Spectrum Math Grade 7 Chapter 2 Lesson 3 Answer Key Multiplying Integers

This handy Spectrum Math Grade 7 Answer Key Chapter 2 Lesson 2.3 Multiplying Integers provides detailed answers for the workbook questions.

Spectrum Math Grade 7 Chapter 2 Lesson 2.3 Multiplying Integers Answers Key

The product of two integers with the same sign is positive.

3 × 3 = 9
-3 × -3 = 9
The product of two integers with different signs is negative.
3 × (-3) = -9
-3 × 3 = -9

Multiply.

Question 1.
a. 3 × 2 = ____
Answer: 6
3 × 2 = 6
The product of two positive integers is always positive.
The product of two negative integers is always positive.
The product of one positive and one negative integer is always negative.
Therefore, here 3 and 2 both are positive integers hence their product is also positive.

b. -4 × 6 = ____
Answer: -24
-4 × 6 = -24
The product of two positive integers is always positive.
The product of two negative integers is always positive.
The product of one positive and one negative integer is always negative.
Here -4 is a negative integer and 6 is a positive integer therefore the result of their product is a negative integer.

c. 8 × (-3) = ____
Answer: -24
8 × (-3) = -24
The product of two positive integers is always positive.
The product of two negative integers is always positive.
The product of one positive and one negative integer is always negative.
Here -3 is a negative integer and 8 is a positive integer therefore the result of their product is a negative integer.

d. -3 × (-4) = _____
Answer: 12
-3 × (-4) = 12
The product of two positive integers is always positive.
The product of two negative integers is always positive.
The product of one positive and one negative integer is always negative.
Here -3 and -4 both are negative integers hence their product is also a negative integer.

Question 2.
a. -8 × 7 = ____
Answer: -56
-8 × 7 = -56
The product of two positive integers is always positive.
The product of two negative integers is always positive.
The product of one positive and one negative integer is always negative.
Here -8 is a negative integer and 7 is a positive integer therefore the result of their product is a negative integer.

b. 6 × (-5) = ____
Answer: -30
6 × (-5) = -30
The product of two positive integers is always positive.
The product of two negative integers is always positive.
The product of one positive and one negative integer is always negative.
Here -5 is a negative integer and 6 is a positive integer therefore the result of their product is a negative integer.

c. -3 × (-8) = ____
Answer: 24
-3 × (-8) = 24
The product of two positive integers is always positive.
The product of two negative integers is always positive.
The product of one positive and one negative integer is always negative.
Here -3 and -8 both are negative integers therefore the result of their product is a positive integer.

d. -4 × 11 = ____
Answer: -44
-4 × 11 = -44
The product of two positive integers is always positive.
The product of two negative integers is always positive.
The product of one positive and one negative integer is always negative.
Here -4 is a negative integer and 11 is a positive integer therefore the result of their product is a negative integer.

Question 3.
a. 16 × (-2) = ____
Answer: -32
16 × (-2) = -32
The product of two positive integers is always positive.
The product of two negative integers is always positive.
The product of one positive and one negative integer is always negative.
Here -2 is a negative integer and 16 is a positive integer therefore the result of their product is a negative integer.

b. -4 × (-1) = ____
Answer: 4
-4 × (-1) = 4
The product of two positive integers is always positive.
The product of two negative integers is always positive.
The product of one positive and one negative integer is always negative.
Here -4 and -1 both are negative integers therefore the result of their product is a positive integer.

c. 8 × (-11) = ____
Answer: -88
8 × (-11) = -88
The product of two positive integers is always positive.
The product of two negative integers is always positive.
The product of one positive and one negative integer is always negative.
Here -11 is a negative integer and 8 is a positive integer therefore the result of their product is a negative integer.

d. -7 × (-10) = ____
Answer: 70
-7 × (-10) = 70
The product of two positive integers is always positive.
The product of two negative integers is always positive.
The product of one positive and one negative integer is always negative.
Here -7 and -10 both are negative integers therefore the result of their product is a positive integer.

Question 4.
a. 5 × 8 = ____
Answer: 40
5 × 8 = 40
The product of two positive integers is always positive.
The product of two negative integers is always positive.
The product of one positive and one negative integer is always negative.
Therefore, here 5 and 8 both are positive integers hence their product is also positive.

b. 6 × (-6) = ____
Answer: -36
6 × (-6) = -36
The product of two positive integers is always positive.
The product of two negative integers is always positive.
The product of one positive and one negative integer is always negative.
Here -6 is a negative integer and 6 is a positive integer therefore the result of their product is a negative integer.

c. -13 × (-2) = ____
Answer: 26
The product of two positive integers is always positive.
The product of two negative integers is always positive.
The product of one positive and one negative integer is always negative.
Here -13 and -2 both are negative integers therefore the result of their product is a positive integer.

d. -9 × 9 = ____
Answer: -81
-9 × 9 = -81
The product of two positive integers is always positive.
The product of two negative integers is always positive.
The product of one positive and one negative integer is always negative.
Here -9 is a negative integer and 9 is a positive integer therefore the result of their product is a negative integer.

Question 5.
a. 17 × (-1) = ____
Answer: -17
17 × (-1) = -17
The product of two positive integers is always positive.
The product of two negative integers is always positive.
The product of one positive and one negative integer is always negative.
Here -1 is a negative integer and 17 is a positive integer therefore the result of their product is a negative integer.

b. 5 × (-2) = ____
Answer: -10
5 × (-2) = -10
The product of two positive integers is always positive.
The product of two negative integers is always positive.
The product of one positive and one negative integer is always negative.
Here -2 is a negative integer and 5 is a positive integer therefore the result of their product is a negative integer.

c. -14 × 3 = ____
Answer: -42
-14 × 3 = -42
The product of two positive integers is always positive.
The product of two negative integers is always positive.
The product of one positive and one negative integer is always negative.
Here -14 is a negative integer and 3 is a positive integer therefore the result of their product is a negative integer.

d. -7 × (-5) = ____
Answer: 35
-7 × (-5) = 35
The product of two positive integers is always positive.
The product of two negative integers is always positive.
The product of one positive and one negative integer is always negative.
Here -7 and -5 both are negative integers therefore the result of their product is a positive integer.

Question 6.
a. (-6) × 0 = ____
Answer: 0
(-6) × 0 = 0
The product of two positive integers is always positive.
The product of two negative integers is always positive.
The product of one positive and one negative integer is always negative.
The product of any integer with zero is always zero.
Therefore, -6 is a negative integer. The product of -6 and 0 results in 0.

b. 7 × 3 = ____
Answer: 24
7 × 3 = 24
The product of two positive integers is always positive.
The product of two negative integers is always positive.
The product of one positive and one negative integer is always negative.
Therefore, here 7 and 3 both are positive integers hence their product is also positive.

c. 6 × (-10) = ____
Answer: -60
6 × (-10) = -60
The product of two positive integers is always positive.
The product of two negative integers is always positive.
The product of one positive and one negative integer is always negative.
Here -10 is a negative integer and 6 is a positive integer therefore the result of their product is a negative integer.

d. (-3) × (-5) = ____
Answer: 15
(-3) × (-5) = 15
The product of two positive integers is always positive.
The product of two negative integers is always positive.
The product of one positive and one negative integer is always negative.
Here -3 and -5 both are negative integers therefore the result of their product is a positive integer.

Question 7.
a. 8 × (-2) = ____
Answer: -16
8 × (-2) = -16
The product of two positive integers is always positive.
The product of two negative integers is always positive.
The product of one positive and one negative integer is always negative.
Here -2 is a negative integer and 8 is a positive integer therefore the result of their product is a negative integer.

b. (-4) × (-10) = ____
Answer: 40
(-4) × (-10) = 40
The product of two positive integers is always positive.
The product of two negative integers is always positive.
The product of one positive and one negative integer is always negative.
Here -4 and -10 both are negative integers therefore the result of their product is a positive integer.

c. 10 × (-3) = ____
Answer: -30
10 × (-3) = -30
The product of two positive integers is always positive.
The product of two negative integers is always positive.
The product of one positive and one negative integer is always negative.
Here -3 is a negative integer and 10 is a positive integer therefore the result of their product is a negative integer.

d. 3 × 5 = ____
Answer: 15
3 × 5 = 15
The product of two positive integers is always positive.
The product of two negative integers is always positive.
The product of one positive and one negative integer is always negative.
Therefore, here 5 and 3 both are positive integers hence their product is also positive.

Question 8.
a. 9 × (-4) = ____
Answer: -36
9 × (-4) = -36
The product of two positive integers is always positive.
The product of two negative integers is always positive.
The product of one positive and one negative integer is always negative.
Here -4 is a negative integer and 9 is a positive integer therefore the result of their product is a negative integer.

b. 10 × 4 = ____
Answer: 40
10 × 4 = 40
The product of two positive integers is always positive.
The product of two negative integers is always positive.
The product of one positive and one negative integer is always negative.
Therefore, here 10 and 4 both are positive integers hence their product is also positive.

c. 10 × (-4) = ____
Answer:  -40
10 × (-4) = -40
The product of two positive integers is always positive.
The product of two negative integers is always positive.
The product of one positive and one negative integer is always negative.
Here -4 is a negative integer and 10  is a positive integer therefore the result of their product is a negative integer.

d. 5 × 9 = ____
Answer: 45
5 × 9 = 45
The product of two positive integers is always positive.
The product of two negative integers is always positive.
The product of one positive and one negative integer is always negative.
Therefore, here 5 and 9 both are positive integers hence their product is also positive.

Question 9.
a. 0 × (-10) = ____
Answer: 0
0 × (-10) = 0
The product of two positive integers is always positive.
The product of two negative integers is always positive.
The product of one positive and one negative integer is always negative.
The product of any integer with zero is always zero.
Therefore, -10 is a negative integer. The product of -6 and 0 results in 0.

b. 11 × 11 = ____
Answer: 121
11 × 11 = 121
The product of two positive integers is always positive.
The product of two negative integers is always positive.
The product of one positive and one negative integer is always negative.
Therefore, here 11 and 11 both are positive integers hence their product is also positive.

c. 2 × 3 = ___
Answer: 6
2 × 3 = 6
The product of two positive integers is always positive.
The product of two negative integers is always positive.
The product of one positive and one negative integer is always negative.
Therefore, here 2 and 3 both are positive integers hence their product is also positive.

d. (-4) × (-12) = ___
Answer: 48
(-4) × (-12) = 48
The product of two positive integers is always positive.
The product of two negative integers is always positive.
The product of one positive and one negative integer is always negative.
Here -4 and -12 both are negative integers therefore the result of their product is a positive integer

Question 10.
a. (-4) × (-6) = ____
Answer: 24
(-4) × (-6) = 24
The product of two positive integers is always positive.
The product of two negative integers is always positive.
The product of one positive and one negative integer is always negative.
Here -4 and -6 both are negative integers therefore the result of their product is a positive integer.

b. (-10) × (-2) = ____
Answer: 20
(-10) × (-2) = 20
The product of two positive integers is always positive.
The product of two negative integers is always positive.
The product of one positive and one negative integer is always negative.
Here -2 and -10 both are negative integers therefore the result of their product is a positive integer.

c. 3 × 12 = ___
Answer: 36
3 × 12 = 36
The product of two positive integers is always positive.
The product of two negative integers is always positive.
The product of one positive and one negative integer is always negative.
Therefore, here 12 and 3 both are positive integers hence their product is also positive.

d. 4 × 7 = ______
Answer: 28
4 × 7 = 28
The product of two positive integers is always positive.
The product of two negative integers is always positive.
The product of one positive and one negative integer is always negative.
Therefore, here 4 and 7 both are positive integers hence their product is also positive.

Multiply

Question 1.
a. 2 × 4 = ____
Answer: 8
2 × 4 = 8
The product of two positive integers is always positive.
The product of two negative integers is always positive.
The product of one positive and one negative integer is always negative.
Therefore, here 2 and 4 both are positive integers hence their product is also positive.

b. 3 × (-3) = ____
Answer: -9
3 × (-3) = -9
The product of two positive integers is always positive.
The product of two negative integers is always positive.
The product of one positive and one negative integer is always negative.
Here -2 is a negative integer and 3 is a positive integer therefore the result of their product is a negative integer.

c. -12 × (-12) = ____
Answer: 144
-12 × (-12) = 144
The product of two positive integers is always positive.
The product of two negative integers is always positive.
The product of one positive and one negative integer is always negative.
Here -12 and -12 both are negative integers therefore the result of their product is a positive integer.

Question 2.
a. 9 × (-7) = ____
Answer: -63
9 × (-7) = -63
The product of two positive integers is always positive.
The product of two negative integers is always positive.
The product of one positive and one negative integer is always negative.
Here -7 is a negative integer and 9  is a positive integer therefore the result of their product is a negative integer.

b. 9 × 8 = ____
Answer: 72
9 × 8 = 72
The product of two positive integers is always positive.
The product of two negative integers is always positive.
The product of one positive and one negative integer is always negative.
Therefore, here 9 and 8 both are positive integers hence their product is also positive.

c. 4 × (-12) = ____
Answer: -48
The product of two positive integers is always positive.
The product of two negative integers is always positive.
The product of one positive and one negative integer is always negative.
Here -12 is a negative integer and 4 is a positive integer therefore the result of their product is a negative integer.

Question 3.
a. 10 × (-1) = ____
Answer: -10
10 × (-1) = -10
The product of two positive integers is always positive.
The product of two negative integers is always positive.
The product of one positive and one negative integer is always negative.
Here -1 is a negative integer and 10 is a positive integer therefore the result of their product is a negative integer.

b. 7 × 4 = ____
Answer: 28
7 × 4 = 28
The product of two positive integers is always positive.
The product of two negative integers is always positive.
The product of one positive and one negative integer is always negative.
Therefore, here 7 and 4 both are positive integers hence their product is also positive.

c. 6 × (-5) = ____
Answer: -30
6 × (-5) = -30
The product of two positive integers is always positive.
The product of two negative integers is always positive.
The product of one positive and one negative integer is always negative.
Here -5 is a negative integer and 6 is a positive integer therefore the result of their product is a negative integer.

Question 4.
a. (-2) × 1 = ____
Answer: -2
(-2) × 1 = -2
The product of two positive integers is always positive.
The product of two negative integers is always positive.
The product of one positive and one negative integer is always negative.
Here -2 is a negative integer and 1 is a positive integer therefore the result of their product is a negative integer.

b. (-11) × 2 = ___
Answer: -22
(-11) × 2 = -22
The product of two positive integers is always positive.
The product of two negative integers is always positive.
The product of one positive and one negative integer is always negative.
Here -11 is a negative integer and 2 is a positive integer therefore the result of their product is a negative integer.

c. 12 × 3 = ____
Answer: 36
12 × 3 = 36
The product of two positive integers is always positive.
The product of two negative integers is always positive.
The product of one positive and one negative integer is always negative.
Therefore, here 12 and 3 both are positive integers hence their product is also positive.

Question 5.
a. 11 × 2 = ____
Answer: 22
11 × 2 = 22
The product of two positive integers is always positive.
The product of two negative integers is always positive.
The product of one positive and one negative integer is always negative.
Therefore, here 11 and 2 both are positive integers hence their product is also positive.

b. 7 × 11 = ____
Answer: 77
7 × 11 = 77
The product of two positive integers is always positive.
The product of two negative integers is always positive.
The product of one positive and one negative integer is always negative.
Therefore, here 7 and 11 both are positive integers hence their product is also positive.

c. (-12) × 7 = ____
Answer: -84
(-12) × 7 = -84
The product of two positive integers is always positive.
The product of two negative integers is always positive.
The product of one positive and one negative integer is always negative.
Here -12 is a negative integer and 7 is a positive integer therefore the result of their product is a negative integer.

Question 6.
a. 8 × 5 = ____
Answer: 40
8 × 5 = 40
The product of two positive integers is always positive.
The product of two negative integers is always positive.
The product of one positive and one negative integer is always negative.
Therefore, here 5 and 8 both are positive integers hence their product is also positive.

b. 11 × 7 = ____
Answer: 77
11 × 7 = 77
The product of two positive integers is always positive.
The product of two negative integers is always positive.
The product of one positive and one negative integer is always negative.
Therefore, here 11 and 7 both are positive integers hence their product is also positive.

c. 1 × (-6) = ____
Answer: -6
1 × (-6) = -6
The product of two positive integers is always positive.
The product of two negative integers is always positive.
The product of one positive and one negative integer is always negative.
Here -6 is a negative integer and 1 is a positive integer therefore the result of their product is a negative integer.

Question 7.
a. 6 × (-2) = ____
Answer: -12
6 × (-2) = -12
The product of two positive integers is always positive.
The product of two negative integers is always positive.
The product of one positive and one negative integer is always negative.
Here -2 is a negative integer and 6 is a positive integer therefore the result of their product is a negative integer.

b. 9 × (-4) = ____
Answer: -36
9 × (-4) = -36
The product of two positive integers is always positive.
The product of two negative integers is always positive.
The product of one positive and one negative integer is always negative.
Here -4 is a negative integer and 9 is a positive integer therefore the result of their product is a negative integer.

c. (-4) × (-3) = ____
Answer: 12
(-4) × (-3) = 12
The product of two positive integers is always positive.
The product of two negative integers is always positive.
The product of one positive and one negative integer is always negative.
Here -4 and -3 both are negative integers therefore the result of their product is a positive integer.

Question 8.
a. 2 × 7 = ____
Answer: 14
2 × 7 = 14
The product of two positive integers is always positive.
The product of two negative integers is always positive.
The product of one positive and one negative integer is always negative.
Therefore, here 2 and 7 both are positive integers hence their product is also positive.

b. 3 × 8 = ____
Answer: 24
3 × 8 = 24
The product of two positive integers is always positive.
The product of two negative integers is always positive.
The product of one positive and one negative integer is always negative.
Therefore, here 3 and 8 both are positive integers hence their product is also positive.

c. 3 × (-7) = ____
Answer: -21
3 × (-7) = -21
The product of two positive integers is always positive.
The product of two negative integers is always positive.
The product of one positive and one negative integer is always negative.
Here -7 is a negative integer and 3 is a positive integer therefore the result of their product is a negative integer.

Question 9.
a. (-6) × (-3) = _____
Answer: 18
(-6) × (-3) = 18
The product of two positive integers is always positive.
The product of two negative integers is always positive.
The product of one positive and one negative integer is always negative.
Here -6 and -3 both are negative integers therefore the result of their product is a positive integer.

b. (-8) × 8 = ____
Answer: -64
(-8) × 8 = -64
The product of two positive integers is always positive.
The product of two negative integers is always positive.
The product of one positive and one negative integer is always negative.
Here -8 is a negative integer and 8 is a positive integer therefore the result of their product is a negative integer.

c. 2 × 5 = ____
Answer: 10
2 × 5 = 10
The product of two positive integers is always positive.
The product of two negative integers is always positive.
The product of one positive and one negative integer is always negative.
Therefore, here 2 and 5 both are positive integers hence their product is also positive.

Question 10.
a. 6 × 9 = ____
Answer: 54
6 × 9 = 54
The product of two positive integers is always positive.
The product of two negative integers is always positive.
The product of one positive and one negative integer is always negative.
Therefore, here 9 and 6 both are positive integers hence their product is also positive.

b. (-4) × 8 = ____
Answer: -32
(-4) × 8 = -32
The product of two positive integers is always positive.
The product of two negative integers is always positive.
The product of one positive and one negative integer is always negative.
Here -4 is a negative integer and 8 is a positive integer therefore the result of their product is a negative integer.

c. 6 × (-5) = ____
Answer: -30
6 × (-5) = -30
The product of two positive integers is always positive.
The product of two negative integers is always positive.
The product of one positive and one negative integer is always negative.
Here -5 is a negative integer and 6 is a positive integer therefore the result of their product is a negative integer.

Question 11.
a. 12 × 32 = ____
Answer: 384
12 × 32 = 384
The product of two positive integers is always positive.
The product of two negative integers is always positive.
The product of one positive and one negative integer is always negative.
Therefore, here 12 and 32 both are positive integers hence their product is also positive.

b. 7 × (-14) = ____
Answer: -98
7 × (-14) = -98
The product of two positive integers is always positive.
The product of two negative integers is always positive.
The product of one positive and one negative integer is always negative.
Here -14 is a negative integer and 7 is a positive integer therefore the result of their product is a negative integer.

c. -19 × (-4) = ____
Answer: 76
-19 × (-4) = 76
The product of two positive integers is always positive.
The product of two negative integers is always positive.
The product of one positive and one negative integer is always negative.
Here -19 and -4 both are negative integers therefore the result of their product is a positive integer.

Question 12.
a. 11 × (-41) = ____
Answer: -451
11 × (-41) = -451
The product of two positive integers is always positive.
The product of two negative integers is always positive.
The product of one positive and one negative integer is always negative.
Here -41 is a negative integer and 11 is a positive integer therefore the result of their product is a negative integer.

b. 4 × 33 = ____
Answer: 132
4 × 33 = 132
The product of two positive integers is always positive.
The product of two negative integers is always positive.
The product of one positive and one negative integer is always negative.
Therefore, here 4 and 33 both are positive integers hence their product is also positive.

c. 18 × (-18) = ____
Answer: -324
18 × (-18) = -324
The product of two positive integers is always positive.
The product of two negative integers is always positive.
The product of one positive and one negative integer is always negative.
Here -41 is a negative integer and 11 is a positive integer therefore the result of their product is a negative integer.

Question 13.
a. 11 × (-46) = ____
Answer: -506
11 × (-46) = -506
The product of two positive integers is always positive.
The product of two negative integers is always positive.
The product of one positive and one negative integer is always negative.
Here -46 is a negative integer and 11 is a positive integer therefore the result of their product is a negative integer.

b. 21 × 4 = ____
Answer: 84
21 × 4 = 84
The product of two positive integers is always positive.
The product of two negative integers is always positive.
The product of one positive and one negative integer is always negative.
Therefore, here 21 and 4 both are positive integers hence their product is also positive.

c. 13 × (-5) = ____
Answer: -65
13 × (-5) = -65
The product of two positive integers is always positive.
The product of two negative integers is always positive.
The product of one positive and one negative integer is always negative.
Here -5 is a negative integer and 13 is a positive integer therefore the result of their product is a negative integer.

Question 14.
a. (-27) × 16 = ____
Answer: -432
(-27) × 16 = -432
The product of two positive integers is always positive.
The product of two negative integers is always positive.
The product of one positive and one negative integer is always negative.
Here -27 is a negative integer and 16 is a positive integer therefore the result of their product is a negative integer.

b. (-11) × 36 = ____
Answer: -396
(-11) × 36 = -396
The product of two positive integers is always positive.
The product of two negative integers is always positive.
The product of one positive and one negative integer is always negative.
Here -11 is a negative integer and 36 is a positive integer therefore the result of their product is a negative integer.

c. (-6) × (-92) = ____
Answer: 552
(-6) × (-92) = 552
The product of two positive integers is always positive.
The product of two negative integers is always positive.
The product of one positive and one negative integer is always negative.
Here -6 and -92 both are negative integers therefore the result of their product is a positive integer.

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