## 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 × 4^{2} ÷ 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 + 3^{2} = 19

Answer:

Question 6.

6 × 2 – 1 + 5^{2} = 31

Answer:

Question 7.

8 × 3 + 8 – 2^{2} = 84

Answer:

Question 8.

50 – 3 × 6 + 2 + 4^{2} = 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: