How to Divide Negative Numbers

Problem

-42 \div 7

Answer

-6

Division works like multiplication for signs: two negatives make a positive, and one negative makes a negative. Divide first, then fix the sign.

Step-by-step solution

Divide the numbers and ignore the signs for now.
$42 \div 7 = 6$
Why: The size of the quotient comes from the two numbers.
Count the negative signs.
$1\ \text{negative sign}$
Why: Only the dividend is negative.
Apply the sign rule.
$\text{odd count} \Rightarrow \text{negative quotient}$
Why: Division follows the same sign rules as multiplication.
Write the answer with the sign.
$-6$
Why: One negative number, so the quotient is negative.

Making the answer positive because 42 is larger than 7. The sign count decides.
Dividing in the wrong order and using 7 divided by 42.
Copying the rule for addition. The sign rules for division are not the same as the rules for adding.

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