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

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

Question 1.
a. 17 + n = ____
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 = ____
n + 0 =
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 = ____
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 = ____
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 = ____
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 = ____
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 = _______
(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 = _____
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 = _____
(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 = ____
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 = _____
(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 = ____
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 = ____
(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 _____
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 _____
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) ____
(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 _____
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 _____
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 ______
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 ____