This handy **Spectrum Math Grade 7 Answer Key**** Chapter 1 Lesson 1.8 Adding Using Mathematical Properties** provides detailed answers for the workbook questions.

## Spectrum Math Grade 7 Chapter 1 Lesson 1.8 Adding Using Mathematical Properties Answers Key

The Commutative Property of Addition states: o + b = b + o

The Associative Property of Addition states: (a + b) + c = a + (b + c)

The Identity Property of Addition states: a + 0 = a

**Rewrite each equation using your knowledge of addition properties.**

Question 1.

a. 17 + n = ____

Answer: n + 17

17 + n = **n + 17**

The above equation is an example for commutative property.

According to the commutative property of addition, the sum is unaffected by changes in the order of the numbers being added. The commutative property of addition can be defined as the fact that adding two integers in any sequence results in the same result. Therefore, the commutative property of addition, when we add two integers, the answer will remain unchanged even if the position of the numbers are changed.

b. n + 0 = ____

Answer: n

n + 0 = **n **

The above equation is an example of identity property.

An identity in mathematics is a number, n, that results in the same number, n, when other numbers are added to it. The identity of the additive is always zero. This brings us to the identity property of addition, which simply states that when you add zero to any number, it equals the number itself.

Question 2.

a. ____ = (x + y) + 2

Answer: x + (y + 2)

x + (y + 2) = **(x + y) + 2**

The above equation is an example of associative property.

The associative property of addition is a mathematical statement that states that the arrangement of three or more integers does not change their sum. This means that no matter how the numbers are grouped, the sum of three or more integers remains the same.

b. r + s = ____

Answer: s + r

r + s = **s + r**

The above equation is an example for commutative property.

According to the commutative property of addition, the sum is unaffected by changes in the order of the numbers being added. The commutative property of addition can be defined as the fact that adding two integers in any sequence results in the same result. Therefore, the commutative property of addition, when we add two integers, the answer will remain unchanged even if the position of the numbers are changed.

Question 3.

a. 0 + x = ____

Answer: x

0 + x = **x**

The above equation is an example of identity property.

An identity in mathematics is a number, n, that results in the same number, n, when other numbers are added to it. The identity of the additive is always zero. This brings us to the identity property of addition, which simply states that when you add zero to any number, it equals the number itself.

b. (3 + g) + h = ____

Answer: 3 + (g + h)

(3 + g) + h = **3 + (g + h)**

The above equation is an example of associative property.

The associative property of addition is a mathematical statement that states that the arrangement of three or more integers does not change their sum. This means that no matter how the numbers are grouped, the sum of three or more integers remains the same.

Question 4.

a. (9 + r) + 5 = ____

Answer: 9 + (r + 5)

(9 + r) + 5 = **9 + (r + 5)**

The above equation is an example of associative property.

The associative property of addition is a mathematical statement that states that the arrangement of three or more integers does not change their sum. This means that no matter how the numbers are grouped, the sum of three or more integers remains the same.

b. t + h = ____

Answer: h + t

t + h = **h + t**

The above equation is an example for commutative property.

According to the commutative property of addition, the sum is unaffected by changes in the order of the numbers being added. The commutative property of addition can be defined as the fact that adding two integers in any sequence results in the same result. Therefore, the commutative property of addition, when we add two integers, the answer will remain unchanged even if the position of the numbers are changed.

**Solve each equation. Use the properties of addition to help.**

Question 5.

a. 11 + 18 + 12 = ____

Answer: 41

11 + 18 + 12 = **41**

The above equation is an example for commutative property.

According to the commutative property of addition, the sum is unaffected by changes in the order of the numbers being added. The commutative property of addition can be defined as the fact that adding two integers in any sequence results in the same result. Therefore, the commutative property of addition, when we add two integers, the answer will remain unchanged even if the position of the numbers are changed.

b. (5 + 3) + 0 = _______

Answer: 8

(5 + 3) + 0 = 5 + (3 + 0) =** 8**

The above equation is an example of associative property.

The associative property of addition is a mathematical statement that states that the arrangement of three or more integers does not change their sum. This means that no matter how the numbers are grouped, the sum of three or more integers remains the same.

Question 6.

a. 14 + 15 + 16 = _____

Answer: 45

14 + 15 + 16 = **45**

The above equation is an example for commutative property.

According to the commutative property of addition, the sum is unaffected by changes in the order of the numbers being added. The commutative property of addition can be defined as the fact that adding two integers in any sequence results in the same result. Therefore, the commutative property of addition, when we add two integers, the answer will remain unchanged even if the position of the numbers are changed.

b. (17 + 0) + 2 = _____

Answer: 19

(17 + 0) + 2 = 17 + (0 + 2) = **19**

The above equation is an example of associative property.

The associative property of addition is a mathematical statement that states that the arrangement of three or more integers does not change their sum. This means that no matter how the numbers are grouped, the sum of three or more integers remains the same.

Question 7.

a. 23 + 24 + 25 = ____

Answer: 72

23 + 24 + 25 = **72**

The above equation is an example for commutative property.

According to the commutative property of addition, the sum is unaffected by changes in the order of the numbers being added. The commutative property of addition can be defined as the fact that adding two integers in any sequence results in the same result. Therefore, the commutative property of addition, when we add two integers, the answer will remain unchanged even if the position of the numbers are changed.

b. (4 + 5) + 0 = _____

Answer: 9

(4 + 5) + 0 = 4 + (5 + 0) = **9**

The above equation is an example of associative property.

The associative property of addition is a mathematical statement that states that the arrangement of three or more integers does not change their sum. This means that no matter how the numbers are grouped, the sum of three or more integers remains the same.

Question 8.

a. 54 + 43 + 19 = ____

Answer: 116

54 + 43 + 19 = **116**

The above equation is an example for commutative property.

According to the commutative property of addition, the sum is unaffected by changes in the order of the numbers being added. The commutative property of addition can be defined as the fact that adding two integers in any sequence results in the same result. Therefore, the commutative property of addition, when we add two integers, the answer will remain unchanged even if the position of the numbers are changed.

b. (8 + 0) + 10 = ____

Answer: 18

(8 + 0 ) + 10 = 8 + (0 + 10) = **18**

The above equation is an example of associative property.

The associative property of addition is a mathematical statement that states that the arrangement of three or more integers does not change their sum. This means that no matter how the numbers are grouped, the sum of three or more integers remains the same.

**Tell which property is used in each equation (commutative, associative, or identity).**

Question 9.

a. 7 + (-7) = 0 _____

Answer: commutative property

7 + (-7) = 0 = **commutative property**

The above equation is an example for commutative property.

According to the commutative property of addition, the sum is unaffected by changes in the order of the numbers being added. The commutative property of addition can be defined as the fact that adding two integers in any sequence results in the same result. Therefore, the commutative property of addition, when we add two integers, the answer will remain unchanged even if the position of the numbers are changed.

b. 4 + 6 = 6 + 4 _____

Answer: commutative property

4 + 6 = 6 + 4 = **commutative property**

The above equation is an example for commutative property.

According to the commutative property of addition, the sum is unaffected by changes in the order of the numbers being added. The commutative property of addition can be defined as the fact that adding two integers in any sequence results in the same result. Therefore, the commutative property of addition, when we add two integers, the answer will remain unchanged even if the position of the numbers are changed.

Question 10.

a. (11 + 2) + 8 = 11 + (2 + 8) ____

Answer: associative property

(11 + 2) + 8 = 11 + (2 + 8) = **associative property**

The above equation is an example of associative property.

The associative property of addition is a mathematical statement that states that the arrangement of three or more integers does not change their sum. This means that no matter how the numbers are grouped, the sum of three or more integers remains the same.

b. 9 + 0 = 9 _____

Answer: identity property

9 + 0 = 9 = **identity property**

The above equation is an example of identity property.

An identity in mathematics is a number, n, that results in the same number, n, when other numbers are added to it. The identity of the additive is always zero. This brings us to the identity property of addition, which simply states that when you add zero to any number, it equals the number itself.

Question 11.

a. 6 + (4 + 3) = (6 + 4) + 3 _____

Answer: associative property

6 + (4 + 3) = (6 + 4) + 3 = **associative property**

The above equation is an example of associative property.

The associative property of addition is a mathematical statement that states that the arrangement of three or more integers does not change their sum. This means that no matter how the numbers are grouped, the sum of three or more integers remains the same.

b. 5 + 9 = 9 + 5 ______

Answer: commutative property

5 + 9 = 9 + 5 =** commutative property**

The above equation is an example for commutative property.

According to the commutative property of addition, the sum is unaffected by changes in the order of the numbers being added. The commutative property of addition can be defined as the fact that adding two integers in any sequence results in the same result. Therefore, the commutative property of addition, when we add two integers, the answer will remain unchanged even if the position of the numbers are changed.

Question 12.

a. 15 + 0 = 15 ____

Answer: identity property

15 + 0 = 15 = **identity property**

The above equation is an example of identity property.

An identity in mathematics is a number, n, that results in the same number, n, when other numbers are added to it. The identity of the additive is always zero. This brings us to the identity property of addition, which simply states that when you add zero to any number, it equals the number itself.

b. 18 + 7 = 7 + 18 ______

Answer: commutative property

18 + 7 = 7 + 18 = **commutative property**

The above equation is an example for commutative property.

According to the commutative property of addition, the sum is unaffected by changes in the order of the numbers being added. The commutative property of addition can be defined as the fact that adding two integers in any sequence results in the same result. Therefore, the commutative property of addition, when we add two integers, the answer will remain unchanged even if the position of the numbers are changed.