# Spectrum Math Grade 6 Chapter 1 Lesson 1 Answer Key Number Properties

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 ____
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 ______
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 ____
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 ____
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 ____
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 ____
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 ____
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 ____
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 = ____
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 = ____
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 = _________
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) = ____
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 = ____
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 = ____
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 = __________
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 = ____
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 = _____
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 = _____
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.