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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. In Number Foundations, the goal is not just to get an answer but to recognize the structure of the problem, choose a reliable strategy, and explain why the result is reasonable. The practice set now includes targeted skill work, transfer questions, and mixed review so students build fluency and retention.

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.
  4. Connect the calculation back to Adding and Subtracting Integers so the method, not just the arithmetic, is clear.

Answer: 3

Lesson preview: this page shows 5 practice items. The interactive activity contains 28 practice items and 15 quiz items (typed response and multiple choice). Counts include repeated prompts and variants.

Practice problems

1. Compute -14 + 6.

Show solution
  1. The signs are different.
  2. 14 - 6 = 8, and -14 has the larger distance from zero.
  3. The answer is -8.

Answer: -8

2. Compute -5 + -7.

Show solution
  1. Both numbers are negative.
  2. Add 5 + 7 and keep the negative sign.

Answer: -12

3. What is 10 + -3?

Choices: 13 · 7 · -7 · -13

Show solution
  1. The signs are different.
  2. 10 - 3 = 7, and 10 is farther from zero.

Answer: 7

4. Compute 7 - 12.

Show solution
  1. Rewrite 7 - 12 as 7 + -12.
  2. 12 is farther from zero than 7.
  3. The answer is -5.

Answer: -5

5. Compute -9 - 4.

Show solution
  1. Rewrite as -9 + -4.
  2. Both numbers are negative, so add and keep the negative sign.

Answer: -13

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