Pre-Algebra · Integers and negative numbers

How to Multiply Negative Numbers

Problem

-6 \times 4

Answer

-24

A product is negative when an odd number of its factors are negative. Count the negative signs, multiply the numbers, then attach the sign the count gives.

Step-by-step solution

Multiply the numbers and ignore the signs for now.
$6 \times 4 = 24$
Why: The value of the product comes from the numbers themselves.
Count the negative signs.
$1\ \text{negative sign}$
Why: The sign of the answer depends only on how many factors are negative.
Apply the sign rule.
$\text{odd count} \Rightarrow \text{negative product}$
Why: An odd number of negative factors makes the product negative. An even count makes it positive.
Write the answer with the sign.
$-24$
Why: One negative factor, so the product is negative.

Common mistakes

Making the answer positive because 6 and 4 are larger than the sign. The sign count decides, not the size.
Adding the numbers instead of multiplying. -6 times 4 is not -2.
Forgetting the rule: one negative factor gives a negative product.

Practice problems

Use the same method. Work each problem on paper, then open the answer to check.

$-3 \times 5$

Show answer

$-15$
$-7 \times (-2)$

Show answer

$14$
$8 \times (-4)$

Show answer

$-32$
$-9 \times (-3)$

Show answer

$27$
$-5 \times 6$

Show answer

$-30$