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.