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Multiplying and Dividing Signed Numbers

22 min Signed Numbers

Multiplying and Dividing Signed Numbers

Sign Rules

Signs	Result
$(+)(+)$ or $(-)(-)$	Positive
$(+)(-)$ or $(-)(+)$	Negative

Same signs → positive. Different signs → negative.

Example 1

$(-6) \times (-4)$

Same signs → positive. $(-6)(-4) = 24$.

Example 2

$(-3) \times 5$

Different signs → negative. $(-3)(5) = -15$.

Example 3

$(-20) \div (-5)$

Same signs → positive. $(-20) \div (-5) = 4$.

Example 4

$18 \div (-3)$

Different signs → negative. $18 \div (-3) = -6$.

Multiple Factors

Rule

Count the negative signs: even → positive; odd → negative.

Example 5

$(-2)(-3)(-4)$

3 negatives (odd) → negative. $2 \times 3 \times 4 = 24$. Answer: $-24$.

Exponents with Signed Numbers

Critical Distinction

$-3^2 = -(3^2) = -9$ ← exponent applies only to 3

$(-3)^2 = (-3)(-3) = 9$ ← exponent applies to $-3$

Example 6

Evaluate: $(-2)^3$ and $(-2)^4$

$(-2)^3 = -8$ (odd exponent → negative).

$(-2)^4 = 16$ (even exponent → positive).

Practice Problems

1. $(-7)(8)$

2. $(-9)(-6)$

3. $36 \div (-4)$

4. $(-48) \div (-6)$

5. $(-2)(3)(-5)$

6. $(-1)^{10}$

7. $-5^2$

8. $(-5)^2$

9. $(-4)(-2)(-1)(-3)$

10. $\dfrac{(-3)(12)}{-9}$

11. $(-3)^3$

12. $(-1)^{55}$

13. $(-10)(0)(-5)$

14. $\dfrac{-72}{-8}$

15. $(-2)^5$

Show Answer Key

1. $-56$

2. $54$

3. $-9$

4. $8$

5. $30$

6. $1$

7. $-25$

8. $25$

9. $24$ (4 negatives → positive)

10. $4$

11. $-27$

12. $-1$

13. $0$

14. $9$

15. $-32$

Adding and Subtracting Signed Numbers Order of Operations with Signed Numbers

Multiplying and Dividing Signed Numbers