Category: Envision Math

Envision Math 5th Grade Textbook Answer Key Topic 18 Test Prep

Test Prep

Question 1.
The map shows the approximate placement of some of the Smithsonian museums located on the National Mall. Which museum is located at (0, ^-1)? (18-1)

A = American History Museum
B = Freer
C = Smithsonian Castle
D = Natural History Museum
E = Hirshhorn Museum
F = Air and Space Museum

A. Hirshhorn Museum
B. Freer
C. Smithsonian Castle
D. Air and Space Museum
Answer:

Question 2.
Complete the table of ordered pairs for y = x – 5. (18-3)

A. -9
B. -2
C. -1
D. +9
Answer:

Question 3.
The graph shows the Fahrenheit temperature in Old Town taken every hour after 8:00 A.M. What was the temperature at noon? (18-2)

A. 58°F
B. 54°F
C. 47°F
D. 45°F
Answer:

Question 4.
Which ordered pair is a point on the line y = x + 3? (18-3)
A (⁺1, ⁺3)
B (⁺2, ⁺4)
C (⁺1, ⁺2)
D (^–1, ⁺2)
Answer:

Question 5.
On a map, Todd’s school has coordinates (⁺6, ⁺7). From a starting point, Todd walks east (right) 3 blocks, north (up) 5 blocks and ends up at school. What are the coordinates for where Todd started? (18-4)
A. (⁺9, ⁺2)
B. (⁺3, ⁺12)
C. (⁺11, ⁺4)
D. (⁺3, ⁺2)
Answer:

Question 6.
Which ordered pair is located on the line for the equation x = 2? (18-3)

A. (⁺2, ⁺3)
B. (^–2, ⁺2)
C. (⁺1, ⁺2)
D. (⁺3, ⁺2)
Answer:

Question 7.
Martina drew the graph shown. Which equation did she graph? (18-3)

A. y = x + 2
B. y = x + 1
C. y = x – 2
D. y = x – 1
Answer:

Question 8.
The graph shows the average miles per gallon for vehicles in the United States. Based on the trend, what would be a reasonable estimate of the average miles per gallon for U.S. vehicles in 2010? (18-2)

A. 11
B. 13
C. 18
D. 25
Answer:

Question 9.
What is the ordered pair for Point Xon the graph? (18-1)

A. (⁺2, ^–4)
B. (^–4, ⁺2)
C. (⁺4, ^–2)
D. (^–2, ⁺4)
Answer:

Envision Math 6th Grade Textbook Answer Key Topic 2 Reteaching

Reteaching

Set A, pages 28-29

Variables stand for unknown values.
The number sentence 24 + n means “the sum of 24 and a number.” The unknown number is a variable that is expressed by a letter, n.
Answer Terms
Addition → Sum
Subtraction → Difference
Multiplication → Product
Division → Quotient

Remember that you can use any letter as a variable that stands for an unknown value.

Write the phrases as algebraic expressions.
Question 1.
22 less forks than a number, f
Answer:

Question 2.
48 times a number of game markers, g
Answer:

Question 3.
a number of eggs, e, divided by 12
Answer:

Question 4.
3 times the number of milk cartons, m, used by the 6th grade class
Answer:

Set B, pages 30-31

The properties of operations help you evaluate expressions.

Evaluate the expression: 4 + 8 + 3 + 2
Following properties of operations:
4 + 8 + 3 + 2 = 4 + 3 + 8 + 2 = 7 + 10 = 17

Remember that when the properties of operations are not followed, numerical expressions are computed incorrectly.

Tell what properties are shown
Question 1.
3(4 × 32) = (3 × 4)32
Answer:

Question 2.
21 × 10 = 10 × 21
Answer:

Question 3.
9 + 8 + 4 = 8 + 4 + 9
Answer:

Question 4.
9 + 0 = 9
Answer:

Question 5.
6 × 8 = 8 × 6
Answer:

Question 6.
5 + 4 = 4 + 5
Answer:

Question 7.
6 × (4 × 3) = (6 × 4) × 3
Answer:

Question 8.
8 + (2 + 4) = (8 + 2) + 4
Answer:

Question 9.
9 + 6 = 6 + 9
Answer:

Question 10.
12 + 0 = 12
Answer:

Question 11.
425 × 1 = 425
Answer:

Question 12.
(8 × 5) × 4 = 4 × (5 × 8)
Answer:

Set C, pages 32–34

The order of operations helps you get the correct answer. The order of operations rules are:
Step 1: Compute inside parentheses.
Step 2: Evaluate terms with exponents.
Step 3: Multiply and divide from left to right.
Step 4: Add and subtract from left to right.

Evaluate 8 + 6 × 9 – 4 ÷ 2.
First, multiply and divide. 8 + 54 – 2
Then, add and subtract. 60

Remember that when the order of operations rules are followed, it helps you get the correct answer.

Use parentheses to make each sentence true.
Question 1.
9 + 8 – 2 × 7 + 1 = 1
Answer:

Question 2.
40 – 4 × 4² ÷ 2 = 8
Answer:

Question 3.
5 × 5 – 3 – 2 = 0
Answer:

Question 4.
8 + 12 ÷ 4 + 6 = 11
Answer:

Question 5.
9 + 8 ÷ 2 × 4 + 3² = 19
Answer:

Question 6.
6 × 2 – 1 + 5² = 31
Answer:

Question 7.
8 × 3 + 8 – 2² = 84
Answer:

Question 8.
50 – 3 × 6 + 2 + 4² = 42
Answer:

Set D, pages 36-37

Use the Distributive Property to evaluate mentally.
8(42)
Break the numbers apart to find numbers that
are easier to multiply mentally.
8(40 + 2)
Apply the Distributive Property.
8(40) + 8(2)
Multiply the separate sections. Add the products.
320 + 16 = 336

Remember that the Distributive Property says that multiplying a sum by a number is the same as multiplying each addend by the number and adding the products.

Use the Distributive Property to evaluate mentally.
Question 1.
5(41) + 5(9)
Answer:

Question 2.
3(45)
Answer:

Question 3.
4(23)
Answer:

Question 4.
9(32) + 9(8)
Answer:

Question 5.
3(27)
Answer:

Question 6.
6(7) + 6(23)
Answer:

Set E, pages 38-40

Find 4 × 18 × 25 using compatible numbers to compute mentally.
Look for compatible 4 × 18 × 25
numbers that are easy
to compute. 4 × 25 × 18
Then, do the remaining calculation. 100 × 18 = 1,800
So, 4 × 18 × 25 = 1,800.

Remember to find compatible numbers to make your mental math easier.

Compute mentally.
Question 1.
15 + 67 + 25
Answer:
107
Explanation:

Question 2.
463 – 333
Answer:
130
Explanation:

Question 3.
6 × 23 × 5
Answer:
690
Explanation:

Question 4.
250 × 6 × 4
Answer:
6,000
Explanation:

Question 5.
921 + 529
Answer:
1,450
Explanation:

Question 6.
297 – 100
Answer:
197
Explanation:

Question 7.
2 × 8 × 5
Answer:
80
Explanation:

Question 8.
20 × 16 × 5
Answer:
1,600
Explanation:

Set F, pages 42-43

Evaluate this expression for x = 2 and y = 3.
Question 1.
7x – 3y
Answer:
7(2) – 3(3) ← Use substitution.
14 – 9 = 5 ← Compute.

Question 2.
4x + 2y
Answer:
4(2) + 2(3) ← Use substitution.
8 + 6 = 14 ← Compute.

Question 3.
9x ÷ 3y
Answer:
9(2) ÷ 3(3) ← Use substitution.
18 ÷ 9 = 2 ← Compute.

Remember that using substitution means to replace the variables with the chosen values.

Evaluate each expression for x = 4 and y = 6.
Question 1.
12x – 7y
Answer:
6
Explanation:

Question 2.
3x + 18
Answer:
30
Explanation:

Question 3.
11 x + 4
Answer:
48
Explanation:

Question 4.
8x + 2y
Answer:
44
Explanation:

Question 5.
6x ÷ 2y
Answer:
2
Explanation:

Question 6.
8x – 5y
Answer:
2
Explanation:

Question 7.
7x – 4y
Answer:
4
Explanation:

Question 8.
4y – 9
Answer:
15
Explanation:

Question 9.
22y – 6
Answer:
126
Explanation:

Question 10.
9x – 3y
Answer:
18
Explanation:

Question 11.
4x ÷ (y – 2)
Answer:
4
Explanation:

Question 12.
10y – 8x
Answer:
28
Explanation:

Set G, pages 44–45

You can write an algebraic expression that explains an input/output relationship. If x is 4, how can you express 9?

Try: 2x + 1 = 9
See if that works for the other input values.
2 × 8 + 1 = 17
2 × 11 + 1 = 23
Yes, it works!

Remember that input/ output tables can help you see patterns in expressions.

Use this input/ output table for 1 and 2.

Question 1.
Students earn prize points for selling fundraising items. Write an algebraic expression that explains the relationship between input and output values for a student who sells between $41 and $60.
Answer:
3x
Explanation:

Question 2.
How many prize points would a student earn for selling $115 worth of items?
Answer:
4 × 115 = 460
Explanation:

Set H, pages 46-48

Making a table to organize your data helps to identify patterns and quickly find solutions. When making a table, include labels for the variable and the expression. Enter the values of x you want to find. Then solve the expression for each value.
Ginny is paid $12 a week for doing chores. She puts the money in her savings account. If she started out with $112, find out how much money she has in her account after x weeks.
Step 1: Identify the expression.
$112 + $12x
Step 2: Make a table.

Remember to choose labels based on the information to be found.

Write an equation for each problem. Then make a table to solve it.
Question 1.
Anna walks her dog 2 miles a day, 5 days a week. Find out how far Anna and her dog walked after x weeks.
Answer:
(2 × 5)x
Explanation:

Question 2.
Todd earns $500 a week, plus $50 every time he sells a computer. Find out how much money Todd earns per week when he sells x computers.
Answer:
500 + 50x
Explanation:

Envision Math 6th Grade Textbook Answer Key Topic 2.8 Problem Solving

Problem Solving

Make a Table
The Douglas family had $700 in their road-trip fund. They spent $75 each day on their trip. If x equals the number of days, write an expression that describes the amount of money left in the fund after x days.

Question.
Make a table to show the values of the expression for x = 3 days, x = 5 days, and x = 9 days.
Answer:

Guided Practice

Do you know HOW?
Question 1.
The sixth-grade chess club is washing cars for a fund-raiser. They started with $150 in their fund and are charging $5 per car. Use the expression 150 + 5x to copy and complete the table, to find how much money the chess club will have after washing 25, 31, and 54 cars.

Answer:

Do you UNDERSTAND?
Question 2.
How do you know what labels to use in a table?
Answer:

Question 3.
Write a Problem Use the table to write a word problem that could be solved using the table below.

Answer:

Independent Practice

Question 4.
For every A Josh earns on his report card, he is given 2 movie passes. He still has 2 movie passes left from his last report card. If x equals the number of A’s Josh earns, use the expression 2x + 2 to copy and complete the table to find how many movie passes Josh will have for 1,2, or 3 A’s.

Answer:

Plan and Solve
Write an expression that describes the amount of money left in the fund after x days.

Total in fund – $75(number of days)
700 – 75x

Plan and Solve
Make a table to solve for different values of x. Include labels for the variable and the expression.
Enter the values of x you want to find. Then solve the expression for each value.

Question 5.
Kat is playing a game called “500.” Each player starts with 500 points and loses 10 points for each question answered correctly. The first player to reach 0 points wins. Which expression represents how many points Kat will have if she answers x questions correctly?
A. 500x
B. 500 – 10x
C. 500 + 10x
D. 10x – 500
Answer:
B. 500 – 10x
Explanation:

Question 6.
Copy and complete the table for Exercise 5 to find how many points Kat will have if she answers 9, 13, and 24 questions correctly.
Answer:

Explanation:

Question 7.
Jordan is playing in a charity basketball game. The local barber pledged to pay $2 for every point he scores. The local grocery store will give a one-time donation of $75. Which expression represents how much money Jordan will raise if he scores x points?
A. 75 + 2x
B. 77x
C. 75 + 4x
D. 75 – 2x
Answer:
A. 75 + 2x
Explanation:

Question 8.
Jeremy started a club to help senior citizens use computers. On the first day, he was the only member. On the second day, two friends joined. Each day after that, two more members joined. If x equals the number of days, evaluate the expression 1 + 2(x – 1) to find the membership of the club on the 10th day.
Answer:
19 people
Explanation:

Question 9.
The camp chef is making waffles for breakfast. The recipe calls for 3 cups of milk for every batch. If x equals the number of batches, copy and complete the table to show how much milk the chef needs for 3, 7, and 10 batches.
Answer:

Explanation:

Independent Practice

Use the information at right for 10 through 14.

Question 10.
Carver bought some plants at the Garden Center sale. On his bill, he saw that he had paid $20 for 5 plants. What size did Carver buy?
Answer:
He bought 5 large plants.
Explanation:

Question 11.
Sally and her mother went to the sale at the Garden Center. Sally bought x large plants and y small plants. She paid with a twenty-dollar bill. Make a table using the expression 20 – (4x + 2y) to show how much change she received if she bought 2 large plants and 4 small plants; 4 large plants and 2 small plants; or 1 large plant and 7 small plants.
Answer:
See margin.
Explanation:

Tips: Make a separate column for each variable.
Question 12.
Elyse has a small flower garden in her backyard. She wants to plant seven rows of flowers. She drew a plan of her garden.

a. If each row can hold 3 large plants, 4 medium plants, or 8 small plants, how many of each should Elyse buy?
Answer:
See margin.
Explanation:

b. What will the total cost be for all of Elyse’s plants?
Answer:
$100
Explanation:

Question 13.
Maggie wants to plant a 10 ft row of large plants. A large plant needs 1.5 ft between plants. Maggie will put her first plant 0.5 ft in from the end. How much money will Maggie need to fill the row? Explain how you found your answer.
Answer:
$28; sample answer; I drew a picture to show 7 plants.
Explanation:

Question 14.
Art has $32. How many large plants could he buy? Medium plants? Small plants?
Answer:
8 large; 10 medium; 16 small
Explanation:

Think About the Process
Question 15.
William and Anne are selling magazines. For each magazine sold, their soccer team raises $2.25. Which value completes this table?

A. 19.25
B. 382.5
C. 3825
D. 38.25
Answer:
D. 38.25

Question 16.
Tanya has a job delivering newspapers. Every week, her customers pay her $1.50. She also receives an allowance of $5 a week. If Tanya has x newspaper clients, which expression best describes how much money Tanya receives each week?
A. 5x – 1.5
B. 5x + 1.5
C. 5 + 1.5x
D. 5 – 1.5x
Answer:

Stop and Practice

Skills Review Write each phrase as an algebraic expression.
Question 1.
7 less than a number x
Answer:

Question 2.
5 times a number p
Answer:

Question 3.
4 times a number m, minus 3 times a number k
Answer:

Question 4.
8 plus two times a number j
Answer:

Use the properties of operations to fill in the blanks in each expression.
Question 5.
28 × 5 = 5 × ☐
Answer:

Question 6.
12 × 25 × 32 = 12 × ☐ × 25 × 32
Answer:

Question 7.
7 + (30 + 15) = (7 + 30) + ☐
Answer:

Question 8.
23 + 8 = 23 + 8 + ☐
Answer:

Evaluate each expression for x = 3 and y = 5.
Question 9.
5x + 8
Answer:

Question 10.
(10 – y) (10)
Answer:

Question 11.
10y + 23
Answer:

Question 12.
Write an algebraic expression for the value of y that explains the relationship between x and y. Then finish the table.

Answer:

Error Search Find each answer that is not correct. Write it correctly and explain the error.
Question 13.
8 + 2 × 6 = 60
Answer:

Question 14.
8 × 0 + (4 × 1) = 4
Answer:

Question 15.
4(24) = 4(6) + 4(4)
Answer:

Question 16.
32 + 73 = (30 + 70) + (2 + 3)
Answer:

Question 17.
58(40) = 50(40) × 8(40)
Answer:

Question 18.
4(51 + 32) = 4(80) + 4(3)
Answer:

Number Sense

Insert parentheses to make each sentence true.
Question 19.
3 × 8 + 3 × 2 = 66
Answer:

Question 20.
2 × 5 + 4 – 8 = 10
Answer:

Question 21.
15 – 2 × 3 + 5² = 64
Answer:

Question 22.
4x – 5 = 4x – 20
Answer:

Question 23.
6 + 8 – 3 × 7 = 41
Answer:

Question 24.
4 + 4 × 3 + 5 = 29
Answer:

Question 25.
3² – 8 × 0 = 9
Answer:

Question 26.
80 ÷ 2 × 2 + 2 × 3 = 26
Answer:

Question 27.
25 – 10 + 3 ÷ 2 + 4 = 3
Answer:

Envision Math 6th Grade Textbook Answer Key Topic 2.4 The Distributive Property

The Distributive Property

How can you use the Distributive Property to evaluate expressions?
Answer:
The Distributive Property states that multiplying a sum (or difference) by a number gives the same result as multiplying each number in the sum
(or difference) by the number and adding (or subtracting) the products.

Guided Practice

Do you know HOW?
In 1 through 4, find each missing number.
Question 1.
8(7 + 23) = 8(7) + 8(☐)
Answer:
23
Explanation:

Question 2.
4(28) = 4(20) + 4 (☐)
Answer:
8
Explanation:

Question 3.
8(57) – 8(7) = 8(☐)
Answer:
50
Explanation:

Question 4.
5(26 – 3) = 5 (☐) – 5(3)
Answer:
26
Explanation:

Use mental math to evaluate 5 and 6.
Question 5.
6(32) = ☐
Answer:
192
Explanation:

Question 6.
20(5) – 20(2) = ☐
Answer:
60
Explanation:

Do you UNDERSTAND?
Question 7.
Why is it easier to evaluate 7 × 60 than to evaluate 7 × 55 + 7 × 5?
Answer:
See margin.
Explanation:

Question 8.
Tony read 22 pages in the morning and 28 pages in the afternoon for 5 days. Lois read 47 pages each day for 5 days. Explain howto use the Distributive Property to find how many pages each of them read.
Answer:
See margin.
Explanation:

Independent Practice

Leveled Practice In 9 through 16, find each missing number.
Question 9.
3(28) + (3)2 = ☐ (30)
Answer:
3
Explanation:

Question 10.
9(23) = 9(☐) + 9(3)
Answer:
20
Explanation:

Question 11.
6(46) – 6(6) = 6(☐)
Answer:
40
Explanation:

Question 12.
4(33) = 4(30) + 4(☐)
Answer:
3
Explanation:

Question 13.
30(22 – 10) = 30(22) – 30(☐)
Answer:
10
Explanation:

Question 14.
8(99) = 8(100) – 8(☐)
Answer:
1
Explanation:

Question 15.
20(33 – 5) = 20(☐)
Answer:
28
Explanation:

= 20(☐) + 20(8)
Answer:
20
Explanation:

Question 16.
5(42) + 5(5) = 5(☐)
Answer:
47
Explanation:

= 5(☐) + 5(7)
Answer:
40
Explanation:

Use the Distributive Property to break apart a number to find the product for 5 × 27.
5 × 27 ← Break 27 apart.

5(20) +5 (7) ← Multiply each addend.
100 + 35 ← Add.
135
5 × 27 = 135

Use the Distributive Property to join numbers together to find 8(32) – 8(2).
8(32) – 8(2)
8(32 — 2) ← Join factors.
8(30) ← Subtract.
240 ← Multiply.
8(32) – 8(2) = 240

Independent Practice

Use the Distributive Property and mental math to evaluate.
Tips: When doing mental math, choose to join or break apart based on which is easier.
Question 17.
7(29)
Answer:
203
Explanation:

Question 18.
6(21) + 6(31)
Answer:
312
Explanation:

Question 19.
5(22) + 5(8)
Answer:
150
Explanation:

Question 20.
8(47)
Answer:
376
Explanation:

Question 21.
6(41) + 6(9)
Answer:
300
Explanation:

Question 22.
30(3) + 30(5)
Answer:
240
Explanation:

Question 23.
3(21) – 3(11)
Answer:
30
Explanation:

Question 24.
5(25 – 3)
Answer:
110
Explanation:

Problem Solving

Question 25.
Writing to Explain The 6th graders ordered lunch from the Big Group Menu.They ordered 22 organic chilis and 8 veggie plates.Their order can be expressed as 6(22) + 6(8). Explain what mental math steps you would use to find the total cost of the order.

Answer:
See margin.

Question 26.
Using the Big Group Menu, write and solve a problem where you can use the Distributive Property.
Answer:
See margin.

Question 27.
Writing to Explain Jamal said that 9.45 is greater than 9.8 because 45 is greater than 8. Is he correct? Explain.
Answer:
No; sample answer: 0.8 = 0.80 and 80 > 45.
Explanation:

Question 28.
Hiroko put money in a savings account each week. After 9 weeks, there was $49.50 in the account. If Hiroko put the same amount in each week, how much did she save each week?

Answer:
$5.50
Explanation:

Question 29.
Think About the Process Which choice shows a problem with common factors that could be used for mental math?
A. 3(45) + 3(5)
B. 4(18) – 7(8)
C. 2(22) + 3(33)
D. 8(39) + 4(40)
Answer:
A. 3(45) + 3(5)

Envision Math 6th Grade Textbook Answer Key Topic 1 Test Prep

Test Prep

Question 1.
The table gives the number of members in some Native American tribes. Which lists the tribes from the least to the greatest membership? (1-2)

A. Ute, Ottawa, Yakama, Crow
B. Ottawa, Ute, Yakama, Crow
C. Yakama, Ottawa, Ute, Crow
D. Ute, Crow, Ottawa, Yakama
Answer:
A. Ute, Ottawa, Yakama, Crow
Explanation:

Question 2.
What is the value of the 7 in the number 3.0871? (1-4)
A. seven ten-thousandths
B. seven thousandths
C. seven hundredths
D. seven thousands
Answer:
B. seven thousandths
Explanation:

Question 3.
In the fall of 2004, the University of California had an undergraduate enrollment of 158,431 students. Which of the following is this number written in expanded form? (1-3)
A. (1 × 10⁶) + (5 × 10⁵) + (8 × 10⁴) + (4 × 10³) + (3 × 10²) + (1 × 10¹)
B. (1× 10⁴) + (5 × 10³) + (8 × 10²) + (4 × 10¹) + (3 × 10⁰) + 1
C. (1 × 10⁵) + (5 × 10⁴) + (8 × 10³) + (4 × 10²) + (3 × 10¹) + (1 × 10⁰)
D. (1 × 10⁶) + (5 × 10⁵) + (8 × 10³) + (4 × 10²) + (31 × 10¹)
Answer:
C. (1 × 10⁵) + (5 × 10⁴) + (8 × 10³) + (4 × 10²) + (3 × 10¹) + (1 × 10⁰)
Explanation:

Question 4.
What is the value of the 6 in 196,937,500? (1-1)
A. 6 billion
B. 6 million
C. 6 hundred million
D. 6 hundred thousand
Answer:
B. 6 million
Explanation:

Question 5.
Which of the following is equal to 5⁴? (1-3)
A. 4 × 4 × 4 × 4 × 4
B. 5 × 4
C. (4 × 5)4
D. 5 × 5 × 5 × 5
Answer:
D. 5 × 5 × 5 × 5
Explanation:

Question 6.
Which of the following is between 0.007 and 0.016? (1-5)
A. 0.0008
B. 0.070
C. 0.0015
D. 0.010
Answer:
D. 0.010
Explanation:

Question 7.
Which of the following is a way to write four and eight hundred two ten-thousandths? (1-4)
A. 4.802
B. 4.082
C. 4.0802
D. 4.0082
Answer:
C. 4.0802
Explanation:

Question 8.
Which of the following lists the decimals in order from greatest to least? (1-5)
A. 2.1027, 2.1127, 2.0127
B. 2.1027, 2.0127, 2.1127
C. 2.1127, 2.0127, 2.1027
D. 2.1127, 2.1027, 2.0127
Answer:
D. 2.1127, 2.1027, 2.0127
Explanation:

Question 9.
The record for the fastest car belongs to a British jet car which traveled at 763.035 miles per hour. What is this number written in expanded form? (1-4)
A. 700 + 60 + 3 + 0.03 + 0.05
B. 700 + 60 + 3 + 0.3 + 0.5
C. 700 + 60 + 3 + 0.3 + 0.05
D. 700 + 60 + 3 + 0.03 + 0.005
Answer:
D. 700 + 60 + 3 + 0.03 + 0.005

Question 10.
The maximum climbing speed of a three-toed sloth is 0.15 miles per hour. Which speed is less than 0.15 mph? (1-5)

A. 0.146 mph
B. 0.162 mph
C. 0.157 mph
D. 0.153 mph
Answer:
A. 0.146 mph
Explanation:

Question 11.
Which country listed in the table has a population greater than 188,078,227? (1-2)
Population

A. Bangladesh
B. Indonesia
C. Pakistan
D. Russia
Answer:
B. Indonesia
Explanation:

Question 12.
Pluto’s mean distance from the sun is about 5 billion 900 million kilometers. What is this number written in expanded form? (1-1)
A. 5,000,000,000 + 900,000,000
B. 5,000,000 + 900,000
C. 500,000,000 + 90,000,000
D. 5,000,000,000,000 + 900,000,000
Answer:
A. 5,000,000,000 + 900,000,000
Explanation:

Question 13.
Which is 10,000,000 written in exponential form? (1-3)
A. 7¹⁰
B. 10⁷
C. 10⁸
D. 8¹⁰
Answer:
B. 10⁷
Explanation:

Question 14.
In a recent year, the United States had about two trillion, two hundred two billion, six hundred million dollars in outstanding consumer credit. What is this number in standard form? (1-1)
A. $2,202,600,000
B. $2,000,202,600,000
C. $2,202,600,000,000
D. $200,202,600,000,000
Answer:
C. $2,202,600,000,000
Explanation:

Question 15.
Make an organized list to determine all the possible combinations of pennies, nickels, dimes and quarters that total 25 cents. How many combinations are possible? (1-6)
A. 13
B. 11
C. 9
D. 4
Answer:
A. 13

Envision Math 6th Grade Textbook Answer Key Topic 1.3 Exponents and Place Value

Exponents and Place Value

How can you write a number
using exponents?
Answer:
Each place in a place-value chart has a value that is 10 times as great as the place to its right. Use this pattern to write 1,000,000 as repeated multiplication.

Another Example
How do you write the expanded form of a number using exponents?
Answer:
Standard form: 562,384
Expanded form: (5 × 100,000) + (6 × 10,000) + (2 × 1,000) + (3 × 100) + (8 × 10) + 4
Expanded form
using exponents: (5 × 10⁵) + (6 × 10⁴) + (2 × 10³) + (3 × 10²) + (8 × 10¹ ) + (4 × 10⁰)
Any number raised to the first power always equals that number. 10¹ = 10.

Explain It

Question 1.
How many times is 9 used as a factor in the exponent 98?
Answer:
8 times
Explanation:

Question 2.
Why does 3 × 100 = 3?
Answer:
10⁰ = 1, so 3 × 10⁰ = 3

Other Examples
Write each in exponential form.
100,000 = 10⁵ 10 × 10 × 10 = 10³ 1 trillion = 10¹²
Evaluate numbers in exponential form.
5³ = 5 × 5 × 5 = 125 3⁴ = 3 × 3 × 3 × 3 = 81

You can write the repeated multiplication of a number in exponential form.

Each place in the place-value chart can be written using an exponent.

Guided Practice

Do you know HOW?
Question 1.
Write 10,000 as repeated multiplication.
Answer:
10,000 = 10 × 10 × 10 × 10
Explanation:

Question 2.
Write 7 × 7 × 7 × 7 in exponential form.
Answer:
7⁴
Explanation:

Question 3.
Write 37,169 in expanded form using exponents.
Answer:
(3 × 10⁴) + (7 × 10³) + (1 × 10²) + (6 × 10¹) + (9 × 10⁰)
Explanation:

Question 4.
Write 5³ in standard form.
Answer:
125
Explanation:

Do you UNDERSTAND?
Question 5.
In the example at the top, why was the number 10 used as the base to write 1,000,000 in exponential form?
Answer:
See margin.
Explanation:

Question 6.
Using the example, how many times would 10 be repeatedly multiplied to equal 100,000?
Answer:
5 times. 100,000 = 10 × 10 × 10 × 10 × 10 = 10
Explanation:

Question 7.
How many zeros are in 107 when it is written in standard form?
Answer:
7
Explanation:

Independent Practice

Leveled Practice What number is the base?
Question 8.
4⁹
Answer:
4
Explanation:

Question 9.
17⁹
Answer:
17
Explanation:

What number is the exponent?
Question 10.
31⁹
Answer:
9
Explanation:

Question 11.
2¹⁰⁰
Answer:
100
Explanation:

Write each in exponential form.
Question 12.
1,000
Answer:
10³
Explanation:

Question 13.
1,000,000,000
Answer:
10⁹
Explanation:

Question 14.
10 × 10 × 10 × 10 × 10
Answer:
10⁵
Explanation:

Write each number in expanded form using exponents.
Answer:
See margin
Explanation:

Question 15.
841
Answer:

Question 16.
5,832
Answer:

Question 17.
1,874,161
Answer:

Question 18.
22,600,000
Answer:

Evaluate 19 through 22.
Question 19.
6² = ☐
Answer:
36
Explanation:

Question 20.
10⁴ = ☐
Answer:
10,000
Explanation:

Question 21.
4³ = ☐
Answer:
64
Explanation:

Question 22.
2⁷ = ☐
Answer:
128
Explanation:

Problem Solving

Question 23.
The population of one U.S. state is approximately 33,871,648. What is this number in expanded form using exponents?
Answer:
See margin
Explanation:

Question 24.
Reasoning What number raised to both the first power and the second power equals 1?
Answer:
1; 1¹ = 1 and 1² = 1
Explanation:

Question 25.
Writing to Explain Explain how to compare 24 and 42.
Answer:
2⁴ = 2 × 2 × 2 × 2 = 16; 4² = 4 × 4 = 16; So 2⁴ = 4².
Explanation:

Question 26.
In Exercise 23, what is the place of the digit 7?
A. hundreds
B. thousands
C. ten thousands
D. millions
Answer:
C. ten thousands
Explanation:

Question 27.
Writing to Explain Kalesha was asked to write 80,808 in expanded form using exponents. Her response was (8 × 10²) + (8 × 10¹) + (8 × 10⁰). Explain where she made mistakes and write the correct response.
Answer:
See margin
Explanation:

Question 28.
Think About the Process You invest $1 in a mutual fund. Every 8 years, your money doubles. If you don’t add more money, which expression shows how much your investment is worth after 48 years?
A. 1 48
B. 1 × 2 × 2 × 2 × 2 × 2
C. 1 + 2 + 2 + 2 + 2 + 2 + 2
D. 1 × 2 × 2 × 2 × 2 × 2 × 2
Answer:
Explanation:
D. 1 × 2 × 2 × 2 × 2 × 2 × 2

Question 29.
Number Sense Using the map, write the population of the United States in expanded form using exponents.

Answer:
See margin
Explanation:

Question 30.
In 1900, there were 76,803,887 people in the United States. How many more people were there in the United States in a recent year than in 1900?
Answer:
See margin
Explanation:

Algebra Connections

Solution Pairs
An equation is a mathematical sentence that uses an equals sign to show that two expressions are equal. Any values that make an equation true are solutions to the equation.

An inequality is a mathematical sentence that contains <, >, ≤, or ≥. Any value that makes the inequality true is a solution. You can graph the solutions of an inequality on a number line.

Example: Find two values for each variable that make the equation,
y = x + 3, true.
If x = 1, then y = 1 + 3 = 4 is true.
If x = 5, then y = 5 + 3 = 8 is true.
(1, 4) and (5, 8) are solution pairs.

Example: Graph three values that make the inequality, x > 3, true.
x = 3.1, x = 4, x = 5
Draw a number line. Plot three points that are greater than 3

For 1 through 4, copy the table and find two values for each variable that make the equation true.
Question 1.
y = 4 + x
Answer:

Explanation:

Question 2.
b = a – 2
Answer:

Explanation:

Question 3.
t = 3w
Answer:

Explanation:

Question 4.
y = x ÷ 2
Answer:

Explanation:

Question 5.
Copy the number line and graph 3 values that make the inequality, d ≥ 9, true.

Answer:
Any 3 points right of 9; or 9
Explanation:

Question 6.
Copy the number line and graph 3 values that make the inequality,\(\frac{x}{3}\) < 4, true.

Answer:
Any 3 points to left of 12
Explanation:

Envision Math 6th Grade Textbook Answer Key Topic 1.2 Comparing and Ordering Whole Numbers

Comparing and Ordering Whole Numbers

How can you compare numbers?
Answer:
Use the data in the table to compare the heights of the buildings. Which is taller, the Petronas Towers or the Sears Tower?

Another Example

How do you compare and order more than two numbers?
Answer:
Order the heights of the buildings in the above table from least to greatest.
Step 1:
Write the numbers, lining up the places. Compare the digits.

Step 2:
Write the remaining numbers, lining up the places. Compare.

Step 3:
Order the numbers and the heights of the buildings from least to greatest.
1,380; 1,450; 1,483; 1,670
Jin Mao Tower, Sears Tower, Petronas Towers, Taipei 101

Guided Practice

Do you know HOW?
In 1 and 2, use < or > to compare.
Question 1.
27,318 _____ 28,001
Answer:
27,318 28,001
Explanation:

Question 2.
1,000,001 _____ 1,000,010
Answer:
1,000,001 1,000,010
Explanation:

In 3, order the numbers from least to greatest.
Question 3.
3,964 4,160 3,395 4,000
Answer:
3,395; 3,964; 4,000; 4,160
Explanation:

Do you UNDERSTAND?
Question 4.
In the example at the top, where do you begin comparing digits?
Answer:
Thousands place
Explanation:

Question 5.
Two International Finance Centre is 1,362 feet tall. Use the table above to find which is taller,Two International Finance Centre or the Jin Mao Tower?
Answer:
Jin Mao Tower
Explanation:

Step 1:
Write the numbers in a column to line up the places.
1,483
1,450
Compare the digits from left to right.

Step 2:
Find the first place where
the digits are different.
1,483
1,450
Use > or < to compare. 8 > 5
So, 1,483 > 1,450

Step 3:
Write your answer.
1,483 > 1,450
or
1,450 < 1,483
The Petronas Towers are taller than the Sears Tower

Independent Practice

For 6 through 8, use < or > to compare.
Question 6.
8,867 ____ 8,896
Answer:
8,867 8,896
Explanation:

Question 7.
102,086 _______ 100,266
Answer:
102,086 100,266

Question 8.
5,743,834 _____ 5,745,618
Answer:
5,743,834 5,745,618
Explanation:

For 9 and 10, order the numbers from least to greatest.
Tips: Compare each place from left to right.
Question 9.
85,634; 86,364; 86,446; 68,989
Answer:
68,989; 85,634; 86,364; 86,446
Explanation:

Question 10.
4,088,777; 4,221,000; 4,202,006
Answer:
4,088,777; 4,202,006; 4,221,000
Explanation:

For 11 and 12, order the numbers from greatest to least.
Question 11.
400 billion; 857 thousand; 3 trillion
Answer:
3 trillion; 400 billion; 857 thousand
Explanation:

Question 12.
5,743,834; 5,754,618; 5,900,962
Answer:
5,900,962; 5,754,618; 5,743,834
Explanation:

Problem Solving

Question 13.
Writing to Explain The SR-71 spy plane can fly at an altitude of 85,000 feet. Explain how you would compare this altitude with the altitude of the Helios shown below. Tell which plane could fly higher.

Answer:
See margin.
Explanation:

Question 14.
Number Sense When comparing 1,290 km and 1,130 km, which place do you use to determine which number is greater?
Answer:
Hundreds place
Explanation:

Question 15.
Geometry Which measurement of this rectangular vegetable garden has the greatest value?

A. length
B. width
C. perimeter
D. length + width
Answer:
C. perimeter
Explanation:

Envision Math 5th Grade Textbook Answer Key Topic 2 Reteaching

Set A, pages 24-26

Add 53 + 11 + 7 using mental math.

53 and 7 are compatible numbers, and the Commutative Property of Addition allows you to add in any order.

53 + 11 + 7 = 53 + 7 + 11
= 60 + 11
= 71

Remember that you can use compatible numbers or compensation to find sums and differences.

Question 1.
67 + 28
Answer:

Question 2.
130 + 470
Answer:

Question 3.
35 + 14 + 6
Answer:

Question 4.
276 – 99
Answer:

Question 5.
96 + 234 + 4
Answer:

Set B, pages 28–29

Round 12.087 to the underlined place.
12.087 Look at the digit following the underlined digit. Look at 7.
Round the 8 to the next higher digit because 7 > 5.
12.087 is about 12.09.

Remember that rounding a number means replacing it with another number that tells about how much or how many.

Question 1.
10.245
Answer:

Question 2.
9.145
Answer:

Question 3.
67,901
Answer:

Question 4.
99,102
Answer:

Set C, pages 30–32
Estimate 19.9 + 17.03

19.9 + 17.03 is about 37.

Remember that you can also use compatible numbers to estimate.

Question 1.
76 + 23
Answer:

Question 2.
15.01 – 4.4
Answer:

Question 3.
8,001 + 2,890
Answer:

Question 4.
25,003 – 12,900
Answer:

Set D, pages 34–36

Find 6,259 – 2,488.
Estimate: 6,000 – 2,000 = 4,000.
Subtract each place, starting from the right.

The answer 3,771 is reasonable because it is close to the estimate.

Remember to first estimate and then check that your answer is reasonable.

Question 1.

Answer:

Question 2.

Answer:

Question 3.

Answer:

Question 4.

Answer:

Question 5.
72,555 + 38,055
Answer:

Set E, pages 38-41

Find 7.83 – 3.147.
Estimate: 8 – 3 = 5.
Step 1
Write the numbers. Line up the decimal points. Annex zeros to show place value.

Step 2
Subtract as you would whole numbers. Bring the decimal point straight down in the answer.

Step 3
Check your answer by adding. The answer checks.

The difference is reasonable because 4.683 is close to the estimate of 5.

Remember to line up the decimal points before you add or subtract.

Question 1.
3.77 + 4.66
Answer:

Question 2.
12.68 + 31.919
Answer:

Question 3.
6.142 + 1.322
Answer:

Question 4.
67.8 + 14.755
Answer:

Question 5.
7.029 + 48.7
Answer:

Question 6.
10.93 + 0.967
Answer:

Question 7.
9.21 – 1.72
Answer:

Question 8.
15.51 – 11.302
Answer:

Question 9.
5.7 – 0.623
Answer:

Question 10.
16.209 – 14.5
Answer:

Question 11.
17.099 – 9.7
Answer:

Question 12.
81.12 – 37.202
Answer:

Set F, pages 42-44

Steve exercises 910 minutes a week in the summer. This is 190 minutes more than he exercises each week during the school year. How many minutes a week does he exercise during the school year?
Draw a bar diagram to show the main idea.

Let m = minutes per week of exercise during the school year.

Martin exercises 720 minutes a week during the school year.

Remember that drawing a picture can help you before writing an equation to solve a problem.

Draw a picture and write an equation. Solve.

Question 1.
Jay’s parents celebrated their 25th wedding anniversary in 2005. In what year did they get married?
Answer:

Question 2.
One football stadium, built in 1982, has 64,035 seats. Another stadium, built in 1987, has 74,916 seats. How many more seats does the newer stadium have?
Answer:

Question 3.
The two fifth-grade classes at school are having a fundraiser. The first class raised $2,187. Both classes raised $4,136 together. How much did the second class raise?
Answer:

Envision Math 5th Grade Textbook Answer Key Topic 2.5 Adding Decimals

Adding Decimals

How can you add decimals?
What was the combined time for the first two legs of the relay race?

Choose an Operation Add to join groups.
Find 21.49 + 21.59.
Estimate: 21 + 22 = 43

Guided Practice*

Do you know HOW?
In 1 through 6, add the decimals.

Question 1.
0.82 + 4.21
Answer:

Question 2.
9.1 + 7.21
Answer:

Question 3.
9.7 + 0.24
Answer:

Question 4.
3.28 + 6.09
Answer:

Question 5.
0.26 + 8.3
Answer:

Question 6.
4.98 + 3.02
Answer:

Do you UNDERSTAND?

Question 7.
Reasonableness How do you know the total time for the first two legs of the race is reasonable?
Answer:

Question 8.
Writing to Explain How is finding $4.25 + $3.50 like finding 4.25 + 3.5? How is it different?
Answer:

Independent Practice

In 9 through 26, add the decimals.

Question 9.

Answer:

Question 10.

Answer:

Question 11.

Answer:

Question 12.

Answer:

Question 13.

Answer:

Question 14.

Answer:

Question 15.

Answer:

Question 16.

Answer:

Question 17.

Answer:

Question 18.

Answer:

Question 19.

Answer:

Question 20.

Answer:

Question 21.
$271.90 + $34.22 22.
Answer:

Question 22.
658.2 + 0
Answer:

Question 23.
0.922 + 6.4
Answer:

Question 24.
8.02 + 9.07
Answer:

Question 25.
13.9 + 0.16
Answer:

Question 26.
0.868 + 15.973
Answer:

Step 1

Write the numbers. Line up the decimal points.

Step 2

First, add the hundredths. Regroup if necessary

Step 3

Add the tenths, ones, and tens. The decimal point in the sum is aligned with the decimal point in the addends. Check the sum with your estimate.

The total time for the first two legs of the race was 43.08 seconds.

Problem Solving

Question 27.
A balloon mural of the Chicago skyline measures 17.6 m on two sides and 26.21 m on the other two sides. What is the perimeter of the mural?
A. 38.81 m
B. 48.21 m
C. 55.74 m
D. 87.62 m
Answer:

Question 28.
Writing to Explain Juan adds 3.8 ± 4.6 and gets a sum of 84. Is his answer correct? Tell how you know.
Answer:

Question 29.
Think About the process
Jamie earned $27 taking care of a neighbor’s dog for one week. She spent $19.95 on a new DVD. Later, she earned $15 for raking leaves. Which expression shows how to find the money Jamie has left?
A. $27 + $19.95 + $15
B. $19.95 – $15 + $27
C. $27 – $19.95 – $15
D. $27 – $19.95 – $15
Answer:

Question 30.
At a flower shop, Teri sees that roses are $3 each, carnations are $4 for 3 flowers, and tulips are $4 for 4 flowers. She buys 3 roses and
3 carnations. She has $20. How much change does Teri get back?

Question 31.
Which two cities had the greatest combined rainfall for the period given?
A. Caribou and Boise
B. Springfield and Macon
C. Macon and Boise
D. Caribou and Springfield

Answer:

Question 32.
What is the typical yearly rainfall for all four cities?
Answer:

Question 33.
Which location had less than 45 inches of rain but more than 40 inches of rain
Answer:

Envision Math 5th Grade Textbook Answer Key Topic 1 Reteaching

Reteaching

Set A, pages 4-5

Write the word form and tell the value of the underlined digit for 930,365.

Nine hundred thirty thousand, three hundred sixty-five.

Since the 0 is in the thousands place, its value is 0 thousands or 0.

Write the word form and tell the value of the underlined digit for 65,467,386,941.

Sixty-five billion, four hundred sixty-seven million, three hundred eighty-six thousand, nine hundred forty-one

Since the 6 is in the ten billions place, its value is 60,000,000,000.

Remember that, starting from the right, each group of three digits forms a period. Periods are separated by commas.

Write the word form and tell the value of the underlined digit.

Question 1.
9,000,009
Answer:

Question 2.
300,000,000,000
Answer:

Question 3.
25,678
Answer:

Question 4.
17,874,000,000
Answer:

Question 5.
4,000,345,000
Answer:

Question 6.
105,389
Answer:

Question 7.
876,400,000,00
Answer:

Question 8.
600,309,470
Answer:

Question 9.
135,000
Answer:

Question 10.
2,647,000
Answer:

Question 11.
4,104,327,894
Answer:

Set B, pages 6-8

Write <, >, or = for  in
2,876,547  2,826,547.
Line up the numbers above one another.
2,876,547 Begin at the left and compare.
2,826,547 Notice that the ten thousands are different.

7 ten thousands > 2 ten thousands
So, 2,876,547 > 2,826,547

Remember that lining up place values helps you compare numbers.

Question 1.
9,990  9,099
Answer:

Question 2.
89,128  90,000

Question 3.
1,000,000  999,999

Question 4.
300,300  303,000
Answer:

Question 5.
6,752,100  6,752,000
Answer:

Question 6.
9,314  9,314
Answer:

Question 7.
17,320  17,212
Answer:

Question 8.
45,006  45,060
Answer:

Question 9.
22,009  22,090
Answer:

Question 10.
145,372  147,372
Answer:

Question 11.
8,374  8,374
Answer:

Set C, pages 10-11

write the word form and tell the value of the underlined digit for the number 8.726. Write the numbers on a place value chart.

Eight and seven hundred twenty-six thousandths
The 2 is in the hundredths place. Its value is 0.02

Remember to write the word and for the decimal point.

Question 1.
8.59
Answer:

Question 2.
2.251
Answer:

Question 3.
7.003

Question 4.
3.24
Answer:

Question 5.
6.837
Answer:

Question 6.
0.636
Answer:

Set D, pages 12-13

Write <, >, or = for  in
8.45  8.47.

Line up the numbers above each other by the decimals.
8.45
8.47
5 hundredths < 7 hundredths
So, 8.45 < 8.47

Remember that equivalent decimals, such as 0.45 and 0.450, can help you compare numbers.

Question 1.
0.584  0.58
Answer:

Question 2.
9.327  9.236
Answer:

Question 3.
5.2  5.20
Answer:

Question 4.
5.643  5.675
Answer:

Question 5.
0.07  0.08
Answer:

Question 6.
3.602  3.062
Answer:

Set E, pages 14-16

The table below shows the number of new members each month for a club. If the pattern continues, how many new members will there be in June?

Pattern: The number doubles each month.
May: 120 × 2 × 240
June: 240 × 2 × 480
In June, there will be 480 new members

Remember to look for a pattern.

Question 1.
On the board, Andrea’s teacher wrote the pattern below. Find the next three numbers in the pattern.

Question 2.
Sean bought a rare stamp for $15. He was told that it would increase in value by $11 each year. What will the stamp’s value be after 4 years?
Answer: