{"id":11365,"date":"2023-12-11T17:00:17","date_gmt":"2023-12-11T11:30:17","guid":{"rendered":"https:\/\/envisionmathanswerkey.com\/?p=11365"},"modified":"2023-12-12T12:22:46","modified_gmt":"2023-12-12T06:52:46","slug":"envision-math-common-core-grade-4-answer-key-topic-12","status":"publish","type":"post","link":"https:\/\/envisionmathanswerkey.com\/envision-math-common-core-grade-4-answer-key-topic-12\/","title":{"rendered":"enVision Math Common Core Grade 4 Answer Key Topic 12 Understand and Compare Decimals"},"content":{"rendered":"

Go through the\u00a0enVision Math Common Core Grade 4 Answer Key<\/a>\u00a0Topic 12 Understand and Compare Decimals<\/strong>\u00a0regularly and improve your accuracy in solving questions.<\/p>\n

enVision Math Common Core 4th Grade Answers Key Topic 12 Understand and Compare Decimals<\/h2>\n

Essential Questions:<\/strong>
\nHow can you write a fraction as a decimal? How can you locate points on a number line? How do you compare decimals?
\n\"Envision<\/p>\n

enVision STEM Project: Energy and Decimals<\/strong>
\nDo Research Use the Internet or other sources to research other sports or games where players transfer energy to cause collisions in order to score points and win.
\nJournal: Write a Report Include what you found. Also in your report:<\/p>\n

    \n
  • Explain how the transfer of energy helps the player or team score.<\/li>\n
  • A game of curling is broken into ten rounds called ends. Suppose a team wins 6 of the 10 ends. Write a fraction with a denominator of 10 and an equivalent fraction with a denominator of 100. Then, write an equivalent decimal that represents the same value.<\/li>\n<\/ul>\n

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

    Vocabulary<\/strong><\/p>\n

    Choose the best term from the box. Write it on the blank.<\/p>\n

      \n
    • hundredth<\/li>\n
    • tens<\/li>\n
    • place value<\/li>\n
    • tenth<\/li>\n<\/ul>\n

      Question 1.
      \nA ________ is one of 10 equal parts of a whole, written as \\(\\frac{1}{10}\\).
      \nAnswer: A tenth<\/span> is one of 10 equal parts of a whole, written as \\(\\frac{1}{10}\\).<\/p>\n

      \"Understand<\/p>\n

      Question 2.
      \n__________ is the position of a digit in a number that is used to determine the value of the digit.
      \nAnswer: tens<\/span> is the position of a digit in a number that is used to determine the value of the digit.<\/p>\n

      Question 3.
      \nA __________ is one of 100 equal parts of a whole, written as \\(\\frac{1}{100}\\).
      \nAnswer: A hundredth<\/span> is one of 100 equal parts of a whole, written as \\(\\frac{1}{100}\\).<\/p>\n

      Comparing Fractions<\/strong><\/p>\n

      Write >, <, or = in the \"Envision.
      \nQuestion 4.
      \n\\(\\frac{5}{100}\\) \"Envision \\(\\frac{5}{10}\\)
      \nAnswer: \\(\\frac{5}{100}\\) <\u00a0\\(\\frac{5}{10}\\)<\/p>\n

      Question 5.
      \n\\(\\frac{1}{10}\\) \"Envision \\(\\frac{1}{100}\\)
      \nAnswer: \\(\\frac{1}{10}\\) >\u00a0\\(\\frac{1}{100}\\)<\/p>\n

      Question 6.
      \n\\(\\frac{2}{10}\\) \"Envision \\(\\frac{20}{100}\\)
      \nAnswer: \\(\\frac{2}{10}\\) = \\(\\frac{20}{100}\\)<\/p>\n

      Parts of a Whole<\/strong><\/p>\n

      Complete each fraction to represent the shaded part of the whole.
      \nQuestion 7.
      \n\"Envision
      \nAnswer: There are 10 blocks of which 3 are shaded. So, the fraction of the shaded part of the whole is \\(\\frac{3}{10}\\)<\/p>\n

      Question 8.
      \n\"Envision
      \nAnswer: There are 10 blocks of which 0 are shaded. So, the fraction of the shaded part of the whole is 0.<\/p>\n

      Question 9.
      \n\"Envision
      \nAnswer: There are 10 blocks of which 7 are shaded. So, the fraction of the shaded part of the whole is \\(\\frac{7}{10}\\)<\/p>\n

      Shade the part of the whole that represents the fraction.
      \nQuestion 10.
      \n\"Envision
      \nAnswer:
      \n\"Envision-Math-Common-Core-4th-Grade-Answer-Key-Topic-12-Understand-and-Compare-Decimals-6\"<\/p>\n

      Question 11.
      \n\"Envision
      \nAnswer:
      \n\"Envision-Math-Common-Core-4th-Grade-Answer-Key-Topic-12-Understand-and-Compare-Decimals-7\"<\/p>\n

      Question 12.
      \n\"Envision
      \nAnswer:
      \n\"Envision-Math-Common-Core-4th-Grade-Answer-Key-Topic-12-Understand-and-Compare-Decimals-8\"<\/p>\n

      \"Understand<\/p>\n

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

      Question 13.
      \nReasoning Rob walked \\(\\frac{2}{10}\\) block. Drew walked \\(\\frac{5}{10}\\) block. Write a comparison for the distance Rob and Drew each walked.
      \nAnswer:
      \nGiven,
      \nRob walked \\(\\frac{2}{10}\\) block.
      \nDrew walked \\(\\frac{5}{10}\\) block.
      \nDrew walked more than Rob.<\/p>\n

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

      PROJECT 12A
      \nHow much will it cost to visit a national park?
      \nProject: Write a Travel Journal
      \n\"Envision<\/p>\n

      PROJECT 12B
      \nHow do you know who won the event?
      \nProject: Compare Olympic Racing Times
      \n\"Envision<\/p>\n

      PROJECT 12C
      \nWould you like to win an award for a presentation?
      \nProject: Make a Presentation about Adding Fractions
      \n\"Envision<\/p>\n

      PROJECT 12D
      \nHow did railroads help build Florida?
      \nProject: Build a Miniature Railroad
      \n\"Envision<\/p>\n

      Lesson 12.1 Fractions and Decimals<\/h3>\n

      Solve & Share<\/strong>
      \nAccording to a survey, 7 out of 10 pet owners have a dog. Represent this in a drawing.
      \nI can … relate fractions and decimals.
      \n\"Envision<\/p>\n

      Look Back! How many pet owners do NOT have a dog? Write your answer as a fraction.<\/p>\n

      Essential Question<\/strong>
      \nHow Can You Write a Fraction as a Decimal?<\/p>\n

      Visual Learning Bridge
      \nOn Kelsey Street, 6 out of 10 houses have swing sets. Write \\(\\frac{6}{10}\\) as a decimal.
      \nA decimal is another representation for a fraction and also names parts of wholes. A decimal is a number with one or more digits to the right of the decimal point.
      \nFractions with denominators of 10 and 100 may be written as decimals.
      \n\"Envision<\/p>\n

      Sixth tenths or \\(\\frac{6}{10}\\) of the houses have swing sets.
      \nYou can write \\(\\frac{6}{10}\\) as a decimal by putting a 6 in tenths place. The tenths place is to the right of the decimal point.
      \n\"Envision<\/p>\n

      \\(\\frac{6}{10}\\) and \\(\\frac{60}{100}\\) are equivalent.
      \nYou can write \\(\\frac{60}{100}\\) as a decimal by using tenths and hundredths places The hundredths place is to the right of tenths place.
      \n\"Envision
      \nSo, 0.6 or 0.60 of the houses have swing sets.<\/p>\n

      Convince Me! Reasoning in the Kelsey Street neighborhood, 75 out of 100 houses are two-story homes. Write \\(\\frac{75}{100}\\) as a decimal. Shade the grid to show the equivalent fraction and decimal.
      \n\"Envision<\/p>\n

      Another Example!<\/strong>
      \nYou can use grids to show how money relates to fractions and decimals.
      \n\"Envision<\/p>\n

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

      Do You Understand?<\/strong>
      \nQuestion 1.
      \nHow can you use grids to represent $4.71?
      \nAnswer:<\/p>\n

      \"Understand<\/p>\n

      Do You Know How?<\/strong>
      \nQuestion 2.
      \nWrite a decimal and a fraction for the part of the grid that is shaded.
      \n\"Envision
      \nAnswer: There are 10 blocks of which 5 are shaded and 5 are not shaded.
      \nSo, the decimal of the shaded part is 0.5
      \nThe fraction of the shaded part is \\(\\frac{5}{10}\\)<\/p>\n

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

      For 3-6, write a decimal and fraction for each diagram.
      \nQuestion 3.
      \n\"Envision
      \nAnswer: There are 100 blocks of which 4 are shaded and 96 are not shaded.
      \nSo, the decimal of the shaded part is 0.04
      \nThe fraction of the shaded part is \\(\\frac{4}{100}\\)<\/p>\n

      Question 4.
      \n\"Envision
      \nAnswer: There are 200 blocks of which 154 are shaded and 46 are not shaded.
      \nSo, the decimal of the shaded part is 0.77
      \nThe fraction of the shaded part is \\(\\frac{154}{200}\\)<\/p>\n

      Question 5.
      \n\"Envision
      \nAnswer: There are 100 blocks of which 39 are shaded and 61 are not shaded.
      \nSo, the decimal of the shaded part is 0.39
      \nThe fraction of the shaded part is \\(\\frac{39}{100}\\)<\/p>\n

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

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

      Question 7.
      \nThe arena of the Colosseum in Rome was about \\(\\frac{15}{100}\\) of the entire Colosseum. Write this amount as a decimal.
      \n\"Envision
      \nAnswer:
      \nGiven,
      \nThe arena of the Colosseum in Rome was about \\(\\frac{15}{100}\\) of the entire Colosseum.
      \nThe fraction \\(\\frac{15}{100}\\) can be written as 0.15.<\/p>\n

      Question 8.
      \nWhat fraction of the Colosseum was NOT the arena? Write and solve an equation.
      \nAnswer:
      \n\\(\\frac{100}{100}\\) – \\(\\frac{15}{100}\\) = \\(\\frac{85}{100}\\)<\/p>\n

      Question 9.
      \nVocabulary Write the vocabulary word that best completes the sentence:
      \nJelena says, “One dime is one ________ of a dollar.”
      \nAnswer:
      \nJelena says, “One dime is one tenth of a dollar.”<\/p>\n

      Question 10.
      \nNumber Sense<\/strong> About how much of the rectangle is shaded green? Write this amount as a fraction and as a decimal.
      \n\"Envision
      \nAnswer: \\(\\frac{1}{10}\\) or 0.1<\/p>\n

      Question 11.
      \nCritique Reasoning<\/strong> Cher adds up the money in her piggy bank. She has a one-dollar bill and 3 dimes. Did Cher write the amount of money correctly? If not, what mistake did Cher make? $1.3
      \nAnswer:
      \nGiven,
      \nCher adds up the money in her piggy bank. She has a one-dollar bill and 3 dimes.
      \nThe amount of money is always written in hundredths. Cher should have written $1.30<\/p>\n

      Question 12.
      \nHigher Order Thinking<\/strong> The diagram models the plants in a vegetable garden. Write a fraction and a decimal for each vegetable in the garden.
      \n\"Envision
      \nAnswer:
      \nRadishes: \\(\\frac{23}{100}\\), 0.23
      \nCarrots: \\(\\frac{35}{100}\\), 0.35
      \nCorn: \\(\\frac{15}{100}\\), 0.15
      \nLettuce: \\(\\frac{27}{100}\\), 0.27<\/p>\n

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

      Question 13.
      \nWhich decimal represents \\(\\frac{5}{100}\\)?
      \nA. 0.05
      \nB. 0.5
      \nC. 0.50
      \nD. 0.95
      \nAnswer:
      \nGiven the fraction \\(\\frac{5}{100}\\)
      \nIt can be written in the decimal form as 0.05.
      \nThus the correct answer is option A.<\/p>\n

      Question 14.
      \nWhich fraction and decimal represent twenty-nine hundredths?
      \nA. 0.29 and \\(\\frac{29}{10}\\)
      \nB. 0.29 and \\(\\frac{100}{29}\\)
      \nC. 2.9 and \\(\\frac{29}{100}\\)
      \nD. 0.29 and \\(\\frac{29}{100}\\)
      \nAnswer:
      \ntwenty-nine hundredths mean 29 of hundred.
      \nThe decimal form will be 0.29
      \nThe fraction form is \\(\\frac{29}{100}\\).
      \nThus the correct answer is option D.<\/p>\n

      Lesson 12.2 Fractions and Decimals on the Number Line<\/h3>\n

      Solve & Share<\/strong>
      \nName the fractions and\/or decimals of each lettered point on the number lines. Tell how you decided.
      \nI can … locate and describe fractions and decimals on number lines.
      \n\"Envision<\/p>\n

      Look Back! Is the name for point B above different from the name for point B on the number line below? Explain.
      \n\"Envision<\/p>\n

      Essential Question<\/strong>
      \nHow Can You Locate Points on a Number Line?<\/p>\n

      Visual Learning Bridge
      \nIn long-track speed skating, each lap is \\(\\frac{4}{10}\\) kilometer. During practice, Elizabeth skated 3.75 kilometers. Draw a number line to show \\(\\frac{4}{10}\\) and 3.75.
      \nYou can use a number line to locate and describe fractions and decimals.
      \n\"Envision<\/p>\n

      Locate \\(\\frac{4}{10}\\) on a number line.
      \nDraw a number line and divide the distance from 0 to 1 into 10 equal parts to show tenths.
      \nThe distance from 0 to 0.4 is four tenths the distance from 0 to 1.
      \nDraw a point at \\(\\frac{4}{10}\\)
      \n\"Envision<\/p>\n

      Locate 3.75 on a number line.
      \nYou can show 3.75 on a number line divided into tenths by plotting a point halfway between 3.7 and 3.8.
      \n\"Envision
      \nYou can use a second number line to show the interval between 3.7 and 3.8. The points on both number lines are at 3.75.<\/p>\n

      Convince Me! Be Precise Which decimal shown on the number line is not placed in the correct location? Explain.
      \n\"Envision<\/p>\n

      Another Example!<\/strong>
      \nFractions and decimals can name the same points on a number line.
      \n\"Envision
      \nMixed numbers and decimals can name the the same points on a number line.
      \n\"Envision<\/p>\n

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

      Do You Understand?<\/strong>
      \nQuestion 1.
      \nLocate\\(\\frac{45}{100}\\) on the number line.
      \n\"Envision
      \nAnswer:<\/p>\n

      Question 2.
      \nDraw a number line to represent both the decimal and fraction for eight tenths.
      \nAnswer:<\/p>\n

      Do You Know How?<\/strong>
      \nFor 3-6, name the decimal and fraction for each point on the number line.
      \n\"Envision
      \nQuestion 3.
      \nE
      \nAnswer:
      \nThe decimal at E point is 0.6.
      \nThe fraction at E point is 6\/100.<\/p>\n

      Question 4.
      \nH.
      \nAnswer:
      \nThe decimal at H point is 1.4.
      \nThe fraction at H point is 7\/5.<\/p>\n

      Question 5.
      \nF
      \nAnswer:
      \nThe decimal at F point is 1.33
      \nThe fraction at F point is 133\/100.<\/p>\n

      Question 6.
      \nG
      \nAnswer:
      \nThe decimal at G point is 1.39
      \nThe fraction at G point is 139\/100<\/p>\n

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

      For 7-8, label the number lines with the given fractions and decimals.
      \nQuestion 7.
      \nRepresent the decimals and fractions from 3.08 to 3.13.
      \n\"Envision
      \nAnswer:<\/p>\n

      Question 8.
      \nRepresent the fractions and decimals from \\(\\frac{4}{10}\\) to 1.
      \n\"Envision
      \nAnswer:<\/p>\n

      For 9-16, name the decimal and fraction for each point on the number line.
      \n\"Envision<\/p>\n

      Question 9.
      \nJ
      \nAnswer:
      \nThe decimal at the point J is 4.66
      \nThe fraction at the point J is 233\/50<\/p>\n

      Question 10.
      \nK
      \nAnswer:
      \nThe decimal at the point K is 4.62
      \nThe fraction at the point K is 231\/50.<\/p>\n

      Question 11.
      \nL
      \nAnswer:
      \nThe decimal at the point L is 4.8
      \nThe fraction at the point L is 48\/100.<\/p>\n

      Question 12.
      \nM
      \nAnswer:
      \nThe decimal at the point M is 4.53
      \nThe fraction at the point M is 453\/100.<\/p>\n

      Question 13.
      \nN
      \nAnswer:
      \nThe decimal at the point N is 4.69
      \nThe fraction at the point N is 469\/100.<\/p>\n

      Question 14.
      \nO
      \nAnswer:
      \nThe decimal at the point 0 is 4.76
      \nThe fraction at the point 0 is 119\/25.<\/span><\/p>\n

      Question 15.
      \nP
      \nAnswer:
      \nThe decimal at the point P is 4.6
      \nThe fraction at the point P is 23\/5.<\/p>\n

      Question 16.
      \nQ
      \nAnswer:
      \nThe decimal at the point Q is 3.59
      \nThe fraction at the point Q is 359\/100<\/p>\n

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

      Question 17.
      \nWrite the five missing decimals on the number line.
      \n\"Envision
      \nAnswer:
      \n\"Envision-Math-Common-Core-4th-Grade-Answer-Key-Topic-12-Understand-and-Compare-Decimals-39\"
      \nThe five missing decimals on the number line are 0.4, 0.6, 0.8, 1.2, and 1.4.
      \nThe difference of the numbers in the number line is 0.2<\/p>\n

      Question 18.
      \nWrite the five missing fractions on the number line.
      \n\"Envision
      \nAnswer:
      \n\"Envision-Math-Common-Core-4th-Grade-Answer-Key-Topic-12-Understand-and-Compare-Decimals-40\"
      \nThe five missing fractions on the number line are 41\/100, 43\/100, 46\/100, 47\/100, and 50\/100.
      \nThe difference of the fractions on the number line is 1\/100.<\/p>\n

      Question 19.
      \nDraw a number line to show 60 cents. Use the number line to write 60 cents as a fraction and as a decimal.
      \nAnswer:<\/p>\n

      Question 20.
      \nMake Sense and Persevere Neil is learning about unusual units of volume. There are 2 pecks in 1 kenning. There are 2 kennings in 1 bushel. There are 8 bushels in 1 quarter. There are 5 quarters in 1 load. Write a number sentence to show how many pecks are in 1 load.
      \nAnswer:
      \nGiven that,
      \n2 pecks in 1 kenning.
      \n2 kinnings in 1 bushel.
      \n8 bushels in 1 quarter.
      \n5 quarters in 1 load.
      \nTherefore 2 pecks in 1 load.<\/p>\n

      Question 21.
      \nDraw a number line and plot a point at each number shown.
      \n2\\(\\frac{71}{100}\\) 2.6 2\\(\\frac{82}{100}\\)
      \nAnswer:<\/p>\n

      Question 22.
      \nHigher Order Thinking<\/strong> Use a number line to name two numbers that are the same distance apart as 3.2 and 3.8.
      \nAnswer: 0 and 0.6
      \n\"Envision-Math-Common-Core-2nd-Grade-Answer-Key-Topic-3-Add-Within-100-Using-Strategies-18\"<\/p>\n

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

      Question 23.
      \nWhat decimals or fractions do the points on the number lines show? Choose the decimals and fractions from the box to label the number lines.
      \n\"Envision
      \nAnswer:
      \n\"Envision-Math-Common-Core-4th-Grade-Answer-Key-Topic-12-Understand-and-Compare-Decimals-41\"<\/p>\n

      Question 24.
      \nWhat decimals or fractions do the points on the number lines show? Choose the decimals and fractions from the box to label the number lines.
      \n\"Envision
      \nAnswer:
      \n\"Envision-Math-Common-Core-4th-Grade-Answer-Key-Topic-12-Understand-and-Compare-Decimals-42\"<\/p>\n

      Lesson 12.3 Compare Decimals<\/h3>\n

      Solve & Share<\/strong>
      \nA penny made in 1982 weighs about 0.11 ounce. A penny made in 2013 weighs about 0.09 ounce. Which penny weighs more? Solve this problem any way you choose.
      \nI can … compare decimals by reasoning about their size.
      \n\"Envision<\/p>\n

      Look Back! Construct Arguments Simon and Danielle are eating oranges. Danielle says, “Because we each have 0.75 of an orange left, we have the same amount left to eat.” Do you agree with Danielle? Explain.<\/p>\n

      Essential Question<\/strong>
      \nHow Do You Compare Decimals?<\/p>\n

      Visual Learning Bridge
      \nDonovan ran the 100-meter race in 10.11 seconds. Sal ran the same race in 10.09 seconds. Who had the faster time?
      \nThere is more than one way to compare decimals.
      \n\"Envision<\/p>\n

      One Way<\/strong>
      \nUse hundredths grids.
      \nThe whole numbers are the same. Compare the digits in the tenths place.
      \n\"Envision
      \nSal had the faster time.<\/p>\n

      Another Way<\/strong>
      \nUse place value.
      \nThe whole number parts are the same.
      \nThe decimal parts are both to the hundredths.
      \n11 hundredths is greater than 9 hundredths.
      \n10.11 >10.09
      \nSal had the faster time.<\/p>\n

      Another Way<\/strong>
      \nStart at the left.
      \nCompare each place value. Look for the first place where the digits are different.
      \n10.11 10.09
      \n1 tenth > 0 tenths
      \n10.11 > 10.09
      \nSal had the faster time.<\/p>\n

      Convince Me! Reasoning Write four different digits in the blank spaces to make each comparison true. Explain your reasoning.
      \n0. ______ 8 < 0.______ 0.5 _____ > 0.______ 9<\/p>\n

      Another Example!<\/strong>
      \nYou can also use place-value blocks or number lines to compare.
      \nGrids, place-value blocks, and number lines are all appropriate tools to use for comparing decimals. When using place-value blocks, let
      \nthe flat equal one whole.
      \n\"Envision<\/p>\n

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

      Do You Understand?<\/strong>
      \nQuestion 1.
      \nCy says, \u201c0.20 is greater than 0.2 because 20 is greater than 2.” Do you agree? Explain.
      \nAnswer: No 0.20 and 0.2 are equal in the decimal. Because 0 after 2 will remain the same and 0 before 2 will make a lot of change as it becomes hundredths.<\/p>\n

      Do You Know How?<\/strong>
      \nFor 2-5, write >, <, or = in each \"Envision. Use an appropriate tool as needed to compare.
      \nQuestion 2.
      \n0.70 \"Envision 0.57
      \nAnswer:
      \n0.70 >\u00a00.57<\/p>\n

      Question 3.
      \n0.41 \"Envision 0.14
      \nAnswer:
      \n0.41 >\u00a00.14<\/p>\n

      Question 4.
      \n6.28 \"Envision 7.31
      \nAnswer:
      \n6.28 <\u00a07.31<\/p>\n

      Question 5.
      \n1.1 \"Envision 1.10
      \nAnswer:
      \n1.1 =\u00a01.10<\/p>\n

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

      Leveled Practice For 6-14, write >,<, or = in each \"Envision. Use an appropriate tool as needed to compare.
      \nQuestion 6.
      \n\"Envision
      \nAnswer:
      \n0.17 < 0.2<\/p>\n

      Question 7.
      \n\"Envision
      \nAnswer:
      \n0.31 > 0.29<\/p>\n

      Question 8.
      \n\"Envision
      \nAnswer:
      \n0.44 > 0.22<\/p>\n

      Question 9.
      \n0.1 \"Envision 0.1 0
      \nAnswer:
      \n0.1 = 0.10<\/p>\n

      Question 10.
      \n$2.98 \"Envision $2.56
      \nAnswer:
      \n$2.98 >\u00a0$2.56<\/p>\n

      Question 11.
      \n7.01 \"Envision 7.1
      \nAnswer:
      \n7.01 >\u00a07.1<\/p>\n

      Question 12.
      \n0.08 \"Envision 0.7
      \nAnswer:
      \n0.08 <\u00a00.7<\/p>\n

      Question 13.
      \n3.40 \"Envision 3.4
      \nAnswer:
      \n3.40 =\u00a03.4<\/p>\n

      Question 14.
      \n$21.50 \"Envision $20.99
      \nAnswer:
      \n$21.50 >\u00a0$20.99<\/p>\n

      For 15-20, write a decimal to make each comparison true.
      \nQuestion 15.
      \n______ < 0.23
      \nAnswer:
      \n0.20 < 0.23<\/p>\n

      Question 16.
      \n8.60 = _______
      \nAnswer:
      \n8.60 = 8.60<\/p>\n

      Question 17.
      \n______ > 4.42
      \nAnswer:
      \n3.43 > 4.42<\/p>\n

      Question 18.
      \n13.2 > ______
      \nAnswer:
      \n13.2 > 12.4<\/p>\n

      Question 19.
      \n5.2 < ______
      \nAnswer:
      \n5.2 < 4.3<\/p>\n

      Question 20.
      \n6.2 = ______
      \nAnswer:
      \n6.2 = 6.2<\/p>\n

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

      Question 21.
      \nUse Appropriate Tools Maria timed how long it took her Venus Fly Trap to close. The first time it took 0.43 second to close. The second time took 0.6 second to close. Which was the faster time? Draw place-value blocks to show your comparison.
      \nAnswer:
      \nGiven that,
      \nMaria took a time to her venus fly trap to close for first time = 0.43
      \nMaria took a time to her venus fly trap to close for second time = 0.6
      \nSecond time was the faster time.<\/p>\n

      Question 22.
      \nFishing lures have different weights. Which lure weighs more?
      \n\"Envision
      \nAnswer:
      \nGiven that,
      \nThe weight of the yellow minnow fishing lures = 0.63
      \nThe weight of the green minnow fishing lures = 0.5
      \nYellow minnow fishing lures is more than green minnow fishing lures.
      \nSo, 0.63 > 0.5<\/p>\n

      Question 23.
      \nNumber Sense<\/strong> Ellen wants to give 100 toys to each of 9 charities. In one week, she collects 387 toys. The next week, she collects 515 toys. Has Ellen reached her goal? Use an estimate to explain.
      \nAnswer:
      \nGiven that,
      \nEllen wants to give 100 toys to each of 9 charities.
      \nTotal number of toys she collected in one week = 387
      \nTotal number of toys she collected in next week = 515
      \nTotal number of toys she collected = 387 + 515 = 902
      \n100 toys to each of 9 charities = 9 \u00d7 100 = 900
      \nSo, she reached her goal.<\/p>\n

      Question 24.
      \nHigher Order Thinking<\/strong> Tori has two different-sized water bottles. In the larger bottle, she has 0.81 liter of water. In the smaller bottle, she has 1.1 liters of water. Can you tell whether one bottle has more water? Explain.
      \nAnswer:
      \nGiven that,
      \nIn the longer bottle she has a water = 0.81 liter.
      \nIn the smaller bottle she has a water\u00a0 = 1.1 liter.
      \n0.81 > 1.1
      \nSo, the smaller has more water.<\/p>\n

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

      Question 25.
      \nStanley found the weights of two minerals, quartz and garnet. The quartz weighed 3.76 ounces and the garnet weighed 3.68 ounces.<\/p>\n

      Explain how Stanley can use a tool to find which mineral weighed more.<\/p>\n

      Explain how Stanley can use place value to find which mineral weighed less.
      \nAnswer:
      \nGiven that,
      \nThe weight of a quartz = 3.76 ounces
      \nThe weight of a garnet = 3.68 ounces
      \nTherefore 3.68 > 3.75
      \nThe weight of a quartz is more than the weight of a garnet
      \nUsing the place value
      \n3.68 and 3.75
      \nTen’s place of a numbers are
      \n6 < 7
      \nThe weight of a quartz is more.<\/p>\n

      Lesson 12.4 Add Fractions with Denominators of 10 and 100<\/h3>\n

      Solve & Share<\/strong>
      \nThe mural is divided into 100 equal parts. Marilyn’s class painted io of the mural, and Cal’s class painted 20 of the mural. How much of the mural have the two classes painted? Solve this problem any way you choose.
      \nI can … use equivalence to add fractions with denominators of 10 and 100.
      \n\"Envision
      \nYou can use appropriate tools. Think about how you can use the grid to find how much of the mural the two classes painted. Show your work in the space above!<\/p>\n

      Look Back! How much of the mural remains to be painted? Write the amount as a decimal.<\/p>\n

      Essential Question<\/strong>
      \nHall How Can You Add Fractions with Denominators of 10 and 100?<\/p>\n

      Visual Learning Bridge
      \nSteve and Jana collected money for an animal shelter. Steve collected \\(\\frac{4}{10}\\) of their goal while Jana collected \\(\\frac{5}{100}\\). How much of their goal did Jana and Steve collect?
      \n\"Envision
      \nUse like denominators to add fractions.<\/p>\n

      The red shows \\(\\frac{4}{10}\\) of the goal, and the blue shows \\(\\frac{5}{100}\\) of the goal.
      \nThe amount they collected can be written as to \\(\\frac{4}{10}\\) + \\(\\frac{5}{100}\\)
      \nYou can use equivalent fractions to write tenths as hundredths.<\/p>\n

      Rename \\(\\frac{4}{10}\\) as an equivalent fraction with a denominator of 100.
      \nMultiply the numerator and denominator by 10.
      \n\\(\\frac{4 \\times 10}{10 \\times 10}=\\frac{40}{100}\\)<\/p>\n

      Add the numerators and write the sum over the like denominator.
      \n\\(\\frac{40}{100}\\) + \\(\\frac{5}{100}\\) = \\(\\frac{45}{100}\\)
      \nJana and Steve collected \\(\\frac{45}{100}\\) of their goal.<\/p>\n

      Convince Me! Construct Arguments in the problem above, why is the denominator of the total 100 and not 200?<\/p>\n

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

      Do You Understand?<\/strong>
      \nQuestion 1.
      \nSuppose Jana collected another \\(\\frac{25}{100}\\) of their goal. What fraction of the goal have they now collected?
      \nAnswer:
      \nGiven that,
      \nJana collected money = \\(\\frac{5}{100}\\).
      \nJana collected another \\(\\frac{25}{100}\\).
      \nFraction of goal have they collected =
      \n\\(\\frac{5}{100}\\) + \\(\\frac{25}{100}\\) =
      \nThe fractions have, unlike denominators. First, find the Least Common Denominator and rewrite the fractions with the common denominator.
      \nL.C.M of 10 and 100 is 100.
      \nMultiply both the numerator and denominator of each fraction by the number that makes its denominator equal to the LCD. This is basically multiplying each fraction by 1.
      \n\\(\\frac{5}{100}\\) + \\(\\frac{25}{100}\\) =\\(\\frac{30}{100}\\)<\/p>\n

      Question 2.
      \nWrite a problem that represents the addition shown below, then solve.
      \n\"Envision
      \nAnswer:<\/p>\n

      Do You Know How?<\/strong>
      \nFor 3-8, add the fractions.
      \nQuestion 3.
      \n\\(\\frac{3}{10}+\\frac{4}{100}\\)
      \nAnswer:
      \nThe fractions have, unlike denominators. First, find the Least Common Denominator and rewrite the fractions with the common denominator.
      \nLCM of 10 and 100 is 100.
      \nMultiply both the numerator and denominator of each fraction by the number that makes its denominator equal to the LCD. This is basically multiplying each fraction by 1.
      \n(\\(\\frac{3}{10}\\) \u00d7 \\(\\frac{10}{10}\\)) + (\\(\\frac{4}{100}\\) \u00d7 \\(\\frac{1}{1}\\))
      \n\\(\\frac{30}{100}\\) + \\(\\frac{4}{100}\\) = \\(\\frac{34}{100}\\)<\/p>\n

      Question 4.
      \n\\(\\frac{71}{100}+\\frac{5}{10}\\)
      \nAnswer:
      \nThe fractions have, unlike denominators. First, find the Least Common Denominator and rewrite the fractions with the common denominator.
      \nL.C.M of 10 and 100 is 100.
      \nMultiply both the numerator and denominator of each fraction by the number that makes its denominator equal to the LCD. This is basically multiplying each fraction by 1.
      \n(\\(\\frac{71}{100}\\) \u00d7 \\(\\frac{1}{1}\\)) + (\\(\\frac{5}{10}\\) \u00d7 \\(\\frac{10}{10}\\))
      \n\\(\\frac{71}{100}\\) + \\(\\frac{50}{100}\\) = \\(\\frac{121}{100}\\)<\/p>\n

      Question 5.
      \n\\(\\frac{4}{100}+\\frac{38}{10}\\)
      \nAnswer:
      \nThe fractions have, unlike denominators. First, find the Least Common Denominator and rewrite the fractions with the common denominator.
      \nL.C.M of 10 and 100 is 100.
      \nMultiply both the numerator and denominator of each fraction by the number that makes its denominator equal to the LCD. This is basically multiplying each fraction by 1.
      \n(\\(\\frac{4}{100}\\) \u00d7 \\(\\frac{1}{1}\\)) + (\\(\\frac{38}{10}\\) \u00d7 \\(\\frac{10}{10}\\))
      \n\\(\\frac{4}{100}\\) + \\(\\frac{380}{100}\\) = \\(\\frac{384}{100}\\)<\/p>\n

      Question 6.
      \n\\(\\frac{90}{100}+\\frac{1}{10}\\)
      \nAnswer:
      \nThe fractions have, unlike denominators. First, find the Least Common Denominator and rewrite the fractions with the common denominator.
      \nL.C.M of 10 and 100 is 100.
      \nMultiply both the numerator and denominator of each fraction by the number that makes its denominator equal to the LCD. This is basically multiplying each fraction by 1.
      \n(\\(\\frac{90}{100}\\) \u00d7 \\(\\frac{1}{1}\\)) + (\\(\\frac{1}{10}\\) \u00d7 \\(\\frac{10}{10}\\))
      \n\\(\\frac{90}{100}\\) + \\(\\frac{10}{100}\\) = \\(\\frac{100}{100}\\) = 1<\/p>\n

      Question 7.
      \n\\(\\frac{8}{10}+\\frac{1}{10}+\\frac{7}{100}\\)
      \nAnswer:
      \nThe fractions have, unlike denominators. First, find the Least Common Denominator and rewrite the fractions with the common denominator.
      \nL.C.M of 10 and 100 is 100.
      \nMultiply both the numerator and denominator of each fraction by the number that makes its denominator equal to the LCD. This is basically multiplying each fraction by 1.
      \n(\\(\\frac{9}{10}\\) \u00d7 \\(\\frac{10}{10}\\)) + (\\(\\frac{7}{100}\\) \u00d7 \\(\\frac{1}{1}\\))
      \n\\(\\frac{90}{100}\\) + \\(\\frac{7}{100}\\) = \\(\\frac{97}{100}\\)<\/p>\n

      Question 8.
      \n\\(\\frac{38}{100}+\\frac{4}{10}+\\frac{2}{10}\\)
      \nAnswer:
      \nThe fractions have, unlike denominators. First, find the Least Common Denominator and rewrite the fractions with the common denominator.
      \nL.C.M of 10 and 100 is 100.
      \nMultiply both the numerator and denominator of each fraction by the number that makes its denominator equal to the LCD. This is basically multiplying each fraction by 1.
      \n(\\(\\frac{38}{100}\\) \u00d7 \\(\\frac{1}{1}\\)) + (\\(\\frac{6}{10}\\) \u00d7 \\(\\frac{10}{10}\\))
      \n\\(\\frac{38}{100}\\) + \\(\\frac{60}{100}\\) = \\(\\frac{98}{100}\\)<\/p>\n

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

      Leveled Practice For 9-23, add the fractions.
      \nQuestion 9.
      \n\\(\\frac{21}{100}+\\frac{2}{10}=\\frac{21}{100}+\\frac{ }{100}\\)
      \nAnswer :
      \nGiven,
      \n\\(\\frac{21}{100}+\\frac{2}{10}=\\frac{21}{100}+\\frac{ }{100}\\)
      \nWe have to find the missing number.
      \n\\(\\frac{21}{100}+\\frac{2}{10}\\)
      \nLCM of 10 and 100 is 100.
      \n= \\(\\frac{21}{100}+\\frac{20}{100}\\) = \\(\\frac{41}{100}\\)
      \nSo, the missing fraction is \\(\\frac{20}{100}\\)
      \n\\(\\frac{21}{100}+\\frac{2}{10}=\\frac{21}{100}+\\frac{20}{100}\\)<\/p>\n

      Question 10.
      \n\\(\\frac{ }{10}+\\frac{68}{100}=\\frac{30}{100}+\\frac{68}{100}\\)
      \nAnswer:
      \nGiven,
      \n\\(\\frac{ }{10}+\\frac{68}{100}=\\frac{30}{100}+\\frac{68}{100}\\)
      \nWe have to find the missing number.
      \nLCM of 10 and 100 is 100.
      \n\\(\\frac{30}{100}\\) = \\(\\frac{3}{10}\\)
      \nSo, the missing fraction is \\(\\frac{3}{10}\\)
      \n\\(\\frac{3}{10}+\\frac{68}{100}=\\frac{30}{100}+\\frac{68}{100}\\)<\/p>\n

      Question 11.
      \n\\(\\frac{4}{10}+\\frac{60}{100}=\\frac{ }{10}+\\frac{ }{10}\\)
      \nAnswer:
      \nGiven,
      \n\\(\\frac{4}{10}+\\frac{60}{100}=\\frac{ }{10}+\\frac{ }{10}\\)
      \nWe have to find the missing number.
      \nLCM of 10 and 100 is 100.
      \n\\(\\frac{60}{100}\\) = \\(\\frac{6}{10}\\)
      \n\\(\\frac{4}{10}\\) = \\(\\frac{4}{10}\\)
      \nSo, the missing fraction is \\(\\frac{6}{10}\\) and \\(\\frac{4}{10}\\)
      \n\\(\\frac{4}{10}+\\frac{60}{100}=\\frac{4}{10}+\\frac{6}{10}\\)<\/p>\n

      Question 12.
      \n\\(\\frac{32}{100}+\\frac{28}{100}+\\frac{6}{10}\\)
      \nAnswer:
      \nThe fractions have, unlike denominators. First, find the Least Common Denominator and rewrite the fractions with the common denominator.
      \nL.C.M of 10 and 100 is 100.
      \nMultiply both the numerator and denominator of each fraction by the number that makes its denominator equal to the LCD. This is basically multiplying each fraction by 1.
      \n(\\(\\frac{60}{100}\\) \u00d7 \\(\\frac{1}{1}\\)) + (\\(\\frac{6}{10}\\) \u00d7 \\(\\frac{10}{10}\\))
      \n\\(\\frac{60}{100}\\) + \\(\\frac{60}{100}\\) = \\(\\frac{120}{100}\\)<\/p>\n

      Question 13.
      \n\\(\\frac{11}{10}+\\frac{41}{100}\\)
      \nAnswer:
      \nThe fractions have, unlike denominators. First, find the Least Common Denominator and rewrite the fractions with the common denominator.
      \nL.C.M of 10 and 100 is 100.
      \nMultiply both the numerator and denominator of each fraction by the number that makes its denominator equal to the LCD. This is basically multiplying each fraction by 1.
      \n(\\(\\frac{11}{10}\\) \u00d7 \\(\\frac{10}{10}\\)) + (\\(\\frac{41}{100}\\) \u00d7 \\(\\frac{1}{1}\\))
      \n\\(\\frac{110}{100}\\) + \\(\\frac{41}{100}\\) = \\(\\frac{151}{100}\\)<\/p>\n

      Question 14.
      \n\\(\\frac{72}{100}+\\frac{6}{10}\\)
      \nAnswer:
      \nThe fractions have, unlike denominators. First, find the Least Common Denominator and rewrite the fractions with the common denominator.
      \nL.C.M of 10 and 100 is 100.
      \nMultiply both the numerator and denominator of each fraction by the number that makes its denominator equal to the LCD. This is basically multiplying each fraction by 1.
      \n(\\(\\frac{72}{100}\\) \u00d7 \\(\\frac{1}{1}\\)) + (\\(\\frac{6}{10}\\) \u00d7 \\(\\frac{100}{100}\\))
      \n\\(\\frac{72}{100}\\) + \\(\\frac{600}{100}\\) = \\(\\frac{672}{100}\\)<\/p>\n

      Question 15.
      \n\\(\\frac{5}{10}+\\frac{3}{10}+\\frac{18}{100}\\)
      \nAnswer:
      \nThe fractions have, unlike denominators. First, find the Least Common Denominator and rewrite the fractions with the common denominator.
      \nL.C.M of 10 and 100 is 100.
      \nMultiply both the numerator and denominator of each fraction by the number that makes its denominator equal to the LCD. This is basically multiplying each fraction by 1.
      \n(\\(\\frac{8}{10}\\) \u00d7 \\(\\frac{10}{10}\\)) + (\\(\\frac{18}{100}\\) \u00d7 \\(\\frac{1}{1}\\))
      \n\\(\\frac{80}{100}\\) + \\(\\frac{18}{100}\\) = \\(\\frac{98}{100}\\)<\/p>\n

      Question 16.
      \n\\(\\frac{7}{100}+\\frac{6}{10}\\)
      \nAnswer:
      \nThe fractions have, unlike denominators. First, find the Least Common Denominator and rewrite the fractions with the common denominator.
      \nL.C.M of 10 and 100 is 100.
      \nMultiply both the numerator and denominator of each fraction by the number that makes its denominator equal to the LCD. This is basically multiplying each fraction by 1.
      \n(\\(\\frac{7}{100}\\) \u00d7 \\(\\frac{1}{1}\\)) + (\\(\\frac{6}{10}\\) \u00d7 \\(\\frac{10}{10}\\))
      \n\\(\\frac{7}{100}\\) + \\(\\frac{60}{100}\\) = \\(\\frac{67}{100}\\)<\/p>\n

      Question 17.
      \n\\(\\frac{9}{10}+\\frac{4}{100}\\)
      \nAnswer:
      \nThe fractions have, unlike denominators. First, find the Least Common Denominator and rewrite the fractions with the common denominator.
      \nL.C.M of 10 and 100 is 100.
      \nMultiply both the numerator and denominator of each fraction by the number that makes its denominator equal to the LCD. This is basically multiplying each fraction by 1.
      \n(\\(\\frac{9}{10}\\) \u00d7 \\(\\frac{10}{10}\\)) + (\\(\\frac{4}{100}\\) \u00d7 \\(\\frac{10}{10}\\))
      \n\\(\\frac{90}{100}\\) + \\(\\frac{40}{100}\\) = \\(\\frac{130}{100}\\)<\/p>\n

      Question 18.
      \n\\(\\frac{30}{100}+\\frac{5}{10}\\)
      \nAnswer:
      \nThe fractions have, unlike denominators. First, find the Least Common Denominator and rewrite the fractions with the common denominator.
      \nL.C.M of 10 and 100 is 100.
      \nMultiply both the numerator and denominator of each fraction by the number that makes its denominator equal to the LCD. This is basically multiplying each fraction by 1.
      \n(\\(\\frac{30}{100}\\) \u00d7 \\(\\frac{1}{1}\\)) + (\\(\\frac{5}{10}\\) \u00d7 \\(\\frac{10}{10}\\))
      \n\\(\\frac{30}{100}\\) + \\(\\frac{50}{100}\\) = \\(\\frac{80}{100}\\)<\/p>\n

      Question 19.
      \n\\(\\frac{39}{100}+\\frac{2}{10}\\)
      \nAnswer:
      \nThe fractions have, unlike denominators. First, find the Least Common Denominator and rewrite the fractions with the common denominator.
      \nL.C.M of 10 and 100 is 100.
      \nMultiply both the numerator and denominator of each fraction by the number that makes its denominator equal to the LCD. This is basically multiplying each fraction by 1.
      \n(\\(\\frac{39}{100}\\) \u00d7 \\(\\frac{1}{1}\\)) + (\\(\\frac{2}{10}\\) \u00d7 \\(\\frac{10}{10}\\))
      \n\\(\\frac{39}{100}\\) + \\(\\frac{20}{100}\\) = \\(\\frac{59}{100}\\)<\/p>\n

      Question 20.
      \n\\(\\frac{8}{10}+\\frac{9}{100}\\)
      \nAnswer:
      \nThe fractions have, unlike denominators. First, find the Least Common Denominator and rewrite the fractions with the common denominator.
      \nL.C.M of 10 and 100 is 100.
      \nMultiply both the numerator and denominator of each fraction by the number that makes its denominator equal to the LCD. This is basically multiplying each fraction by 1.
      \n(\\(\\frac{8}{10}\\) \u00d7 \\(\\frac{10}{10}\\)) + (\\(\\frac{9}{100}\\) \u00d7 \\(\\frac{1}{1}\\))
      \n\\(\\frac{80}{100}\\) + \\(\\frac{9}{100}\\) = \\(\\frac{89}{100}\\)<\/p>\n

      Question 21.
      \n\\(\\frac{44}{100}+\\frac{34}{100}+\\frac{9}{10}\\)
      \nAnswer:
      \nThe fractions have, unlike denominators. First, find the Least Common Denominator and rewrite the fractions with the common denominator.
      \nL.C.M of 10 and 100 is 100.
      \nMultiply both the numerator and denominator of each fraction by the number that makes its denominator equal to the LCD. This is basically multiplying each fraction by 1.
      \n(\\(\\frac{78}{100}\\) \u00d7 \\(\\frac{1}{1}\\)) + (\\(\\frac{9}{10}\\) \u00d7 \\(\\frac{10}{10}\\))
      \n\\(\\frac{78}{100}\\) + \\(\\frac{90}{100}\\) = \\(\\frac{168}{100}\\)<\/p>\n

      Question 22.
      \n\\(\\frac{70}{10}+\\frac{33}{100}\\)
      \nAnswer:
      \nThe fractions have, unlike denominators. First, find the Least Common Denominator and rewrite the fractions with the common denominator.
      \nL.C.M of 10 and 100 is 100.
      \nMultiply both the numerator and denominator of each fraction by the number that makes its denominator equal to the LCD. This is basically multiplying each fraction by 1.
      \n(\\(\\frac{70}{10}\\) \u00d7 \\(\\frac{10}{10}\\)) + (\\(\\frac{33}{100}\\) \u00d7 \\(\\frac{1}{1}\\))
      \n\\(\\frac{700}{100}\\) + \\(\\frac{33}{100}\\) = \\(\\frac{733}{100}\\)<\/p>\n

      Question 23.
      \n\\(\\frac{28}{10}+\\frac{72}{10}+\\frac{84}{100}\\)
      \nAnswer:
      \nThe fractions have, unlike denominators. First, find the Least Common Denominator and rewrite the fractions with the common denominator.
      \nL.C.M of 10 and 100 is 100.
      \nMultiply both the numerator and denominator of each fraction by the number that makes its denominator equal to the LCD. This is basically multiplying each fraction by 1.
      \n(\\(\\frac{100}{10}\\) \u00d7 \\(\\frac{10}{10}\\)) + (\\(\\frac{84}{100}\\) \u00d7 \\(\\frac{1}{1}\\))
      \n\\(\\frac{1000}{100}\\) + \\(\\frac{84}{100}\\) = \\(\\frac{1084}{100}\\)<\/p>\n

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

      Question 24.
      \nAlgebra A mail carrier made a total of 100 deliveries in a day. \\(\\frac{76}{100}\\) of the deliveries were letters, \\(\\frac{2}{10}\\) were packages, and the rest were postcards. Write and solve an equation to find the fraction that represents how many of the deliveries were letters and packages.
      \nAnswer:
      \nGiven,
      \nA mail carrier made a total of 100 deliveries in a day.
      \n\\(\\frac{76}{100}\\) of the deliveries were letters, \\(\\frac{2}{10}\\) were packages, and the rest were postcards.
      \n\\(\\frac{76}{100}\\) + \\(\\frac{2}{10}\\)
      \n\\(\\frac{76}{100}\\) + \\(\\frac{20}{100}\\) = \\(\\frac{96}{100}\\)<\/p>\n

      Question 25.
      \nMake Sense and Persevere Balloons are sold in bags of 30. There are 5 giant balloons in each bag. How many giant balloons will you get if you buy 120 balloons? Explain.
      \n\"Envision
      \nAnswer:
      \nGiven that,
      \nTotal number of balloons solids in bags = 30
      \nBalloons in each bag = 5
      \nIf you buy 120 balloons how many bags do you have = 120\/5 = 24
      \nFor 120 balloons 24 bags are filled.<\/p>\n

      Question 26.
      \nHigher Order Thinking<\/strong> of the first 100 elements on the periodic table, \\(\\frac{13}{100}\\) were discovered in ancient times, and \\(\\frac{21}{100}\\) were discovered in the Middle Ages. Another \\(\\frac{5}{10}\\) were discovered in the 1800s. What fraction of the first 100 elements was discovered after the 1800s? Explain.
      \n\"Envision
      \nAnswer:
      \n\\(\\frac{13}{100}\\) were discovered in ancient times.\\(\\frac{21}{100}\\) were discovered in the Middle Ages.
      \n<\/span>Another \\(\\frac{5}{10}\\) discovered after 1800.
      \n<\/span>Find how many discovered after 1800 is
      \nThe fractions have, unlike denominators. First, find the Least Common Denominator and rewrite the fractions with the common denominator.
      \nL.C.M of 10 and 100 is 100.
      \nMultiply both the numerator and denominator of each fraction by the number that makes its denominator equal to the LCD. This is basically multiplying each fraction by 1.
      \n(\\(\\frac{34}{100}\\) \u00d7 \\(\\frac{1}{1}\\)) + (\\(\\frac{5}{10}\\) \u00d7 \\(\\frac{10}{10}\\))
      \n\\(\\frac{35}{100}\\) + \\(\\frac{50}{100}\\) = \\(\\frac{85}{100}\\)
      \n\\(\\frac{85}{100}\\) are discovered after 1800.<\/p>\n

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

      Question 27.
      \nDelia hiked \\(\\frac{7}{10}\\) mile one day and \\(\\frac{67}{10}\\) mile the next. She wanted to know how far she hiked in all. Her work is shown below.
      \n\"Envision
      \nIs Delia’s work correct? Explain.
      \nAnswer:
      \nDelia hiked \\(\\frac{7}{10}\\) mile one day
      \n\\(\\frac{67}{10}\\) mile the next.
      \nShe hiked in all is
      \nThe fractions have, unlike denominators. First, find the Least Common Denominator and rewrite the fractions with the common denominator.
      \nL.C.M of 10 and 100 is 100.
      \nMultiply both the numerator and denominator of each fraction by the number that makes its denominator equal to the LCD. This is basically multiplying each fraction by 1.
      \n(\\(\\frac{7}{10}\\) \u00d7 \\(\\frac{10}{10}\\)) + (\\(\\frac{67}{10}\\) \u00d7 \\(\\frac{10}{10}\\))
      \n\\(\\frac{70}{100}\\) + \\(\\frac{670}{100}\\) = \\(\\frac{737}{100}\\)
      \nDelia hiked in all =\\(\\frac{737}{100}\\)<\/p>\n

      Lesson 12.5 Solve Word Problems involving Money<\/h3>\n

      Solve & Share<\/strong>
      \nA flash drive costs $24, including tax. A customer purchases 3 flash drives and pays the cashier $80. How much change should the cashier give back to the customer? Solve this problem any way you choose.
      \nI can … use fractions or decimals to solve word problems involving money.
      \n\"Envision<\/p>\n

      Look Back! Generalize How can you estimate and check if your solution is reasonable?<\/p>\n

      Essential Question<\/strong>
      \nHow Can You Solve Word Problems Involving Money?<\/p>\n

      Visual Learning Bridge
      \nMarcus buys a toy airplane and a toy car. How much does Marcus spend? How much more does the toy airplane cost than the toy car?
      \n\"Envision
      \nYou can draw or use bills and coins to solve problems involving money.<\/p>\n

      Find $3.32 + $1.12.
      \n\"Envision
      \nAdd the bills, then count on to add each type of coin.
      \n$4.00 + $0.40 + $0.04 = $4.44
      \nMarcus spent $4.44.<\/p>\n

      Find $3.32 – $1.12.
      \nStart with the cost of the airplane, then subtract the cost of the car.
      \n\"Envision
      \nCount the remaining bills and coins.
      \n$2.00 + $0.20 = $2.20
      \nThe toy airplane costs $2.20 more than the toy car.<\/p>\n

      Convince Me! Use Structure in the examples above, how can you use place value to help add or subtract?<\/p>\n

      Another Example!<\/strong>
      \nFind $6.33 \u00f7 3. Draw or use bills and coins.
      \nYou can use multiplication or division to solve problems involving money.
      \n\"Envision<\/p>\n

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

      Do You Understand?<\/strong>
      \nQuestion 1.
      \nWrite a fraction and a decimal to describe how the quantities are related.
      \n\"Envision
      \nAnswer:
      \nOne coin = 1\/10 of a dollar = $0.10
      \nThree coins = 1\/10 + 1\/10 + 1\/10 = $0.3<\/p>\n

      Question 2.
      \nWrite a fraction and a decimal to describe how the quantities are related.
      \n\"Envision
      \nAnswer:
      \nOne coin = 1\/100 of a dollar = $0.01
      \nThree coins = 1\/100 + 1\/100 + 1\/100 = $0.01<\/p>\n

      Do You Know How?<\/strong><\/p>\n

      For 3, use the bills and coins to solve.
      \nQuestion 3.
      \nMarcus has $15.00. He buys a movie ticket for $11.25. How much money does Marcus have left?
      \n\"Envision
      \nAnswer:
      \nGiven that,
      \n<\/span>Marcus has a total amount = $15.00
      \nMarcus buy a movie ticket for $11.25
      \nMarcus left amount = $15.00 – $11.25 = 3.75<\/p>\n

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

      For 4-5, you may draw or use bills and coins to solve.
      \nQuestion 4.
      \nSarah bought 3 wool scarves. The price of each scarf was $23.21. How much did 3 scarves cost?
      \nAnswer:
      \nGiven that,
      \nSarah bought wool scarves = 3
      \nThe price for each scarf= $23.21
      \nTotal amount for 3 scarves = $23.21 \u00d7 3 = 69.63<\/p>\n

      Question 5.
      \nCarlos spends $14.38 on equipment. How much change should Carlos receive if he gives the clerk $20.00?
      \nAnswer:
      \nGiven that,
      \nCarlos spends on equipment = $14.38
      \nHe give the clerk = $20.00
      \nCarlos received tha change = $20.00 – $14.38 =$6.62<\/p>\n

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

      Question 6.
      \nUse Structure Leo went to lunch with his parents. The bill was $17.85. Complete the table to show two different combinations of coins and bills that can represent $17.85.
      \n\"Envision
      \nAnswer:<\/p>\n

      Question 7.
      \nKenya purchases a new tablet for $109.78. She pays with six $20 bills. Show how you would estimate how much change Kenya should receive.
      \nAnswer:
      \nGiven that,
      \nKenya purchases a new tablet for $109.78
      \nShe pay with six $20 bills = 6 \u00d7 20 = 120
      \nKenya received change = $120 – $109.78 =$11.78<\/p>\n

      Question 8.
      \nAlgebra Marco paid $12 for 3 jump ropes. If each jump rope costs the same amount, how much does 1 jump rope cost? Write and solve an equation.
      \nAnswer:
      \nGiven that,
      \nAlgebra Marco paid $12 for 3 jump ropes.
      \nFor each jump = 12\/3 = $4
      \nFor each jump cost = $4<\/p>\n

      Question 9.
      \nNumber Sense<\/strong> Jiang has a collection of 3,788 toy building bricks. He used 1,229 bricks to build a city. About how many bricks does Jiang have left? Explain how you estimated.
      \nAnswer:
      \nGiven that,
      \nJiang has a collection of toy building bricks = 3788
      \nJiang used bricks to build a city = 1229
      \nJiang has left = 3788 – 1229 = 2559<\/p>\n

      Question 10.
      \nHigher Order Thinking<\/strong> Edward bought 7 concert tickets for himself and six friends for a total of $168. Each friend paid Edward back for his or her ticket. If one of Edward’s friends gave him a $50 bill, how much change should Edward return? Explain.
      \nAnswer:
      \nEdward bought a concert tickets for himself and six friends for total = $168
      \nMoney for each ticket = 168\/7 = $<\/p>\n

      \n
      \n