Go through the **Spectrum Math Grade 6 Answer Key Chapter 1 Lesson 1.1 Number Properties** and get the proper assistance needed during your homework.

## Spectrum Math Grade 6 Chapter 1 Lesson 1.1 Number Properties Answers Key

There are certain rules or properties of math that are always true.

The Commutative Properties of addition and multiplication state that the order in which numbers are added or multiplied does not change the result.

a + b = b + a and a × b = b × a

2 + 3 = 5 5 × 2 = 10

3 + 2 = 5 2 × 5 = 10

The Associative Properties of addition and multiplication state that the way in which addends or factors are grouped does not change the result.

(a + b) + c = a + (b + c) and (a × b) × c = a × (b × c)

(2 + 3) + 4 = 2 + (3 + 4) (2 × 4) × 5 = 2 × (4 × 5)

5 + 4 = 2 + 7 8 × 5 = 2 × 20

9 = 9 40 = 40

The Identity Property of Addition states that the sum of an addend and 0 is the addend.

5 + 0 = 5

The Identity Property of Multiplication states that the product of a factor and 1 is that factor. 4 × 1 = 4

The Properties of Zero also state that the product of a factor and 0 is 0 ÷ 5 = 0

**Name the property shown by each statement.
** Question 1.

a. 2 × 8 = 8 × 2 ____

Answer:

Multiplication of 2 × 8 = 8 × 2, we get the product as16. (Commutative Properties of multiplication)

Explanation:

The Commutative Properties of addition and multiplication state that the order in which numbers are added or multiplied does not change the result.

a × b = b × a

=> 2 × 8 = 16.

8 × 2 = 16.

b. 2 + (3 + 4) = (2 + 3) + 4 ______

Answer:

Sum of 2 + (3 + 4) = (2 + 3) + 4 = 9. (Associative Properties of addition)

Explanation:

The Associative Properties of addition and multiplication state that the way in which addends or factors are grouped does not change the result.

(a + b) + c = a + (b + c)

=> 2 + (3 + 4) = 2 + 7 = 9.

(2 + 3) + 4 = 5 + 4 = 9.

Question 2.

a. 35 × 1 = 35 ____

Answer:

35 × 1 = 35. (Identity Property of Multiplication)

Explanation:

The Identity Property of Multiplication states that the product of a factor and 1 is that factor.

35 × 1 = 35.

b. 32 + 25 = 25 + 32 ____

Answer:

32 + 25 = 25 + 32 = 57. (Commutative Properties of addition)

Explanation:

The Commutative Properties of addition and multiplication state that the order in which numbers are added or multiplied does not change the result.

a + b = b + a

=> 32 + 25 = 57.

25 + 32 = 57.

Question 3.

a. 4 × (6 × 2) = (4 × 6) × 2 ____

Answer:

4 × (6 × 2) = (4 × 6) × 2 = 48.

Explanation:

The Associative Properties of addition and multiplication state that the way in which addends or factors are grouped does not change the result.

(a × b) × c = a × (b × c)

=> 4 × (6 × 2) = 4 × 12 = 48.

(4 × 6) × 2 = 24 × 2 = 48.

b. 0 × 9 = 0 ____

Answer:

0 × 9 = 0. (Properties of Zero)

Explanation:

The Properties of Zero also state that the product of a factor and 0 is 0 ÷ 5 = 0.

0 × 9 = 0.

Question 4.

a. 45 + 0 = 45 ____

Answer:

45 + 0 = 45. (Identity Property of Addition)

Explanation:

The Identity Property of Addition states that the sum of an addend and 0 is the addend.

45 + 0 = 45.

b. 18 × 0 = 0 × 18 ____

Answer:

18 × 0 = 0 × 18 = 0. (Properties of Zero)

Explanation:

The Properties of Zero also state that the product of a factor and 0 is 0 ÷ 5 = 0.

=> 18 × 0 = 0.

0 × 18 = 0.

**Rewrite each expression using the property indicated.
**Question 5.

a. Associative; (3 + 5) + 2 = ____

Answer:

Associative; (3 + 5) + 2 = 3 + (5 + 2) = 10.

Explanation:

The Associative Properties of addition and multiplication state that the way in which addends or factors are grouped does not change the result.

=> (3 + 5) + 2 = 3 + (5 + 2)

= 3 + 7

= 10.

b. Commutative; 5 × 7 = ____

Answer:

Commutative; 5 × 7 = 7 × 5 = 35.

Explanation:

The Commutative Properties of addition and multiplication state that the order in which numbers are added or multiplied does not change the result.

a × b = b × a

=> 5 × 7 = 7 × 5

= 35.

Question 6.

a. Identity; 0 + 4 = _________

Answer:

Identity; 0 + 4 = 4.

Explanation:

The Identity Property of Addition states that the sum of an addend and 0 is the addend.

0 + 4 = 4.

b. Associative; 3 × (2 × 5) = ____

Answer:

Associative; 3 × (2 × 5) = (3 × 2) × 5 = 30.

Explanation:

The Associative Properties of addition and multiplication state that the way in which addends or factors are grouped does not change the result.

3 × (2 × 5) = (3 × 2) × 5

= 6 × 5

= 30.

Question 7.

a. Commutative; 7 + 9 = ____

Answer:

Commutative; 7 + 9 = 9 + 7 = 16.

Explanation:

The Commutative Properties of addition and multiplication state that the order in which numbers are added or multiplied does not change the result.

a + b = b + a

=> 7 + 9 = 9 + 7

= 16.

b. Associative; (2 + 5) + 4 = ____

Answer:

Associative; (2 + 5) + 4 = 2 + (5 + 4) = 11.

Explanation:

The Associative Properties of addition and multiplication state that the way in which addends or factors are grouped does not change the result.

(2 + 5) + 4 = 2 + (5 + 4)

= 2 + 9

= 11.

Question 8.

a. Identity; 7 × 1 = __________

Answer:

Identity; 7 × 1 = 7.

Explanation:

The Identity Property of Multiplication states that the product of a factor and 1 is that factor. 7 × 1 = 7.

b. Identity; 37 + 0 = ____

Answer:

Identity; 37 + 0 = 37.

Explanation:

The Identity Property of Addition states that the sum of an addend and 0 is the addend.

37 + 0 = 37.

Question 9.

a. Properties of Zero; 0 × 12 = _____

Answer:

Properties of Zero; 0 × 12 = 0.

Explanation:

The Properties of Zero also state that the product of a factor and 0 is 0 ÷ 5 = 0.

=> 0 × 12 = 0.

b. Properties of Zero; 0 ÷ 6 = _____

Answer:

Properties of Zero; 0 ÷ 6 = 0.

Explanation:

The Properties of Zero also state that the product of a factor and 0 is 0 ÷ 5 = 0.

=> 0 ÷ 6 = 0.