Pre-Algebra · Integers and negative numbers

How to Add a Positive and a Negative Number

Problem

−7+4-7 + 4

Answer

−3-3

Adding a positive number and a negative number is a tug of war. The larger size wins, and the answer keeps the sign of the larger number.

Step-by-step solution

  1. Start at -7 on the number line.

    −7-7

    Why: The first number is the starting point.

  2. Move 4 places to the right.

    4 steps right4\ \text{steps right}

    Why: Adding a positive number moves right.

  3. Read the landing point.

    −7+4=−3-7 + 4 = -3

    Why: The move stops at -3, which is 4 units above -7.

Common mistakes

  • Moving left when adding a positive number.
  • Writing 11 by adding 7 + 4 and ignoring the signs.
  • Losing the sign of the larger number. The result stays negative.

Practice problems

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

  1. −9+3-9 + 3

    Show answer

    −6-6

  2. 5+(−8)5 + (-8)

    Show answer

    −3-3

  3. −12+12-12 + 12

    Show answer

    00

  4. −6+10-6 + 10

    Show answer

    44

  5. 8+(−15)8 + (-15)

    Show answer

    −7-7