# 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 = ____
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 = ____
-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) = ____
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) = _____
-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 = ____
-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) = ____
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) = ____
-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 = ____
-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) = ____
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) = ____
-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) = ____
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) = ____
-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 = ____
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) = ____
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) = ____
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 = ____
-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) = ____
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) = ____
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 = ____
-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) = ____
-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 = ____
(-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 = ____
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) = ____
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) = ____
(-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) = ____
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) = ____
(-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) = ____
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 = ____
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) = ____
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 = ____
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) = ____
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 = ____
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) = ____
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 = ____
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 = ___
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) = ___
(-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) = ____
(-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) = ____
(-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 = ___
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 = ______
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 = ____
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) = ____
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) = ____
-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) = ____
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 = ____
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) = ____
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) = ____
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 = ____
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) = ____
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 = ____
(-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 = ___
(-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 = ____
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 = ____
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 = ____
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 = ____
(-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 = ____
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 = ____
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) = ____
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) = ____
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) = ____
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) = ____
(-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 = ____
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 = ____
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) = ____
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) = _____
(-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 = ____
(-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 = ____
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 = ____
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 = ____
(-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) = ____
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 = ____
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) = ____
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) = ____
-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) = ____
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 = ____
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) = ____
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) = ____
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 = ____
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) = ____
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 = ____
(-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 = ____