Pre-Algebra · Integers and negative numbers

How to Add and Subtract Negative Numbers

Problem

-7 + 3 - (-4)

Answer

0

Negative numbers sit to the left of zero on the number line. Every addition moves you along the line: right for a positive number, left for a negative number.

Step-by-step solution

Start at -7 and move right 3 on the number line.
$-7 + 3 = -4$
Why: Adding a positive number moves you to the right.
Rewrite the subtraction as adding the opposite.
$-4 - (-4) = -4 + 4$
Why: Subtracting a negative number is the same as adding its opposite.
Add the last two numbers.
$-4 + 4 = 0$
Why: A number and its opposite add to zero.
Write the answer.
$0$
Why: The expression has one value.

Common mistakes

Treating -7 + 3 as -10. Adding a positive number moves right, toward zero.
Keeping the minus sign: -4 - (-4) is 0, not -8.
Ignoring the direction of the moves on the number line.

Practice problems

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

$-5 + 8$

Show answer

$3$
$4 - 9$

Show answer

$-5$
$-3 + (-6)$

Show answer

$-9$
$7 - (-2)$

Show answer

$9$
$-8 + 5 - 1$

Show answer

$-4$