## Envision Math 6th Grade Textbook Answer Key Topic 2.2 Properties of Operations

Properties of Operations

How can you use properties of operations to rewrite expressions?
The Commutative Property of Addition states the order in which numbers are added does not change the sum of the numbers. The Commutative Property of Multiplication states the order in which numbers are multiplied does not change the product of the numbers. Guided Practice

Do you know HOW?
Find each missing number.Tell what property is shown.
Question 1.
19 + (42 + 8) = (☐ + 42) + 8
19; Associative Property of Addition
Explanation:

Question 2.
12 + 8 = ☐ +12
8; Commutative Property of Addition
Explanation:

Question 3.
42 × 8 × 3 = 42 × 8 × ☐ × 3
1; Identity Property of Multiplication
Explanation:

Question 4.
32 × 85 = 85 × ☐
32; Commutative Property of Multiplication
Explanation:

Do you UNDERSTAND?
Question 5.
For the Identity Property, why does addition involve a zero and multiplication involve a one? Why don’t they both use one or both use zero?
See margin.
Explanation:

Question 6.
Yuen Lee put 3 cartons of markers in the closet. Each carton contains 3 rows of 7 boxes. Use one of the Associative Properties to show two different ways of finding the number of marker boxes.
(3 × 3) × 7; 3 × (3 × 7)
Explanation:

Independent Practice

Find each missing number. Tell what property or properties are shown.
See margin.
Explanation:

Question 7.
☐ × (14 × 32) = (5 × 14) × 32

Question 8.
5 + 23 + 4 = 23 + 4 + ☐

Question 9.
25 + 0 + (3 + 16) = (25 + ☐) + 3

Question 10.
(7 + 1 2) + 4 = (7 + ☐) + 12

Question 11.
(5 × 7) (3 × 8) = (5 × 3) × (8 × ☐)

Question 12.
(43 × 1) × 4 = ☐ × 43

Question 13.
(6 + 3) + 4 = 6 + (3 + ☐)

Question 14.
(8 × 9) × ☐ = 8 × (9 × 10)

Question 15.
7 × ☐ = 6 × 7

Question 16.
15 + 48 = ☐ + 15

Question 17.
8 + ☐ = 4 + 8

Question 18.
(1 × 2) × 3 = ☐ × (2 × 3)

The Associative Property of Addition states that the way numbers are grouped does not affect the sum.
a + (b + c) = (a + b) + c
2 + (8 + 10) = (2 + 8) + 10
The Associative Property of Multiplication states that the way numbers are grouped does not affect the product.
a × (b × c) = (a × b) × c
2 × (4 × 5) = (2 × 4) × 5
The Identity Property of Addition states that adding zero to a number does not change the number.
a + 0 = a
24 + 0 = 24
The Identity Property of Multiplication states that the product of a number and one is that number.
a × 1 × a
36 × 1 × 36

Find each missing number. Tell what property or properties are shown.
Question 19.
(41 × 43) × (3 × 19) = (41 × ☐) × (19 × 43)

Question 20.
(5 × 3) × ☐ = 5 × (8 × 3)

Question 21.
328 × 1 = ☐

Question 22.
(12 + 0) × (1 × 12) = ☐ × ☐

Problem Solving
For 23 and 24, use the table to the right. Question 23.
Donnie and Pete live in Coldwater. They rode their bikes to Blanco and then to Pulga. Then they rode back home, using the same route. Write a number sentence using the Commutative Property of Addition to show the distances they rode each way.

Question 24.
Once they rode from Pulga to Littleville, from Littleville to Zion, and then rode back to Pulga. How many miles did they ride that time?

Question 25.
Think About the Proces Stage 15 of the Tour de France bicycle race includes legs from Gap to Embrun, Embrun to Guillestre, and Guillestre to Arvieux. One way to express these legs is 33.5 + (20.5 + 21.5). Which expression below is another way to express these legs?
A. (23 + 33.5) + (20.5 – 21.5)
B. (33.5 + 20.5) + 21.5
C. 33.5 + (20.5 × 21.5)
D. (33.5 × 21.5) + 20.5