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Adding and Subtracting Integers

A free Pre-Algebra lesson from the “Number Foundations” unit, with a worked example and practice problems including step-by-step solutions.

To add integers with the same sign, add their distances from zero and keep the sign. With different signs, subtract the smaller distance from the larger distance and keep the sign of the number farther from zero. Subtracting an integer is the same as adding its opposite.

What you'll learn

Why it matters: Account deposits and withdrawals, temperature swings, and football yardage gains and losses all need adding and subtracting signed numbers. Subtracting a negative shows up whenever a previous loss is reversed.

Worked example

Problem. Evaluate -6 + 9.

  1. The signs are different, so compare distances from zero.
  2. 9 is 3 more than 6.
  3. The positive number has the greater distance, so the answer is 3.

Answer: 3

Practice problems

1. Compute -14 + 6.

Show solution
  1. Warm-up: First identify exactly what the question is asking: Compute -14 + 6.
  2. For signed numbers, track both distance from zero and direction so the sign of the answer makes sense.
  3. The signs are different.
  4. 14 - 6 = 8, and -14 has the larger distance from zero.
  5. The answer is -8.
  6. Check the result by substituting or estimating: the response should match -8 and make sense in the original problem.

Answer: -8

2. Compute -5 + -7.

Show solution
  1. Warm-up: First identify exactly what the question is asking: Compute -5 + -7.
  2. For signed numbers, track both distance from zero and direction so the sign of the answer makes sense.
  3. Both numbers are negative.
  4. Add 5 + 7 and keep the negative sign.
  5. Check the result by substituting or estimating: the response should match -12 and make sense in the original problem.

Answer: -12

3. What is 10 + -3?

Choices: 13 · 7 · -7 · -13

Show solution
  1. Warm-up: First identify exactly what the question is asking: What is 10 + -3?
  2. For signed numbers, track both distance from zero and direction so the sign of the answer makes sense.
  3. The signs are different.
  4. 10 - 3 = 7, and 10 is farther from zero.
  5. Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.

Answer: 7

4. Compute 7 - 12.

Show solution
  1. Core Practice: First identify exactly what the question is asking: Compute 7 - 12.
  2. Choose the operation or relationship that matches the wording, then carry it out one clear step at a time.
  3. Rewrite 7 - 12 as 7 + -12.
  4. 12 is farther from zero than 7.
  5. The answer is -5.
  6. Check the result by substituting or estimating: the response should match -5 and make sense in the original problem.

Answer: -5

5. Compute -9 - 4.

Show solution
  1. Core Practice: First identify exactly what the question is asking: Compute -9 - 4.
  2. For signed numbers, track both distance from zero and direction so the sign of the answer makes sense.
  3. Rewrite as -9 + -4.
  4. Both numbers are negative, so add and keep the negative sign.
  5. Check the result by substituting or estimating: the response should match -13 and make sense in the original problem.

Answer: -13

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