Multiplication and Division of Integers

Rule:
Like Sign → Positive
Unlike Sign → Negative

If the number is positive, remove the parenthesis.

A. Like Sign is Postiive

Multiplication

4 × 3 = 12

(−4)(−3) = 12

Division

12 ÷ 3 = 4

(−12) ÷ (−3) = 4

B. Unlike Sign is Negative

Multiplication

4(−3) = −12

(−4)3 = −12

Division

12 ÷ (−3) = −4

(−12) ÷ 3 = −4

C. Expressions with 3 or More Terms

Rule:
Even number of negative numbers = Positive
Odd number of negative numbers = Negative

Even numbers: 2, 4, 6, 8, 10
Odd numbers: 1, 3, 5, 7, 9

Example 1 — Multiplication

(−1)(−2)(−3)

Step 1 — Multiply the first two terms (−1)(−2)(−3) 2(−3) Step 2 — Multiply the result by the third term 2(−3) −6

Final Answer: (−1)(−2)(−3) = −6

Example 2 — Division

−36 ÷ (−4) ÷ (−9)

Step 1 — Divide the first two terms −36 ÷ (−4) ÷ (−9) 9 ÷ (−9) Step 2 — Divide the result by the third term 9 ÷ (−9) −1

Final Answer: −36 ÷ (−4) ÷ (−9) = −1

D. Quiz

1. 7(−3) =

A. 21 B. −21 C. −10 D. 10

Solution: 7 × (−3) = −21

2. (−5)4 =

A. 20 B. 1 C. −20 D. −9

Solution: (−5) × 4 = −20

3. (−8)(−2) =

A. 16 B. −16 C. 10 D. −10

Solution: (−8) × (−2) = 16

4. 9(−1) =

A. 10 B. 8 C. 9 D. −9

Solution: 9 × (−1) = −9

5. (−6)3 =

A. 18 B. −18 C. −9 D. 9

Solution: (−6) × 3 = −18

6. 30 ÷ (−6) =

A. −5 B. 5 C. −6 D. 6

Solution: 30 ÷ (−6) = −5

7. (−48) ÷ 8 =

A. 8 B. 7 C. 5 D. −6

Solution: (−48) ÷ 8 = −6

8. (−27) ÷ (−9) =

A. −3 B. 9 C. 3 D. −9

Solution: (−27) ÷ (−9) = 3

9. 56 ÷ (−7) =

A. 7 B. −8 C. 8 D. −7

Solution: 56 ÷ (−7) = −8

10. (−36) ÷ 6 =

A. −6 B. 6 C. −5 D. 5

Solution: (−36) ÷ 6 = −6