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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

Recognize opposite signs

\[-7~+~3\]

One addend is negative and the other is positive, so compare magnitudes and find their difference.

02

Compare and subtract magnitudes

\[|-7|~=~7~>~3;~7~-~3~=~4\]

The unmatched magnitude after canceling three positive-negative pairs is 4.

03

Apply the sign and answer

\[-4\]

The larger magnitude came from -7, so the sum is negative four.

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Another way

  1. Start at -7 and move 3 units toward zero, landing at -4.

!

Common mistake

Do not add the magnitudes to get 10. Opposite signs cancel, so subtract the smaller magnitude from the larger.

Solution walkthrough video