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All courses Math Foundations · MF.SN.2 24 of 60
Add and subtract signed numbers and explain the meaning of the sign changes.

Add signed numbers

Problem
Find the sum: -7 + 3
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Hint

Look at the signs in -7 + 3. Since one number is negative and one is positive, start by comparing their magnitudes: 7 and 3.

For opposite signs, subtract the magnitudes and keep the sign of the number with the greater magnitude.

Solution walkthrough

01

Notice the signs are different

\[-7~+~3\]

One addend is negative and the other is positive. For opposite signs, find the difference of their magnitudes and keep the sign of the number with greater magnitude.

02

Compare the magnitudes

\[|{-7}|~=~7~\text{and}~|3|~=~3\]

The negative number has magnitude 7, which is larger than 3. That means the result will be negative.

03

Subtract the magnitudes

\[7~-~3~=~4\]

With opposite signs, subtract instead of adding the magnitudes.

04

State the sum

\[-7~+~3~=~-4\]

The larger magnitude came from -7, so the sum keeps a negative sign. The sum is -4.

+

Another way

  1. Use a number line: start at -7 and move 3 units to the right. You land on -4.

!

Common mistake

A common mistake is to add the magnitudes and write -10 or 10. Because the signs are different, you should subtract 7 and 3, then keep the sign of the number with greater magnitude, which is -7.