\/1000 = 0.001.
    \n\"Envision-Math-Common-Core-6th-Grade-Answers-Key-Topic-6-Understand<\/p>\n

    Question 13.
    \n0.4% = 0.4 \u00f7 100
    \n\"Envision<\/p>\n

    Answer:
    \n0.4% = 0.4 \/ 100.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n0.4% = 0.4 \/ 100.
    \n0.4\/100 = 4\/10.
    \n4\/10 = 0.4.
    \n\"Envision-Math-Common-Core-6th-Grade-Answers-Key-Topic-6-Understand<\/p>\n

    Question 14.
    \n322%<\/p>\n

    Answer:
    \n322% = 322\/100.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n322% = 322\/100.
    \n322\/100 = 3.22.
    \n322% = 3.22.<\/p>\n

    Question 15.
    \n210%<\/p>\n

    Answer:
    \n210% = 2.10.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n210% = 210\/100.
    \n210\/100 = 2.10.
    \n210% = 2.10.<\/p>\n

    Question 16.
    \nReasoning<\/strong> Use the art at the right. How do you express the length of the Queen Mary 2 as it compares to the height of the Washington Monument as a fraction and as a decimal?
    \n\"Envision<\/p>\n

    Answer:
    \nThe height of the Washington Monument is = 2.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe length of the Queen Mary 2 as it compares to the height of the Washington Monument.
    \n200% = 200\/100.
    \n200\/100 = 2.
    \nso the height of the Washington Monument is 2.<\/p>\n

    Question 17.
    \nAbout \\(\\frac{7}{10}\\)% of the passengers on a cruise ship swam in the ship’s pool on the first day of the cruise. How would you express this number as a decimal and as a percent?<\/p>\n

    Answer:
    \nThe number can be written as a decimal and as a percent = 0.007 and 7\/10%.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nAbout \\(\\frac{7}{10}\\)% of the passengers on a cruise ship swam in the ship’s pool on the first day of the cruise.
    \n7\/10% = 7\/1000.
    \n7\/1000 = 0.007.
    \nso the number can be written as a decimal and as a percent = 0.007.<\/p>\n

    Question 18.
    \nThe fastest boat can reach speeds more than 710% as fast as the Queen Mary 2. How would you express this number as a fraction and as a decimal?<\/p>\n

    Answer:
    \nThe number as a fraction and as a decimal is 710\/100 and 7.1.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nThe fastest boat can reach speeds more than 710% as fast as the Queen Mary 2.
    \n710% = 710\/100.
    \n710\/100 = 71\/10.
    \n71\/10 = 7.1.
    \nso the number as a fraction and as a decimal is 710\/100 and 7.1.<\/p>\n

    Question 19.
    \nThe weight of the Washington Monument is about 105% as much as the Queen Mary 2. Write this percent as a fraction and as a decimal.<\/p>\n

    Answer:
    \nThe number can be written as a fraction and as a decimal = 1.5.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nThe weight of the Washington Monument is about 105% as much as the Queen Mary 2.
    \n105% = 105\/100.
    \n105\/100 = 15\/10.
    \n15\/10 = 1.5.
    \nso the number can be written as a fraction and as a decimal = 1.5.<\/p>\n

    Question 20.
    \nStudents set a goal for the number of cans to collect for the canned food drive. They reached 120% of their goal. What is 120% expressed as a fraction and as a decimal?
    \n\"Envision<\/p>\n

    Answer:
    \nThe fraction is 120\/100 and 1.2.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nStudents set a goal for the number of cans to collect for the canned food drive.
    \n120\/100 = 12\/10.
    \n12\/10 = 1.2.
    \nso the fraction is 120\/100 and 1.2.<\/p>\n

    Question 21.
    \nUse Structure Popcorn sales at a Saturday afternoon matinee were 108% of the sales at the 8:00 showing of the movie. Calvin expressed 108% as 10.8. Is Calvin correct? Explain.<\/p>\n

    Answer:
    \nNo, Calvin was not correct.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nPopcorn sales at a Saturday afternoon matinee were 108% of the sales at the 8:00 showing of the movie.
    \n108% = 108\/100.
    \n18\/10 = 1.8.
    \nso Calvin was not correct.<\/p>\n

    Question 22.
    \nConstruct Arguments There are 350% more students enrolled in Spanish class than Latin class. How does expressing 350% as a decimal prove that more than 3 times as many students are enrolled in Spanish class as are enrolled in Latin class?<\/p>\n

    Answer:
    \n350% = 350\/100.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nThere are 350% more students enrolled in Spanish classes than in Latin classes.
    \n350% = 350\/100.
    \n350\/100 = 35\/10.
    \n35\/10 = 3.5.<\/p>\n

    Question 23.
    \nCritique Reasoning<\/strong> Free round-trip tickets to Orlando, Florida were given to 0.4% of the people staying at a hotel. Larry says that tickets were given to 40 of the people at the hotel. What did Larry do wrong when he calculated 0.4% as a fraction? What is the correct fraction?<\/p>\n

    Answer:
    \nLarry was correct.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nFree round-trip tickets to Orlando, Florida were given to 0.4% of the people staying at a hotel.
    \nLarry says that tickets were given to 40 of the people at the hotel.
    \n40\/100 = 0.4.
    \nso Larry was correct.<\/p>\n

    Question 24.
    \nThe unemployment rate decreased by \\(\\frac{1}{10}\\)% in one month. Write \\(\\frac{1}{10}\\)% as a fraction and as a decimal.<\/p>\n

    Answer:
    \nThe unemployment rate decreased by 1\/10\/100 and 0.001.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nThe unemployment rate decreased by \\(\\frac{1}{10}\\)% in one month.
    \n1\/10% = 1\/10\/100.
    \n1\/10 x 1\/100 = 1\/1000.
    \n1\/1000 = 0.001.
    \nsp the unemployment rate decreased by 1\/10\/100 and 0.001.<\/p>\n

    Question 25.
    \nHigher Order Thinking<\/strong> A photo of a mosquito in a science book is magnified to 635% of the mosquito’s actual size. If the mosquito is 16 millimeters long, what is the length of the mosquito in the picture?
    \n\"Envision<\/p>\n

    Answer:
    \nThe length of the mosquito in the picture = 6.35 mm.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nA photo of a mosquito in a science book is magnified to 635% of the mosquito’s actual size.
    \nIf the mosquito is 16 mm long.
    \n635% = 635\/100.
    \n635\/100 = 6.35.
    \nso the actual length of the mosquito in the picture = 6.35 mm.<\/p>\n

    Assessment Practice<\/strong><\/p>\n

    Question 26.
    \nAt a Florida zoo, one adult female panther weighs 100 pounds. An adult male panther at the same zoo weighs 159% of the female panther’s weight. What is the weight of the adult male panther? Show your work.<\/p>\n

    Answer:
    \nThe weight of the adult male panther = 1.59.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nAt a Florida zoo, one adult female panther weighs 100 pounds.
    \nAn adult male panther at the same zoo weighs 159% of the female panther’s weight.
    \n159\/100 = 1.59.
    \nso the weight of the adult male panther = 1.59.<\/p>\n

    Question 27.
    \nThe results of a survey show that 0.32% of the people in the survey have never sent a text message. Select all the fractions and decimals that can be expressed as 0.32%.
    \n\u2610 \\(\\frac{32}{100}\\)
    \n\u2610 \\(\\frac{2}{625}\\)
    \n\u2610 0.0032
    \n\u2610 \\(\\frac{8}{2,500}\\)
    \n\u2610 0.032<\/p>\n

    Answer:
    \nOptions A, B, C, and D are correct.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n0.32% = 0.32\/100.
    \n2\/625 = 0.0032.
    \n8\/2500 = 0.0032.
    \nso options A, B, C, and D are correct.<\/p>\n

    Topic 6 Mid-Topic Checkpoint<\/h3>\n

    Question 1.
    \nVocabulary Explain how fractions, decimals, and percents are related. Lesson 6-2<\/p>\n

    Answer:
    \nPercent is a ratio that can be written as a fraction, and a fraction can be written as a decimal.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \npercent is a ratio that can be written as a fraction, and a fraction can be written as a decimal.
    \ncovert the fraction first to a decimal, then move the decimal point 2 places to the right and add the % symbol.
    \nfor example:
    \n3\/4 is a fraction.
    \n0.75 is a decimal.
    \n75% is a percent.<\/p>\n

    Question 2.
    \nSarai is mixing a solution. She pours all the liquid from a full small beaker into a large beaker. The liquid fills the large beaker to 15% of its capacity. If the small beaker holds 300 ml, how much does the large beaker hold? Lessons 6-1 and 6-3<\/p>\n

    Answer:
    \nThe large beaker can hold = 0.05 ml.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nSarai is mixing a solution.
    \nShe pours all the liquid from a full small beaker into a large beaker.
    \nThe liquid fills the large beaker to 15% of its capacity.
    \n15\/300 = 0.05.
    \nso the large beaker can hold = 0.05 ml.<\/p>\n

    Question 3.
    \nThe Murphy family is on a road trip. On the first day, they traveled 30% of their total distance. On the second day, they traveled another of the total distance. What fraction of the total distance do they have left after the second day? What percent? Lesson 6-2<\/p>\n

    Answer:
    \nThe fraction of the total distance do they have left after the second day = 3\/10.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nThe Murphy family is on a road trip.
    \nOn the first day, they traveled 30% of their total distance.
    \nOn the second day, they traveled another of the total distance.
    \n30% = 30\/100.
    \n30\/100 = 3\/10.
    \n3\/10 = 0.3.
    \nso the fraction of the total distance do they have left after the second day = 3\/10.<\/p>\n

    Question 4.
    \nComplete the table. Lessons 6-2 and 6-3
    \n\"Envision<\/p>\n

    Answer:
    \n70% = 70\/100 = 0.7.
    \n125% = 125\/100 = 1.25.
    \n55% = 11\/20 = 0.55.
    \n0.2% = 0.2\/100 = 0.002.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe percents, decimals, and fractions are given.
    \n70% = 70\/100 = 0.7.
    \n125% = 125\/100 = 1.25.
    \n55% = 11\/20 = 0.55.
    \n0.2% = 0.2\/100 = 0.002.
    \n\"Envision-Math-Common-Core-6th-Grade-Answers-Key-Topic-6-Understand<\/p>\n

    Question 5.
    \nA basketball player made 17 out of 20 free throws at practice. What percent of the free throws did the player miss? Lesson 6-1<\/p>\n

    Answer:
    \nThe percent of the free throws did the player miss = 85%.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nA basketball player made 17 out of 20 free throws at practice.
    \n17\/20 = 0.85.
    \n85\/100 = 0.85.
    \nso the percent of the free throws did the player miss = 85%.<\/p>\n

    Question 6.
    \nA section of rope 5 inches long represents 20% of the length of the entire rope. How long is the rope? Lesson 6-1<\/p>\n

    Answer:
    \nThe length of the rope = 25 in.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nA section of rope 5 inches long represents 20% of the length of the entire rope.
    \n5\/20%.
    \n5\/ 20\/100.
    \n500\/20 = 50\/2.
    \n50\/2 = 25.
    \nso the length of the rope is 25 in.<\/p>\n

    Topic 6 Mid-Topic Performance Task<\/h3>\n

    The students in Mr. Anderson’s class conducted a survey of 1,000 people. They asked each person to name his or her favorite color. The results are shown in the table.
    \n\"Envision<\/p>\n

    PART A
    \nComplete the table to write each result as a fraction, a decimal, and a percent.
    \n\"Envision<\/p>\n

    Answer:
    \nFraction = 450\/815, Decimal = 0.55, and Percent = 55%.
    \nFraction = 300\/815, Decimal = 0.36, and Percent = 36%.
    \nFraction = 50\/815, Decimal = 0.06, and percent = 6%.
    \nFraction = 10\/815, Decimal = 0.01, and percent = 1%.
    \nFraction = 5\/815, Decimal = 0.006, percent = 0.6%.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe number of the color is shown in the table.
    \n450\/815 = 0.55 = 55%.
    \n300\/815 = 0.36 = 36%.
    \n50\/815 = 0.06 = 6%.
    \n10\/815 = 0.01 = 1%.
    \n5\/815 = 0.006 = 0.6%.<\/p>\n

    PART B
    \nGreen was chosen by 18% of the people. Which number is equivalent to 18%? Select all that apply.
    \n\u2610 \\(\\frac{18}{1,000}\\)
    \n\u2610 0.18
    \n\u2610 \\(\\frac{9}{5}\\)
    \n\u2610 \\(\\frac{18}{100}\\)
    \n\u2610 0.018<\/p>\n

    Answer:
    \nOption B and D are correct.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nThe number is equivalent to 18%.
    \n18\/100 = 0.18.
    \nso options B and D are correct.<\/p>\n

    PART C
    \nCecilia noticed that not all of the survey responses were recorded in the table. What percent of the responses were not recorded in the table? Explain.<\/p>\n

    Answer:
    \nThe percent of the responses was not recorded in the table = 200%.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nCecilia noticed that not all of the survey responses were recorded in the table.
    \nThe students in Mr. Anderson’s class conducted a survey of 1,000 people.
    \n5\/1000 = 1\/200.
    \nso the percent of the responses were not recorded in the table = 200%.<\/p>\n

    Lesson 6.4 Estimate to Find Percent<\/h3>\n

    Explore It!<\/strong>
    \nSarah wants to score 78% on her next test. She knows that the test will have 40 questions.<\/p>\n

    I can.. estimate the percent of a number using equivalent fractions, rounding, or compatible numbers.
    \n\"Envision<\/p>\n

    A. How can Sarah represent the situation to help her determine how many questions she needs to answer correctly?
    \n\"Envision<\/p>\n

    Answer:
    \nShe needs to answer correctly = 31 questions.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nSarah wants to score 78% on her next test.
    \nShe knows that the test will have 40 questions.
    \n78\/100 x 40.
    \n78\/100 = 0.78.
    \n0.78 x 40 = 31.2.
    \n312\/10 = 31.2.
    \nso Sarah needs to answer correctly = 31 questions.<\/p>\n

    B. How could you use the model to help solve the problem?<\/p>\n

    Answer:<\/p>\n

    Focus on math practices
    \nUse Structure on her last test, Sarah answered 82% of 60 questions correctly. About how many questions did Sarah answer correctly? Use estimation.<\/p>\n

    Answer:
    \nSarah answer correctly = 49 questions.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nSarah answered 82% of the 60 questions correctly.
    \n82\/100 = 0.82.
    \n0.82 x 60 = 49.2.
    \nso Sarah answer correctly = 49 questions.<\/p>\n

    Essential Question<\/strong>
    \nHow can you estimate to find the percent of a number?<\/p>\n

    Try It!<\/strong><\/p>\n

    Suppose the graph shows eye colors among 120 students in sixth grade. About how many sixth grade students would have green eyes? Explain how you can use estimation to find the answer.<\/p>\n

    Answer:
    \nThe number of students who would have green eyes = 1.2.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe graph shows eye colors among 120 students in sixth grade.
    \n120\/100 = 12\/10.
    \n12\/10 = 1.2.
    \nso the number of students who would have green eyes = 1.2.<\/p>\n

    Convince Me! How does understanding fraction equivalents help you estimate how many students in sixth grade have green eyes?<\/p>\n

    Try It!<\/strong><\/p>\n

    Students in another survey were asked whether they plan to attend summer camp. Out of the 56 students in the survey, 44% said yes. Use rounding and compatible numbers to estimate how many students plan to attend summer camp.
    \n\"Envision<\/p>\n

    Answer:
    \n4\/10 = 2\/5.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nwe are rounding 44% to estimate 40%.
    \n40\/100 = 4\/10.
    \n4\/10 = 2\/5.
    \n56 rounds to 55.
    \n2\/5 x 55 = 22.
    \nAbout 22 students plan to attend summer camp.
    \n\"Envision-Math-Common-Core-6th-Grade-Answers-Key-Topic-6-Understand<\/p>\n

    KEY CONCEPT<\/strong>
    \nFraction equivalents, rounding, or compatible numbers can be used to estimate the percent of a number.
    \n\"Envision<\/p>\n

    Do You Understand?<\/strong>
    \nQuestion 1.
    \nEssential Question<\/strong> How can you estimate to find the percent of a number?<\/p>\n

    Answer:
    \nWe can estimate the percent of a number to the nearest number.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nwe can estimate the percent of a number to the nearest number.
    \nfor example:
    \n8% is approximately equal to 10%.
    \n10\/100 = 1\/10.
    \n1\/10 = 0.1.<\/p>\n

    Question 2.
    \nIs there more than one fraction you could use to estimate 27% of 200? Explain.<\/p>\n

    Answer:
    \nYes, there is more than one fraction.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n27% of 200.
    \n27% is approximately equal to 25%.
    \n25\/100 x 200.
    \n1\/4 x 200 = 50.<\/p>\n

    Question 3.
    \nWhat compatible number could you use to estimate 75% of 35? Why is this number compatible with 75%?<\/p>\n

    Answer:
    \n75% of 35 = 26.25.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n75% of 35.
    \n75\/100 = 0.75.
    \n0.75 = 3\/4.
    \n3\/4 x 35 = 26.25.<\/p>\n

    Question 4.
    \nUse Structure Out of 195 students, 9% have hazel eyes. How can you estimate the number of students with hazel eyes?<\/p>\n

    Answer:
    \nThe number of students with hazel eyes = 18.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nout of 195 students, 9% have hazel eyes.
    \n9% = 9\/100.
    \n9\/100 = 0.09.
    \n195 is approximately equal to 200.
    \n0.09 x 200 = 18.
    \nso the number of students with hazel eyes = 18.<\/p>\n

    Do You Know How?<\/strong>
    \nIn 5-8, estimate the percent of each number.
    \nQuestion 5.
    \n47% of 77
    \n47% \u2248 ______ 77 \u2248 ________
    \n______ of ______ = ________<\/p>\n

    Answer:
    \n47% of 77 = 40.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n47% of 77.
    \n47% \u2248 50%.
    \n77%\u2248 80.
    \n50\/100 = 5\/10.
    \n5\/10 = 1\/2.
    \n1\/2 x 80 = 40.<\/p>\n

    Question 6.
    \n18% of 48
    \n18% \u2248 ______ 48 \u2248 ________
    \n______ of ______ = ________<\/p>\n

    Answer:
    \n18% of 48 = 10.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n18% of 48.
    \n18% \u2248 20%.
    \n48%\u2248 50.
    \n20\/100 = 2\/10.
    \n2\/10 = 1\/5.
    \n1\/5 x 50 = 10.<\/p>\n

    Question 7.
    \n73% of 800<\/p>\n

    Answer:
    \n73% of 800 = 600.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n73% of 800.
    \n73% \u2248 75%.
    \n75\/100 = 0.75.
    \n800 x 0.75 = 600.<\/p>\n

    Question 8.
    \n31% of 94<\/p>\n

    Answer:
    \n31% of 94 = 28.5.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n31% of 94.
    \n31% \u2248 30%.
    \n94 \u2248 95.
    \n30\/100 = 3\/10.
    \n3\/10 = 0.3.
    \n3\/10 x 95 = 28.5.<\/p>\n

    Question 9.
    \nTara sent party invitations to 98 people. Eighty two percent of the people said they will come to the party. About how many people said they will come to the party? Explain.<\/p>\n

    Answer:
    \nThe number of people who said they will come to the party = 85.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nTara sent party invitations to 98 people.
    \nEighty-two percent of the people said they will come to the party.
    \n98 x 82\/100.
    \n98 is equal to 100.
    \n85\/100 = 0.85.
    \n0.85 x 100 = 85.<\/p>\n

    Practice & Problem Solving<\/strong><\/p>\n

    Leveled Practice in 10-15, estimate the percent of each number.
    \nQuestion 10.
    \n74% of 63
    \n74% \u2248 ______ 63 \u2248 ________
    \n______ of ______ = ________<\/p>\n

    Answer:
    \n74% of 63 = 50.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n74% of 63.
    \n74% \u2248 75%.
    \n63%\u2248 65.
    \n75\/100 = 0.75.
    \n0.75 x 65 = 50.<\/p>\n

    Question 11.
    \n8% of 576
    \n8% \u2248 ______ 576 \u2248 ________
    \n______ of ______ = ________<\/p>\n

    Answer:
    \n8% of 576 = 58.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n8% of 576.
    \n8% = 10.
    \n10\/100 = 1\/10.
    \n1\/10 = 0.1.
    \n576 = 580.
    \n0.1 x 580 = 58.<\/p>\n

    Question 12.
    \n34% of 55<\/p>\n

    Answer:
    \n34% of 55 = 20.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n34% of 55.
    \n34% = 35.
    \n35\/100 = 0.35.
    \n0.35 x 55 = 20.<\/p>\n

    Question 13.
    \n27% of 284<\/p>\n

    Answer:
    \n27% of 284 = 85.5.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n27% of 284.
    \n27% = 30.
    \n30\/100 = 3\/10.
    \n3\/10 = 0.3.
    \n284 = 285.
    \n0.3 x 285 = 85.5.<\/p>\n

    Question 14.
    \n65% of 89<\/p>\n

    Answer:
    \n65% of 89 = 65.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n65% of 89.
    \n65% = 65.
    \n65\/100 = 0.65.
    \n89 = 100.
    \n0.65 x 100 = 65.<\/p>\n

    Question 15.
    \n4% of 802<\/p>\n

    Answer:
    \n4% of 802 = 32.2.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n4% of 802.
    \n4% = 5.
    \n4\/100 = 0.04.
    \n802 = 805.
    \n805 x 0.04 = 32.2.<\/p>\n

    Question 16.
    \nThere are about 320 million residents in the United States. If 38% of them live in the South, estimate how many live in other areas of the United States.
    \n\"Envision<\/p>\n

    Answer:
    \nThe number of people who live in other areas of the united states = 121.6.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nThere are about 320 million residents in the United States.
    \n38% of the U.S. population lives in this region.
    \n38\/100 x 320.
    \n0.38 x 320.
    \n121.6.
    \nso the number of people who live in other areas of the united states = 121.6.<\/p>\n

    Question 17.
    \nLisa and Bill made 60 magnets for a craft fair. They sold 55% of the magnets. Lisa says that they sold about 30 magnets. Bill says that they sold about 36 magnets. Could they both be correct? Explain.<\/p>\n

    Answer:
    \nNo, both of them are not correct.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nLisa and Bill made 60 magnets for a craft fair.
    \nThey sold 55% of the magnets.
    \nLisa says that they sold about 30 magnets.
    \nBill says that they sold about 36 magnets.
    \n55% of 60.
    \n55\/100 x 60.
    \n0.55 x 60 = 33<\/p>\n

    Question 18.
    \nMake Sense and Persevere Roland has 180 coins in his collection. Approximately 67% of the coins are quarters. About how much money does Roland have in quarters? Explain.<\/p>\n

    Answer:
    \nThe money does Ronald has in quarters = 120.6.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nRoland has 180 coins in his collection.
    \nApproximately 67% of the coins are quartered.
    \n67% of 180.
    \n67\/100 x 180.
    \n0.67 x 180 = 120.6.<\/p>\n

    Question 19.
    \nOut of 9,799 whistles that a company manufactured, some were rejected for shipment to stores because they did not pass the quality control standards of the company. Estimate the number of whistles that did not pass.
    \n\"Envision<\/p>\n

    Answer:
    \nThe number of whistles that did not pass = 1861.81.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nOut of 9,799 whistles that a company manufactured, some were rejected for shipment to stores because they did not pass the quality control standards of the company.
    \n19% of 9799.
    \n19\/100 x 9799.
    \n0.19 x 9799 = 1861.81.
    \nso the number of whistles that did not pass = 1861.81.<\/p>\n

    Question 20.
    \nThere are 8,249 people registered to vote in the town of Mayfield. About how many people voted in the election? Explain
    \n\"Envision<\/p>\n

    Answer:
    \nThe number of people who voted in the election = 6104.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nThere are 8,249 people registered to vote in the town of Mayfield.
    \nvoter turnout reaches 74%.
    \n74% of 8249.
    \n74\/100 x 8249.
    \n0.74 x 8249 = 6104.26.
    \nso the number of people voted in the election = 6104.<\/p>\n

    Question 21.
    \nHigher Order Thinking<\/strong> Lea spent 25% of x hours at her part-time job. What is x if 25% of x is about 30 hours? Explain how you estimated and which property of equality you used to find x.<\/p>\n

    Answer:
    \nThe property of equality = 7.5.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nLea spent 25% of x hours at her part-time job.
    \n25% of 30 hours.
    \n25\/100 x 30.
    \n0.25 x 30 = 7.5.
    \nso the property of equality = 7.5.<\/p>\n

    Question 22.
    \nReasoning<\/strong> Vanessa scored 78% on a test with 120 questions. What benchmark fraction would you use to estimate the number of questions that Vanessa answered correctly? Explain.<\/p>\n

    Answer:
    \nThe number of questions that Vanessa answered correctly = 93.6.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nVanessa scored 78% on a test with 120 questions.
    \n78% of 120.
    \n78\/100 x 120.
    \n0.78 x 120 = 93.6.
    \nso the number of questions that Vanessa answered correctly = 93.6.<\/p>\n

    Question 23.
    \nJason has saved 41% of what he needs to buy a skateboard. About how much has Jason saved? Explain.
    \n\"Envision<\/p>\n

    Answer:
    \nThe amount has Jason saved = 29.93.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nJason has saved 41% of what he needs to buy a skateboard.
    \n41% of $73.
    \n41\/100 x $73.
    \n0.41 x $73 = 29.93.
    \nso the amount has Jason saved = 29.93.
    \nAssessment Practice<\/strong><\/p>\n

    Question 24.
    \nThere were 240 shoppers at an electronics store on opening day. The specials that day allowed 25% of shoppers to receive a free set of earbuds and 20% of shoppers to receive $10 off their first purchase.
    \nPART A
    \nUse an equivalent fraction to determine how many shoppers received a free set of earbuds. Show your work.<\/p>\n

    Answer:
    \nThe number of shoppers who received a free set of earbuds = 600 and $2.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nThere were 240 shoppers at an electronics store on opening day.
    \nThe specials that day allowed 25% of shoppers to receive a free set of earbuds and 20% of shoppers to receive $10 off.
    \n250% of 240.
    \n250\/100 x 240.
    \n25\/10 x 240.
    \n2.5 x 240 = 600.
    \n20% of $10.
    \n20\/100 x $10.
    \n1\/5 x $10.
    \n0.2 x $10 = $2.<\/p>\n

    PART B
    \nUse an equivalent fraction to determine how many shoppers received $10 off their first purchase. Show your work.<\/p>\n

    Answer:
    \nThe equivalent fraction that a number of shoppers received $10 off their first purchase = $2.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nThe specials that day allowed 25% of shoppers to receive a free set of earbuds and 20% of shoppers to receive $10 off.
    \n20% of $10.
    \n20\/100 x $10.
    \n1\/5 x $10.
    \n0.2 x $10 = $2.
    \nso the equivalent fraction that a number of shoppers received $10 off their first purchase = $2.<\/p>\n

    Lesson 6.5 Find the percent of a Number<\/h3>\n

    Solve & Discuss It!<\/strong>
    \nLauren bought a jacket that was on sale for 60% off. She paid 40% of the original price of $75. How much did Lauren pay for the jacket?
    \nI can… solve problems involving percents.
    \n\"Envision<\/p>\n

    Model with Math
    \nHow can you use a model to represent problems involving percents?<\/p>\n

    Answer:
    \nThe amount did Lauren pay for the jacket = $30.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiving that,
    \nLauren bought a jacket that was on sale for 60% off.
    \nShe paid 40% of the original price of $75.
    \n40% of $75.
    \n40\/100 x $75.
    \n0.4 x $75.
    \n$30.
    \nso the amount did Lauren pay for the jacket = $30.<\/p>\n

    Focus on math practices
    \nGeneralize When finding the percent of a number, how can you tell whether your answer is reasonable? Will the answer be greater than or less than the original amount? Explain.<\/p>\n

    Essential Question<\/strong>
    \nHow can you find percents?<\/p>\n

    Try It!<\/strong><\/p>\n

    Suppose 68% of the students attending the field trip were boys. How can you use the double number line diagram above to find the number of boys and to check whether your answer is reasonable?<\/p>\n

    Answer:
    \nThe number of boys = 86.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nSuppose 68% of the students attending the field trip were boys.
    \n68\/100 = 0.86.
    \nso the number of boys = 86.<\/p>\n

    Convince Me! In finding the percent of a number, when might you want to use the fraction form of the percent instead of the decimal form?<\/p>\n

    Try It!<\/strong><\/p>\n

    What is 0.8% of 35?<\/p>\n

    Answer:
    \n0.8% of 35 = 0.28.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n0.8% of 35.
    \n0.8\/100 x 35.
    \n0.008 x 35 = 0.28.<\/p>\n

    Try It!<\/strong><\/p>\n

    What percent of 120 is 72?<\/p>\n

    Answer:
    \nThe percent of 120 is 86.4.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nx of 120 is 72.
    \n72\/100 x 120.
    \n0.72 x 120 = 86.4.
    \nso the percent of 120 is 86.4.<\/p>\n

    KEY CONCEPT<\/strong>
    \nPercent equations have a part, a whole, and a percent. You can use the equation to solve for the part, the whole, or the percent.
    \nFind the Part
    \nWhat is 12% of 6.75?
    \nx = 0.12 \u2022 6.75
    \nx = 0.81
    \n12% of 6.75 is 0.81.<\/p>\n

    Find the Percent:
    \nWhat percent of 6.75 is 0.81?
    \np \u2022 6.75 = 0.81
    \n6.75p = 0.81
    \n\\(\\frac{6.75 p}{6.75}=\\frac{0.81}{6.75}\\)
    \np = 0.12 or 12%
    \n12% of 6.75 is 0.81.<\/p>\n

    Do You Understand?<\/strong>
    \nQuestion 1.
    \nEssential Question<\/strong> How can you find percents?<\/p>\n

    Answer:
    \nPercent equations have a part, a whole, and a percent.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nPercent equations have a part, a whole, and a percent.
    \nfor example:
    \np x 6.75 = 0.81.
    \n12% of 6.75 is 0.81.<\/p>\n

    Question 2.
    \nDescribe the equation you use to find the unknown part in a percent problem.
    \nAnswer:<\/p>\n

    Question 3.
    \nDescribe the equation you use to find the percent value in a percent problem.
    \nAnswer:<\/p>\n

    Question 4.
    \nBe Precise in the expression 34% of 60, what operation does the word “of” mean?<\/p>\n

    Answer:
    \n34% of 60 = 20.4.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n34% of 60.
    \n34\/100 x 60.
    \n0.34 x 60 = 20.4.
    \n34% of 60 = 20.4.<\/p>\n

    Question 5.
    \nUse Appropriate Tools How can you use a calculator to find what percent of 180 is 108?<\/p>\n

    Answer:
    \n194.4.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n180\/100 x 108.
    \n18\/10 x 108.
    \n1.8 x 108.
    \n194.4.<\/p>\n

    Do You Know How?<\/strong>
    \nIn 6 and 7, find the part.
    \nQuestion 6.
    \nWhat is 26% of 50?<\/p>\n

    Answer:
    \n26% of 50 is 12.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n26% of 50.
    \n26\/100 x 50.
    \n0.26 x 50.
    \n12.
    \nso 26% of 50 is 12.<\/p>\n

    Question 7.
    \nWhat is 2.1% of 60?<\/p>\n

    Answer:
    \n2.1% of 60 = 1.26.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n2.1% of 60.
    \n2.1\/100 x 60.
    \n0.021 x 60.
    \n1.26.
    \n2.1% of 60 = 1.26.<\/p>\n

    In 8 and 9, find the percent.
    \nQuestion 8.
    \nWhat percent of 315 is 126?<\/p>\n

    Answer:
    \nThe percent of 315 is 126 = 396.9.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n315% of 126.
    \n315\/100 x 126.
    \n3.15 x 126.
    \n396.9.
    \nso the percent of 315 is 126 = 396.9.<\/p>\n

    Question 9.
    \nWhat percent of 120 is 28.8?<\/p>\n

    Answer:
    \nThe percent of 120 is 28.8 = 34.56.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n120\/100 x 28.8.
    \n12\/10 x 28.8.
    \n1.2 x 28.8.
    \n34.56.
    \nso the percent of 120 is 28.8 = 34.56.<\/p>\n

    Question 10.
    \nAn electronics company has 450 employees. The company plans to increase its staff by 30%. How many new employees will the company hire?<\/p>\n

    Answer:
    \nThe number of new employees will the company hire = 135.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nAn electronics company has 450 employees.
    \nThe company plans to increase its staff by 30%.
    \n30% of 450.
    \n30\/100 x 450.
    \n3\/10 x 450.
    \n0.3 x 450.
    \n135.
    \nso the number of new employees will the company hire = 135.<\/p>\n

    Question 11.
    \nThe original price of a computer game is $45. The price is marked down by $18. What percent of the original price is the markdown?<\/p>\n

    Answer:
    \nThe percent of the original price is the markdown is $27.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nThe original price of a computer game is $45.
    \nThe price is marked down by $18.
    \n$45 – $18 = $27.
    \nso the percent of the original price is the markdown is $27.<\/p>\n

    Practice & Problem Solving<\/strong><\/p>\n

    Leveled Practice In 12-17, find each part or percent.
    \nQuestion 12.
    \nWhat is 5% of 210?
    \nx = ______ \u00d7 210
    \nx = ______<\/p>\n

    Answer:
    \n5% of 210 = 10.5.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n5% of 210.
    \n5\/100 x 210.
    \n0.05 x 210 = 10.5.
    \n5% of 210 = 10.5.<\/p>\n

    Question 13.
    \nWhat is 8.2% of 500?
    \nx = _____ \u00d7 500
    \nx = _______<\/p>\n

    Answer:
    \n8.2% of 500 = 41.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n8.2% of 500.
    \n8.2\/100 x 500.
    \n0.082 x 500.
    \n41.
    \n8.2% of 500 = 41.<\/p>\n

    Question 14.
    \nWhat percent of 32 is 5.6?
    \np \u2022 32 = _______
    \n32 p = _______
    \n\\(\\frac{32 p}{32}=\\frac{ }{32}\\)
    \np = _______ = _______%<\/p>\n

    Answer:
    \np = 0.00175.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \np x 32 = 5.6%.
    \n32p = 5.6%.
    \n5.6\/100 = 32p.
    \n0.056 = 32p.
    \np = 0.056\/32.
    \np = 0.00175.<\/p>\n

    Question 15.
    \nWhat is 35% of 10?<\/p>\n

    Answer:
    \n35% of 10 is 3.5.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n35% of 10.
    \n35\/100 x 10.
    \n0.35 x 10.
    \n3.5.
    \nso 35% of 10 is 3.5.<\/p>\n

    Question 16.
    \nWhat percent of 75 is 33?<\/p>\n

    Answer:
    \n24.75 percent of 75 is 33.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nx of 75 is 33.
    \n75\/100 x 33.
    \n0.75 x 33.
    \n24.75.<\/p>\n

    Question 17.
    \nWhat is 2.25% of 24?<\/p>\n

    Answer:
    \n2.25% of 24 = 0.54.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n2.25% of 24.
    \n2.25\/100 x 24.
    \n0.0225 x 24.
    \n0.54.
    \n2.25% of 24 = 0.54.<\/p>\n

    Question 18.
    \nThe meal tax at a restaurant is 5.5%. What is the meal tax on a dinner that costs $24?
    \n\"Envision<\/p>\n

    Answer:
    \nThe meal tax on dinner costs $24.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nThe meal tax at a restaurant is 5.5%.
    \n5.5% of $24.
    \n5.5\/100 x $24.
    \n0.055 x 24.
    \n$1.32.
    \nso the meal tax on dinner costs $24.<\/p>\n

    Question 19.
    \nAn electronics store donated a percentage of every sale to charity. The total sales were $7,150, of which the store donated $429. What percent of $7,150 was donated to charity?<\/p>\n

    Answer:
    \nThe percent of the money was donated to charity = $6721.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nAn electronics store donated a percentage of every sale to charity.
    \nThe total sales were $7,150, of which the store donated $429.
    \n$7150 – $429 = $6721.
    \nso the percent of the money was donated to charity = $6721.<\/p>\n

    In 20-22, use the circle graph.
    \nThere are 180 cars in a parking lot. The colors of the cars are represented in the circle graph.
    \n\"Envision
    \nQuestion 20.
    \nHow many blue cars are there?<\/p>\n

    Answer:
    \nThe number of blue cars = 81.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nThere are 180 cars in a parking lot.
    \nBlue cars = 45%.
    \nGreen cars and Black cars = 25%.
    \nRed cars = 30%.
    \n45% of 180.
    \n45\/100 x 180.
    \n0.45 x 180.
    \nso the number of blue cars = 81.<\/p>\n

    Question 21.
    \nHow many red cars are there?<\/p>\n

    Answer:
    \nThe number of red cars = 54.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nThere are 180 cars in a parking lot.
    \nBlue cars = 45%.
    \nGreen cars and Black cars = 25%.
    \nRed cars = 30%.
    \n30% of 180.
    \n30\/100 x 180.
    \n0.3 x 180.
    \nso the number of red cars = 54.<\/p>\n

    Question 22.
    \nReasoning<\/strong> There are 27 more green cars than black cars in the parking lot. What percentage of the cars in the parking lot are green? What percent are black?<\/p>\n

    Answer:
    \nThe percent of cars that are black = 48.6%.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nThere are 27 more green cars than black cars in the parking lot.
    \n27\/100 x 180.
    \n0.27 x 180.
    \n48.6.
    \nso the percent of cars that are black = 48.6%.<\/p>\n

    Question 23.
    \nThe bank contains pennies, nickels, dimes, and quarters. There are 4 more nickels than pennies. How much money does the bank contain?
    \n\"Envision<\/p>\n

    Answer:
    \nThe money does the bank contains = 66%.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nThe bank contains pennies, nickels, dimes, and quarters.
    \nThere are 4 more nickels than pennies.
    \nof the 50 coins, 10% are pennies and 42% are dimes.
    \n10% + 42% + 14%.
    \n66%.
    \nso the money does the bank contains = 66%.<\/p>\n

    Question 24.
    \nModel with Math How can you use the double number line diagram to find what percent of 450 is 270?
    \n\"Envision<\/p>\n

    Answer:
    \nThe percent of 450 is 270 is 1215.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n450% is 270.
    \n450\/100 x 270.
    \n45\/10 x 270.
    \n4.5 x 270.
    \n1215.
    \nso the percent of 450 of 270 is 1215.<\/p>\n

    Question 25.
    \nMake Sense and Persevere A movie complex is showing the same movie in three theaters. In theater A, 112 of the 160 seats are filled. In theater B, 84 seats are filled and 56 seats are empty. In theater C, 63 of the 180 seats are empty. Which theater has the greatest percent of its seats filled?<\/p>\n

    Answer:
    \nThe greatest percent of its seats filled = Theater A.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nA movie complex is showing the same movie in three theaters.
    \nIn theater A, 112 of the 160 seats are filled. In theater B, 84 seats are filled and 56 seats are empty.
    \nIn theater C, 63 of the 180 seats are empty.
    \n112\/100 x 160.
    \n1.12 x 160.
    \n179.2.
    \n84\/100 x 56.
    \n0.84 x 56.
    \n47.04.
    \n63\/100 x 180.
    \n0.63 x 180 = 113.4.
    \nso the greatest percent of its seats filled = Theater A.<\/p>\n

    Question 26.
    \nHigher Order Thinking<\/strong> Thomas has an album that holds 600 baseball cards. Each page of the album holds 6 cards. If 45% of the album is empty, how many pages are filled with baseball cards?<\/p>\n

    Answer:
    \nThe number of pages is filled with baseball cards = 1620.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nThomas has an album that holds 600 baseball cards.
    \nEach page of the album holds 6 cards.
    \nIf 45% of the album is empty.
    \n600 x 6 = 3600.
    \n45\/100 x 3600.
    \n0.45 x 3600.
    \nso the number of pages is filled with baseball cards = 1620.<\/p>\n

    Question 27.
    \nBe Precise Miguel collected aluminum cans for recycling. He collected a total of 150 cans. How many of the cans Miguel collected were not soda cans?
    \n\"Envision<\/p>\n

    Answer:
    \nThe number of cans Miguel collected were not soda cans = 87.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nMiguel collected aluminum cans for recycling.
    \nHe collected a total of 150 cans.
    \n58% of the cans collected were soda cans.
    \n58% of 150.
    \n58\/100 x 150.
    \n0.58 x 150.
    \n87.
    \nso the number of cans Miguel collected were not soda cans = 87.<\/p>\n

    Assessment Practice<\/strong><\/p>\n

    Question 28.
    \nAva’s aquarium is 95% filled with water. The tank holds 1,120 gallons of water. Which is the remaining number of gallons of water needed to fill the aquarium to the top?
    \nA. 1,120 gallons
    \nB. 1,010 gallons
    \nC. 101 gallons
    \nD. 56 gallons<\/p>\n

    Answer:
    \nOption B is correct.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nAva’s aquarium is 95% filled with water.
    \nThe tank holds 1,120 gallons of water.
    \n95% of 1120.
    \n95\/100 x 1120.
    \n0.95 x 1120.
    \n1064.
    \nso option B is correct.<\/p>\n

    Question 29.
    \nStudents set a goal of collecting 900 cans for the canned food drive. The number of cans they have collected so far is 82% of their goal. How many more cans do the students need to collect to reach their goal?
    \nA. 162 cans
    \nB. 180 cans
    \nC. 720 cans
    \nD. 738 cans<\/p>\n

    Answer:<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nStudents set a goal of collecting 900 cans for the canned food drive.
    \nThe number of cans they have collected so far is 82% of their goal.
    \n82% of 900.
    \n82\/100 x 900.
    \n0.82 x 900 =
    \nso option<\/p>\n

    Lesson 6.6 Find the whole Given a Part and the Percent<\/h3>\n

    Solve & Discuss It!<\/strong>
    \nA school soccer team won 80% of its matches. The team won 40 matches. How many matches did the soccer team play?<\/p>\n

    I can… find the whole amount when given a part and the percent.
    \n\"Envision<\/p>\n

    Look for Relationships
    \nHow can you use a diagram to analyze the relationship between the quantities?<\/p>\n

    Focus on math practices
    \nModel with Math Write an equation to find the total number of matches played by the soccer team. Let m represent the total number of matches.<\/p>\n

    Essential Question<\/strong>
    \nHow can you find the whole in a percent problem?<\/p>\n

    Try It!<\/strong><\/p>\n

    Bree took another math test and scored 152 points, which was 95% of the total possible points on the test. What was the total number of possible points?<\/p>\n

    Answer:
    \nThe total number of possible points = 144.4.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nBree took another math test and scored 152 points, which was 95% of the total possible points on the test.
    \n95% of 152.
    \n95\/100 x 152.
    \n0.95 x 152.
    \n144.4.
    \nso the total number of possible points = 144.4.<\/p>\n

    Convince Me! How could you use a double number line diagram to check your answer?<\/p>\n

    Try It!<\/strong><\/p>\n

    a. 300% of what number is 180?<\/p>\n

    Answer:
    \n300% of 180 is 60.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n300% of x is 180.
    \n300%x x 180.
    \n3x = 180.
    \nx = 180\/3.
    \nx = 60.
    \n300% of 180 is 60.<\/p>\n

    b. 0.3% of what number is 24?<\/p>\n

    Answer:
    \nThe value of x is 8000.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n0.3% of x is 24.
    \n0.3\/100x = 24.
    \n0.003x = 24.
    \nx = 24\/0.003.
    \nx = 8000.<\/p>\n

    KEY CONCEPT<\/strong>
    \nYou can use a double number line diagram or an equation to find the whole when the percent and a part are known.
    \nUse a diagram.
    \n\"Envision
    \n150% of 8 is 12.
    \nUse an equation.
    \nLet n = the whole.
    \n150% \u2022 n = 12
    \n\\(\\frac{1.5 n}{1.5}=\\frac{12}{1.5}\\)
    \nn = 8
    \n150% of 8 is 12.<\/p>\n

    Do You Understand?<\/strong>
    \nQuestion 1.
    \nEssential Question<\/strong> How can you find the whole in a percent problem?<\/p>\n

    Answer:<\/p>\n

    Question 2.
    \nWhen you write an equation for a problem such as 300% of what number is 180, what do you use to represent the phrase ‘what number’?<\/p>\n

    Answer:
    \nThe number is 540.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n300% of a number is 180.
    \n300\/100 x 180.
    \n3 x 180 = 540.
    \nso the number is 540.<\/p>\n

    Question 3.
    \nWhen you find the whole in a percent problem in which the percent is greater than 100%, is the whole less than or greater than the part?<\/p>\n

    Answer:
    \n1 is greater than the part.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe percent is greater than 100%.
    \n100% = 100\/100.
    \n100\/100 = 1.
    \nso 1 is greater than the part.<\/p>\n

    Question 4.
    \nBe Precise Tony participated in 6 races, or 10% of the events. Do the 6 races represent the part, the percent, or the whole? Tell what the others represent.<\/p>\n

    Answer:
    \nThe 6 races represent the whole.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nTony participated in 6 races or 10% of the events.
    \n10\/100 x 6.
    \n0.1 x 6 = 0.6.
    \nso the 6 races represent the whole.<\/p>\n

    Do You Know How?<\/strong>
    \nQuestion 5.
    \n40% of what number is 80?
    \n\"Envision<\/p>\n

    Answer:
    \n40% of x is 80 = 32.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n40% of x is 80.
    \nx = 40\/100 x 80.
    \nx = 0.4 x 80.
    \nx = 32.
    \n40% of x is 80 = 32.<\/p>\n

    Question 6.
    \n300% of what number is 90?
    \n\"Envision<\/p>\n

    Answer:
    \n300% of x is 90 is 30.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n300% of x is 90.
    \n300\/100 x x = 90.
    \n3x = 90.
    \nx = 30.
    \n300% of x is 90 is 30.<\/p>\n

    Question 7.
    \n70% of what number is 112?<\/p>\n

    Answer:
    \nThe number is 78.4.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n70% of what number is 112.
    \n70\/100 x 112.
    \n0.7 x 112.
    \n78.4.
    \nso 70% of the number is 112 is 78.4.<\/p>\n

    Question 8.
    \n35% of what number is 28?<\/p>\n

    Answer:
    \nThe number is 78.4.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n70% of what number is 112
    \n70\/100 x 112.
    \n0.7 x 112.
    \n78.4.
    \nso the number is 78.4.<\/p>\n

    Question 9.
    \n7.5% of what number is 15?<\/p>\n

    Answer:
    \nThe number is 200.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n7.5% of x is 15.
    \n7.5\/100 x = 15.
    \n0.075x = 15.
    \nx = 15\/0.075.
    \nx = 200.<\/p>\n

    Practice & Problem Solving<\/strong><\/p>\n

    Leveled Practice In 10-15, find each whole.
    \nQuestion 10.
    \n35% of what number is 91?
    \n\"Envision<\/p>\n

    Answer:
    \n35% of 260 is 91.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n35% x a = 91.
    \n35\/100 x a = 91.
    \n0.35a = 91.
    \na = 91\/0.35.
    \na = 260.
    \n\"Envision-Math-Common-Core-6th-Grade-Answers-Key-Topic-6-Understand<\/p>\n

    Question 11.
    \n125% of what number is 45?
    \n\"Envision<\/p>\n

    Answer:
    \n125% of 36 is 45.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n125% x n = 45.
    \n1.25n = 45.
    \nn = 45\/1.25.
    \nn = 36.
    \n125% of 36 is 45.
    \n\"Envision-Math-Common-Core-6th-Grade-Answers-Key-Topic-6-Understand<\/p>\n

    Question 12.
    \n87.5% of what number is 49?
    \n\"Envision<\/p>\n

    Answer:
    \n87.5% of 56 is 49.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n87.5% of y = 49.
    \n87.5\/100 y = 49.
    \n0.875y = 49.
    \ny = 49\/0.875.
    \ny = 56.
    \n87.5% of y is 49.<\/p>\n

    Question 13.
    \n700% of what number is 1,540?<\/p>\n

    Answer:
    \n700% of 1540 is 220.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n700% of x is 1540.
    \n700\/100x = 1540.
    \n7x = 1540.
    \nx = 1540\/7.
    \nx = 220.
    \n700% of 1540 is 220.<\/p>\n

    Question 14.
    \n0.7% of what number is 35?<\/p>\n

    Answer:
    \n0.7% x is 5000.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n0.7% of x is 35.
    \n0.7\/100 x x = 35.
    \n0.007x = 35.
    \nx = 35\/0.007.
    \nx = 5000.
    \n0.7% x is 5000.<\/p>\n

    Question 15.
    \n56% of what number is 14?<\/p>\n

    Answer:
    \n56% of 25 is 14.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n56% of x is 14.
    \n56\/100 x = 14.
    \n0.56x = 14.
    \nx = 14\/0.56.
    \nx = 25.
    \n56% of x is 25.<\/p>\n

    In 16-18, use the list of state taxes.
    \n\"Envision
    \nQuestion 16.
    \nReasoning<\/strong> Otis had a salad for $4.50, a sandwich for $6.25, and a drink at his favorite restaurant. The tax for the entire meal was $0.54. What was the price of the drink?<\/p>\n

    Answer:
    \nThe price of the drink = $10.21.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nOtis had a salad for $4.50, a sandwich for $6.25, and a drink at his favorite restaurant.
    \nThe tax for the entire meal was $0.54.
    \n4.50 + 6.25 = 10.75.
    \n10.75 – 0.54 = 10.21.
    \nso the price of the drink = $10.21.<\/p>\n

    Question 17.
    \nJill paid a sales tax of $1.40 when she bought a vest. What was the price of the vest not including the tax?<\/p>\n

    Answer:
    \nThe price of the vest not including the tax = $9.35.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nJill paid a sales tax of $1.40 when she bought a vest.
    \n$10.75 – $1.40.
    \n$9.35.
    \nso the price of the vest not including the tax = $9.35.<\/p>\n

    Question 18.
    \nRachel paid $46 in tax for the money she earned as a camp counselor. How much money did Rachel earn?<\/p>\n

    Answer:
    \nThe money did Rachel earn is $35.75.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nRachel paid $46 in tax for the money she earned as a camp counselor.
    \n$10.25 – $46 =
    \n35.75.
    \nso the money did Rachel earn is $35.75.<\/p>\n

    Question 19.
    \nA restaurant wants to study how well its salads sell. The circle graph shows the sales of salads during the past few days. If 5 of the salads sold were Caesar salads, how many total salads did the restaurant sell?
    \n\"Envision<\/p>\n

    Answer:
    \nThe total salads did the restaurant sell = 1.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nA restaurant wants to study how well its salads sell.
    \nThe circle graph shows the sales of salads during the past few days.
    \nif 5 of the salads sold were caesar salads.
    \n20% is caesar salads.
    \n20\/100 x 5.
    \n2\/10 x 5.
    \n0.2 x 5 = 1.
    \nso the total salads did the restaurant sell = 1.<\/p>\n

    Question 20.
    \nMake Sense and Persevere Sydney completed 60% of the math problems assigned for homework. She has 4 more problems to finish. How many math problems were assigned for homework?<\/p>\n

    Answer:
    \nThe number of math problems was assigned for homework = 2.4.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nSydney completed 60% of the math problems assigned for homework.
    \nShe has 4 more problems to finish.
    \n60% of 4.
    \n60\/100 x 4.
    \n0.6 x 4 = 2.4.
    \nso the number of math problems was assigned for homework = 2.4.<\/p>\n

    Question 21.
    \nReasoning<\/strong> Carrie gave her hair stylist a $4.20 tip. The tip was 15% of the cost of the haircut. Write an equation to find h, the cost of the haircut.<\/p>\n

    Answer:
    \nThe cost of the haircut = $28.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nCarrie gave her hairstylist a $4.20 tip.
    \nThe tip was 15% of the cost of the haircut.
    \n15% of h is $4.20.
    \n15\/100 x h = $4.20.
    \nh = $4.20\/0.15.
    \nh = $28.<\/p>\n

    Question 22.
    \nUse Structure Solve each of the number sentences and describe the pattern. 80% of what number is 80? 60% of what number is 60? 127% of what number is 127?<\/p>\n

    Answer:
    \nThe number is 100.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n80% of x is 80.
    \n80\/100 x = 80.
    \n0.8x = 80.
    \nx = 80\/0.8.
    \nx = 100.
    \n60\/100 x = 60.
    \n0.6x = 60.
    \nx = 60\/0.6.
    \nx = 100.
    \n127% of x is 127.
    \n127\/100 x = 127.
    \n1.27 x = 127.
    \nx = 127\/1.27.
    \nx = 100.
    \nso the number is 100.<\/p>\n

    Question 23.
    \nHigher Order Thinking<\/strong> An hour before show time, only 105 people have arrived for a concert. According to ticket sales, 95% of the people have yet to arrive. How many tickets were sold for the concert? Explain.
    \n\"Envision<\/p>\n

    Answer:
    \nThe number of tickets was sold for the concert = 99.75.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nonly 105 people have arrived for a concert.
    \nAccording to ticket sales, 95% of the people have yet to arrive.
    \n95% of 105.
    \n95\/100 x 105.
    \n0.95 x 105.
    \n99.75.
    \nso the number of tickets was sold for the concert = 99.75.<\/p>\n

    Question 24.
    \nNineteen students named lacrosse as their favorite sport. Explain how to use the circle graph to find the total number of students surveyed.
    \n\"Envision<\/p>\n

    Answer:
    \nThe total number of students surveyed = 38.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nNineteen students named lacrosse as their favorite sport.
    \nthe number of students who selected Lacrosse is 38%.
    \n38% of 100.
    \n38\/100 x 100.
    \n38.
    \nso the total number of students surveyed = 38.<\/p>\n

    Assessment Practice<\/strong><\/p>\n

    Question 25.
    \nPeople use water to cook, clean, and drink every day. It is estimated that 16.8% of the water used each day is for cleaning. If a family uses 67.2 gallons of water per day for cleaning, how many total gallons do they use per day? Explain.<\/p>\n

    Answer:
    \nThe total gallons of water do they use per day = 11.2896 gallons.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nPeople use water to cook, clean, and drink every day.
    \nIt is estimated that 16.8% of the water used each day is for cleaning.
    \nIf a family uses 67.2 gallons of water per day for cleaning.
    \n16.8% of 67.2.
    \n16.8\/100 x 67.2.
    \n0.168 x 67.2.
    \n11.2896.
    \nso the total gallons of water do they use per day = 11.2896 gallons.<\/p>\n

    Question 26.
    \nMartha has a budget for groceries, fuel, and utilities. She spent 20% of her budget on groceries. If Martha spent $42.00 on groceries, how much is her budget?<\/p>\n

    Answer:
    \nThe budget is $8.4.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nMartha has a budget for groceries, fuel, and utilities.
    \nShe spent 20% of her budget on groceries.
    \nIf Martha spent $42.00 on groceries.
    \n20% of $42.
    \n20\/100 x $42.
    \n0.2 x $42.
    \n$8.4.
    \nso the budget is $8.4.<\/p>\n

    3-ACT MATH<\/strong><\/p>\n

    3-Act Mathematical Modeling: Ace the Test
    \n\"Envision<\/p>\n

    ACT 1<\/strong>
    \nQuestion 1.
    \nAfter watching the video, what is the first question that comes to mind?
    \nAnswer:<\/p>\n

    Question 2.
    \nWrite the Main Question you will answer.
    \nAnswer:<\/p>\n

    Question 3.
    \nPredict an answer to this Main Question.
    \nAnswer:<\/p>\n

    Question 4.
    \nConstruct Arguments Explain how you arrived at your prediction.
    \n\"Envision
    \nAnswer:<\/p>\n

    \u0410\u0421\u0422 2<\/strong>
    \nQuestion 5.
    \nWhat information in this situation would be helpful to know? How would you use that information?
    \nAnswer:<\/p>\n

    Question 6.
    \nUse Appropriate Tools What tools can you use to solve the problem? Explain how you would use them strategically.
    \n\"Envision
    \nAnswer:<\/p>\n

    Question 7.
    \nModel with Math Represent the situation using mathematics. Use your representation to answer the Main Question.
    \nAnswer:<\/p>\n

    Question 8.
    \nWhat is your answer to the Main Question? Does it differ from your prediction? Explain.
    \n\"Envision
    \nAnswer:<\/p>\n

    ACT 3<\/strong>
    \nQuestion 9.
    \nWrite the answer you saw in the video.
    \n\"Envision
    \nAnswer:<\/p>\n

    Question 10.
    \nReasoning<\/strong> Does your answer match the answer in the video? If not, what are some reasons that would explain the difference?
    \nAnswer:<\/p>\n

    Question 11.
    \nMake Sense and Persevere Would you change your model now that you know the answer? Explain.
    \n\"Envision
    \nAnswer:<\/p>\n

    Reflect<\/strong>
    \nQuestion 12.
    \nModel with Math Explain how you used a mathematical model to represent the situation. How did the model help you answer the Main Question?
    \nAnswer:<\/p>\n

    Question 13.
    \nBe Precise Why are percents more useful in this situation than the number of correct answers?
    \nAnswer:<\/p>\n

    SEOUEL<\/strong>
    \nQuestion 14.
    \nReasoning Suppose each test has 3 additional questions, and she gets 2 of them correct. How will that affect the answer?
    \n\"Envision
    \nAnswer:<\/p>\n

    Topic 6 Review<\/h3>\n

    Essential Question<\/strong>
    \nWhat is the meaning of percent? How can percent be estimated and found?<\/p>\n

    Vocabulary Review
    \nComplete each definition with a vocabulary word.
    \nVocabulary<\/p>\n

      \n
    • compatible numbers<\/li>\n
    • fraction<\/li>\n
    • percent<\/li>\n
    • ratio<\/li>\n<\/ul>\n

      Question 1.
      \nA ratio of a quantity to 100 is a __________<\/p>\n

      Answer:
      \nA ratio of a quantity to 100 is a percent.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nA ratio of a quantity to 100 is a percent.
      \nfor example:
      \n70% is 70\/100.
      \n70\/100 = 0.7.<\/p>\n

      Question 2.
      \nA __________ compares two numbers or the number of items in two groups.<\/p>\n

      Answer:
      \nA ratio compares two numbers or the numbers of items in two groups.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nA ratio compares two numbers or the numbers of items in two groups.
      \nfor example:
      \nthe ratio of two numbers a and b can be written as a to b is a:b.<\/p>\n

      Question 3.
      \n________ are numbers that are easier to compute mentally.<\/p>\n

      Answer:
      \nCompatible numbers are numbers that are easier to compute mentally.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nCompatible numbers are numbers that are easier to compute mentally.
      \nfor example:
      \n560 + 7 = 80.
      \n56 and 7 are compatible.<\/p>\n

      Draw a line to match each fraction, decimal, or percent in Column A to the equivalent value in Column B. Column A
      \n\"Envision<\/p>\n

      Answer:
      \nD, C, A, and B.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \n40\/50 = 0.8, 80% = 0.8.
      \n13% = 0.13.
      \n1.75 = 1(3\/4) = 7\/4 = 1.75.
      \n155% = 155\/100 = 1.55.
      \n1(11\/20) = 31\/20 = 1.55.<\/p>\n

      Use Vocabulary in Writing
      \nOut of 230 students surveyed, 11% chose gymnastics as their favorite sport. Explain how you can estimate the number of students who chose gymnastics. Use vocabulary words in your explanation.<\/p>\n

      Answer:
      \nThe number of students who chose gymnastics = 25.3.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nOut of 230 students surveyed, 11% chose gymnastics as their favorite sport.
      \n11% of 230.
      \n11\/100 x 230.
      \n0.11 x 230.
      \n25.3.
      \nso the number of students who chose gymnastics = 25.3.<\/p>\n

      Concept and Skills Review<\/strong><\/p>\n

      Lesson 6.1 Understand Percent<\/strong><\/p>\n

      Quick Review<\/strong>
      \nA percent is a rate that compares a part to 100. The word percent means “of a hundred.”<\/p>\n

      Example<\/strong>
      \nWrite the percent represented by the shaded part of the grid.
      \n\"Envision
      \n\\(\\frac{54}{100}\\) parts shaded = 54%<\/p>\n

      Practice<\/strong>
      \nIn 1 and 2, write the percent of each figure that is shaded.
      \nQuestion 1.
      \n\"Envision<\/p>\n

      Answer:
      \nThe percent is 21%.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthere are 100 boxes.
      \n21 boxes are filled.
      \n21\/100 x 100.
      \n21%.
      \nso the percent is 21%.<\/p>\n

      Question 2.
      \n\"Envision<\/p>\n

      Answer:
      \nThe percent is 70%.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \n10 boxes are there.
      \n7 boxes are filled.
      \n70\/100 x 100.
      \n70%.
      \nso the percent is 70%.<\/p>\n

      In 3 and 4, write each ratio as a percent.
      \nQuestion 3.
      \n14 losses in 50 games<\/p>\n

      Answer:
      \nThe percent is 7.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \n14 losses in 50 games.
      \n14\/100 x 50.
      \n0.14 x 50 = 7.
      \nso the percent is 7.<\/p>\n

      Question 4.
      \n\\(\\frac{4}{5}\\) of the students ride a bus.<\/p>\n

      Answer:
      \nThe number of students who ride a bus = 0.8.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \n4\/5 = 0.8.
      \nthe number of students who rides a bus = 0.8.<\/p>\n

      Question 5.
      \nIf \\(\\overline{A B}\\) represents 25%, what is the length of a line segment that is 100%?
      \n\"Envision<\/p>\n

      Answer:
      \nThe length of the line segment is 1.25 ft.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \n25% of 5.
      \n25\/100 x 5.
      \n0.25 x 5.
      \n1.25.
      \nso the length of the line segment is 1.25 ft.<\/p>\n

      Lesson 6.2 Relate Fractions, Decimals, and Percents<\/strong><\/p>\n

      Quick Review<\/strong>
      \nFractions, decimals, and percents are three ways to show parts of a whole. You can write a percent as a fraction with 100 as the denominator. Then you can write that fraction as a decimal.<\/p>\n

      Example<\/strong>
      \nWrite 35% as a fraction and a decimal.
      \n35% = \\(\\frac{35}{100}\\) or \\(\\frac{7}{20}\\)
      \n\\(\\frac{35}{100}\\) = 0.35<\/p>\n

      Practice<\/strong>
      \nIn 1-6, write each number using the two other forms of notation: fraction, decimal, or percent.
      \nQuestion 1.
      \n0.16<\/p>\n

      Answer:
      \nFraction: 16\/100.
      \ndecimal: 0.16.
      \nPercent: 16%.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe number is 0.16.
      \n16\/100 = 0.16.
      \n16% = 16\/100.<\/p>\n

      Question 2.
      \n\\(\\frac{63}{100}\\)<\/p>\n

      Answer:
      \nFraction: 63\/100.
      \ndecimal: 0.63.
      \nPercent: 63%.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe number is 63\/100.
      \n63\/100 = 0.63.
      \n63% = 63\/100.<\/p>\n

      Question 3.
      \n27%<\/p>\n

      Answer:
      \nFraction: 27\/100.
      \ndecimal: 0.27.
      \nPercent: 27%.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe number is 27%.
      \n27\/100 = 0.27.
      \n27% = 27\/100.<\/p>\n

      Question 4.
      \n\\(\\frac{7}{8}\\)<\/p>\n

      Answer:
      \nFraction: 875\/100.
      \ndecimal: 0.875.
      \nPercent: 875%.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe number is 7\/8.
      \n7\/8 = 0.875.
      \n875\/100 = 8.75.
      \n875% = 875\/100.<\/p>\n

      Question 5.
      \n0.55<\/p>\n

      Answer:
      \nFraction: 55\/100.
      \ndecimal: 0.55.
      \nPercent: 55%.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe number is 0.55.
      \n55\/100 = 0.55.
      \n55% = 55\/100.<\/p>\n

      Question 6.
      \n7%<\/p>\n

      Answer:
      \nFraction: 7\/100.
      \ndecimal: 0.07.
      \nPercent: 7%.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe number is 7%.
      \n7\/100 = 0.07.
      \n7% = 7\/100.<\/p>\n

      Question 7.
      \nOne piece of wheat bread contains 2 g of fiber or 8% of the amount of fiber that most people need in a day. What is 8% as a decimal and as a fraction?<\/p>\n

      Answer:
      \nDecimal = 0.16.
      \nFraction = 8\/100.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nOne piece of wheat bread contains 2 g of fiber or 8% of the amount of fiber that most people need in a day.
      \n8% of 2.
      \n8\/100 x 2.
      \n0.08 x 2.
      \n0.16.
      \n8% as a decimal = 0.16.
      \nfraction = 8\/100.<\/p>\n

      Lesson 6.3 Represent Percents Greater Than 100 or Less Than 1<\/strong><\/p>\n

      Quick Review<\/strong>
      \nPercents less than 1% are less than \\(\\frac{1}{100}\\), and percents greater than 100% are more than one whole. You can express percents greater than 100 or less than 1 in equivalent forms.<\/p>\n

      Example<\/strong>
      \nWrite 221% as a fraction and as a decimal.
      \nFraction: \\(\\frac{221}{100}\\)
      \nDecimal: \\(\\frac{221}{100}\\) = 221 \u00f7 100 = 2.21
      \nWrite 1% as a fraction and as a decimal.
      \nFraction: \\(\\frac{1}{4} \\%=\\frac{1}{4} \\div 100\\)
      \n\\(=\\frac{1}{4} \\times \\frac{1}{100}=\\frac{1}{400}\\)
      \nDecimal: \\(\\frac{1}{4} \\%=0.25 \\%\\)
      \n= \\(\\frac{0.25}{100}\\)
      \n= \\(\\frac{25}{10,000}\\)
      \n= 0.0025<\/p>\n

      Practice<\/strong>
      \nIn 1-6, write each percent as a fraction and as a decimal.
      \nQuestion 1.
      \n140%<\/p>\n

      Answer:
      \nFraction: 140\/100.
      \ndecimal: 1.4.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \n140%.
      \n140\/100 = 140%.
      \n140\/100 = 1.4.<\/p>\n

      Question 2.
      \n\\(\\frac{7}{10}\\)%<\/p>\n

      Answer:
      \nFraction: 0.7\/100.
      \ndecimal: 0.007.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \n7\/10%.
      \n0.7\/100.
      \n0.007.<\/p>\n

      Question 3.
      \n375%<\/p>\n

      Answer:
      \nFraction: 375\/100.
      \ndecimal: 3.75.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \n375%.
      \n375\/100 = 375.
      \n375% = 3.75.<\/p>\n

      Question 4.
      \n0.33%<\/p>\n

      Answer:
      \nFraction: 33\/100.
      \ndecimal: 0.0033.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \n0.33%.
      \n0.33\/100.
      \n0.0033.<\/p>\n

      Question 5.
      \n0.5%<\/p>\n

      Answer:
      \nFraction: 0.5\/100.
      \ndecimal: 0.005.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \n0.5%.
      \n0.5\/100.
      \n0.005.<\/p>\n

      Question 6.
      \n250%<\/p>\n

      Answer:
      \nFraction: 250\/100.
      \ndecimal: 2.5.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \n250%.
      \n250\/100.
      \n2.5.<\/p>\n

      Question 7.
      \nThe radius of the planet Saturn is 945% of the radius of Earth. What is 945% expressed as a fraction and as a decimal?<\/p>\n

      Answer:
      \nFraction = 945\/100.
      \ndecimal = 9.45.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nThe radius of the planet Saturn is 945% of the radius of Earth.
      \n945% = 945\/100.
      \n945\/100 = 9.45.<\/p>\n

      Lesson 6.4 Estimate to Find Percent<\/strong><\/p>\n

      Quick Review<\/strong>
      \nFraction equivalents, rounding, or compatible numbers can be used to estimate the percent of a number<\/p>\n

      Example<\/strong>
      \nEstimate 24% of 83.
      \n24% \u2248 25% and 25% = \\(\\frac{1}{4}\\)
      \n83 rounds to 80.
      \n\\(\\frac{1}{4}\\) \u00d7 80 = 20
      \n24% of 83 is about 20.<\/p>\n

      Practice<\/strong>
      \nIn 1-6, estimate the percent of each number.
      \nQuestion 1.
      \n22% of 96<\/p>\n

      Answer:
      \n22% of 96 = 19.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \n22% is equal to 20%.
      \n96 round to 95.
      \n20% of 100.
      \n20\/100 x 95.
      \n0.2 x 95.
      \n19.
      \nso 22% of 96 = 19.<\/p>\n

      Question 2.
      \n38% of 58<\/p>\n

      Answer:
      \n38% of 58 = 24.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \n38% is equal to 40%.
      \n58 is round to 60.
      \n40\/100 x 60.
      \n0.4 x 60 = 24.
      \nso 38% of 58 = 24.<\/p>\n

      Question 3.
      \n9% of 89<\/p>\n

      Answer:
      \n9% of 89 = 9.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \n9% of 89.
      \n9% is equal to 10.
      \n89 =90.
      \n10% of 90.
      \n10\/100 x 90.
      \n0.1 x 90 = 9.
      \nso 9% of 89 = 9.<\/p>\n

      Question 4.
      \n76% of 41<\/p>\n

      Answer:
      \n76% of 41 = 9.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \n76% of 41.
      \n76% is equal to 80.
      \n41 is rounded to 40.
      \n80\/100 x 40.
      \n0.8 x 40 = 32.
      \nso 76% of 41 = 9.<\/p>\n

      Question 5.
      \n48% of 71<\/p>\n

      Answer:
      \n48% of 71 = 35.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \n48% of 71.
      \n48% is equal to 50.
      \n71 is rounded to 70.
      \n50\/100 x 70.
      \n0.5 x 70 = 35.<\/p>\n

      Question 6.
      \n27% of 62<\/p>\n

      Answer:
      \n27% of 62 = 18.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \n27% of 62.
      \n27% is equal to 30.
      \n62 is rounded to 60.
      \n30\/100 x 60.
      \n0.3 x 60.
      \n18.
      \nso 27% of 62 = 18.<\/p>\n

      Question 7.
      \nJoanna wants to buy a backpack that costs $37.98. The sales tax rate is 8.75%. Estimate the amount of sales tax that Joanna will pay.<\/p>\n

      Answer:
      \nThe amount of sales tax that Joanna will pay = 3.32.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nJoanna wants to buy a backpack that costs $37.98.
      \nThe sales tax rate is 8.75%.
      \n8.75% x $37.98.
      \n8.75\/100 x 37.98.
      \n0.0875 x 37.98.
      \n3.3232.
      \nso the amount of sales tax that Joanna will pay = 3.32.<\/p>\n

      Lesson 6.5 Find the Percent of a Number<\/strong><\/p>\n

      Quick Review<\/strong>
      \nPercent equations have a percent value, a whole, and a part.<\/p>\n

      Example<\/strong>
      \nWhat is 16% of 73.5?
      \nLet x = the unknown part.
      \nx = 0.16 \u2022 73.5
      \nWrite 16% as a decimal.
      \nx = 11.76
      \n16% of 73.5 is 11.76.<\/p>\n

      What percent of 22 is 9.35?
      \nLet p = the percent value.
      \np \u2022 22 = 9.35
      \n\\(\\frac{22 p}{22}=\\frac{9.35}{22}\\)
      \np = 0.425 = 42.5%
      \n42.5% of 22 is 9.35.<\/p>\n

      Practice<\/strong>
      \nFind each part or percent.
      \nQuestion 1.
      \n9% of 124<\/p>\n

      Answer:
      \n9% of 124 = 11.16.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \n9\/100 x 124.
      \n0.09 x 124.
      \n11.16.
      \n9% of 124 = 11.16.<\/p>\n

      Question 2.
      \nWhat percent of 20 is 3?<\/p>\n

      Answer:
      \n15 percent of 20 is 3.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \np x 20 = 3.
      \np = 3\/20.
      \np = 0.15.
      \n15\/100 = 0.15.<\/p>\n

      Question 3.
      \n24% of 35<\/p>\n

      Answer:
      \n24% of 35 = 8.4.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \n24\/100 x 35.
      \n0.24 x 35.
      \n8.4.
      \n24% of 35 = 8.4.<\/p>\n

      Question 4.
      \nWhat percent of 110 is 71.5?<\/p>\n

      Answer:
      \n65 percent of 110 is 71.5.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \np x 110 = 71.5.
      \n110p = 71.5.
      \np = 71.5\/110.
      \np = 0.65.
      \n65\/100 = 0.65.<\/p>\n

      Question 5.
      \n43% of 82<\/p>\n

      Answer:
      \n43% of 82 = 35.26.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \n43\/100 x 82.
      \n0.43 x 82.
      \n35.26.
      \n43% of 82 = 35.26.<\/p>\n

      Question 6.
      \nWhat percent of 30 is 24?<\/p>\n

      Answer:
      \n8 percent of 30 is 24.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \npx 30 = 24.
      \n30p = 24.
      \np = 24\/30.
      \np = 0.8.<\/p>\n

      Question 7.
      \nOn Tuesday, 620 students attended a middle school. A survey showed that 341 students brought lunch to school that day. What percent of the students brought their lunches?<\/p>\n

      Answer:
      \nThe percent of students who brought their lunches = 2114.2.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nOn Tuesday, 620 students attended a middle school.
      \nA survey showed that 341 students brought lunch to school that day.
      \n341\/100 x 620.
      \n3.41 x 620 = 2114.2.
      \nso the percent of students brought their lunches = 2114.2.<\/p>\n

      Lesson 6.6 Find the Whole Given a part and the Percent<\/strong><\/p>\n

      Quick Review<\/strong>
      \nYou can use an equation or a double number line diagram to find the whole when given the part and the percent.<\/p>\n

      Example<\/strong>
      \n80% of what number is 96?
      \nLet n = the whole. Write an equation, rename the percent as a decimal, and solve for n.
      \n80% \u2022 N = 96
      \n0.8n = 96
      \n\\(\\frac{0.8 n}{0.8}=\\frac{96}{0.8}\\)
      \nn = 120
      \n80% of 120 is 96.<\/p>\n

      Practice<\/strong>
      \nFind each whole.
      \nQuestion 1.
      \n140% of what number is 308?<\/p>\n

      Answer:
      \n140% of 220 is 308.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \n140% of n = 308.
      \n140\/100 . n = 308.
      \n1.4 n = 308.
      \nn = 308\/1.4.
      \nn = 220.
      \n140% of 220 is 308.<\/p>\n

      Question 2.
      \n62% of what number is 186?<\/p>\n

      Answer:
      \n62% of 300 is 186.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \n62% of n = 186.
      \n62\/100. n = 186.
      \n0.62n = 186.
      \nn = 186\/0.62.
      \nn = 300.<\/p>\n

      Question 3.
      \n80% of what number is 120?<\/p>\n

      Answer:
      \n80% of 150 is 120.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \n80% of n = 120.
      \n80\/100. n = 120.
      \n0.8n = 120.
      \nn = 120\/0.8.
      \nn = 150.<\/p>\n

      Question 4.
      \n40% of what number is 10?<\/p>\n

      Answer:
      \n40% of 25 is 10.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \n40% of n = 10.
      \n40\/100. n = 10.
      \n0.4n = 10.
      \nn = 10\/0.4.
      \nn = 25.<\/p>\n

      Question 5.
      \nDesmond paid 8.5% sales tax when he bought a new phone. The sales tax was $12.75. What was the total cost of the phone, including tax?<\/p>\n

      Answer:
      \nThe total cost of the phone, including tax, is $150.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nDesmond paid 8.5% sales tax when he bought a new phone.
      \nThe sales tax was $12.75.
      \n8.5% n = $12.75.
      \n8.5\/100 = $12.75.
      \n0.085n = $12.75.
      \nn = $12.75\/0.085.
      \nn = $150.
      \nso the total cost of the phone, including tax, is $150.<\/p>\n

      Topic 6 Fluency Practice<\/h3>\n

      Crisscrossed<\/strong>
      \nFind each quotient. Write your answers in the cross-number puzzle below. Each digit of your answer goes in its own box.
      \nI can… divide multidigit numbers.
      \n\"Envision<\/p>\n

      ACROSS
      \nA. 94,070 = 46
      \nC. 3,828 = 22
      \nE. 46,680 \u00f7 15
      \nF. 61,065 \u00f7 45
      \nJ. 5,136 \u00f7 214
      \nK. 9,840 \u00f7 48
      \nL. 2,407 \u00f7 29
      \nN. 67,870 \u00f7 55
      \nQ. 9,114 \u00f7 62
      \nR. 8,268 \u00f7 12
      \nT. 80,120 \u00f7 20<\/p>\n

      DOWN
      \nA. 7,644 \u00f7 28
      \nB. 22,016 \u00f7 43
      \nD. 49,980 \u00f7 12
      \nG. 67,704 \u00f7 13
      \nH. 10,582 \u00f7143
      \nK. 4,148 \u00f7 17
      \nM. 10,062 \u00f7 26
      \nP. 63,860 \u00f7 31
      \nQ. 4,508 \u00f7 23
      \nS. 7,238 \u00f7 77<\/p>\n","protected":false},"excerpt":{"rendered":"

      Go through the\u00a0enVision Math Common Core Grade 6 Answer Key\u00a0Topic 6 Understand And Use Percent\u00a0regularly and improve your accuracy in solving questions. enVision Math Common Core 6th Grade Answers Key Topic 6 Understand And Use Percent Topic 6 Essential Question What is the meaning of percent? How can percent be estimated and found? Answer: A …<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2],"tags":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/posts\/16240"}],"collection":[{"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/comments?post=16240"}],"version-history":[{"count":4,"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/posts\/16240\/revisions"}],"predecessor-version":[{"id":27998,"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/posts\/16240\/revisions\/27998"}],"wp:attachment":[{"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/media?parent=16240"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/categories?post=16240"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/tags?post=16240"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}