How to Add and Subtract Integers? (+FREE Worksheet!)

Integers are the whole numbers, their opposites, and zero: …, −3, −2, −1, 0, 1, 2, 3, … Adding and subtracting them is one of the first key skills in Algebra 1, and once you know a few simple sign rules, every problem becomes routine. This guide walks you through the rules step by step, with worked examples, two short video lessons, and a free worksheet so you can practice.

What Are Integers?

An integer is a number with no fraction or decimal part — positive numbers like 7, negative numbers \(\color{blue}{\text{ like } -7}\), and 0. Every integer has an opposite the same distance from zero: the opposite of 5 \(\color{blue}{\text{ is } -5}\), and the opposite \(\color{blue}{\text{ of } -5}\) is 5.

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How to Add Integers

Same signs → add and keep the sign

When both numbers have the same sign, add their values and keep that sign.

1. \(\color{blue}{8 + 5 = 13}\)
2. \(\color{blue}{(–8) + (–5) = –13}\)

Different signs → subtract and take the bigger sign

Subtract the smaller value from the larger, then keep the sign of the number with the larger absolute value.

1. \(\color{blue}{(–9) + 4 = –5}\)
2. \(\color{blue}{10 + (–3) = 7}\)

How to Subtract Integers

The golden rule for subtraction is add the opposite: change the subtraction to addition and flip the sign of the second number, then use the addition rules above.

1. \(\color{blue}{6 – 9 = 6 + (–9) = –3}\)
2. \(\color{blue}{(–4) – (–7) = (–4) + 7 = 3}\)
3. \(\color{blue}{(–5) – 8 = (–5) + (–8) = –13}\)

Step-by-Step Summary

1. If it is subtraction, rewrite it as “add the opposite.”
2. Same signs: add the values and keep the sign.
3. Different signs: subtract the values and keep the sign of the larger one.

Watch: Adding & Subtracting Integers

This Math Antics lesson uses a number line to show why the rules work:

Adding and Subtracting Integers – Worked Examples

Example 1: Find the sum: \(\color{blue}{(–7) + (–6)}\). Same signs, so add and keep the negative: \(\color{blue}{(–7) + (–6) = –13}\).

Example 2: Find the sum: \(\color{blue}{12 + (–5)}\). Different signs: \(\color{blue}{12 – 5 = 7}\); the larger value is positive, so \(\color{blue}{12 + (–5) = 7}\).

Example 3: Find the difference: \(\color{blue}{(–9) – (–15)}\). Add the opposite: \(\color{blue}{(–9) + 15 = 6}\).

Example 4: Simplify: \(\color{blue}{4 + (–30) + (45 – 34)}\). Parentheses first: \(\color{blue}{45 – 34 = 11}\); then \(\color{blue}{4 + (–30) = –26}\) and \(\color{blue}{–26 + 11 = –15}\).

More Practice: Step-by-Step Video Review

Watch this practice video for additional examples and reinforcement:

Exercises for Adding and Subtracting Integers

Find the sum and the difference.

1. \(\color{blue}{(– 12) + (– 4)}\)
2. \(\color{blue}{5 + (– 24)}\)
3. \(\color{blue}{4 + (– 30) + (45 – 34)}\)
4. \(\color{blue}{( – 14) – (– 9) – (18)}\)
5. \(\color{blue}{( – 9) – (– 25)}\)
6. \(\color{blue}{(55) – (– 5) + (– 4)}\)

Download Adding and Subtracting Integers Worksheet

Answers

1. \(\color{blue}{-16}\)
2. \(\color{blue}{-19}\)
3. \(\color{blue}{-15}\)
4. \(\color{blue}{-23}\)
5. \(\color{blue}{16}\)
6. \(\color{blue}{56}\)

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Frequently Asked Questions

What is the rule for adding integers with different signs?

Subtract the smaller value from the larger, then give the answer the sign of the number with the larger absolute value. For example, \(\color{blue}{(–9) + 4 = –5}\).

How do you subtract a negative integer?

Subtracting a negative is the same as adding a positive: \(\color{blue}{a – (–b) = a + b}\). So \(\color{blue}{3 – (–5) = 8}\).

Is adding and subtracting integers the same thing?

Almost — every subtraction can be rewritten as addition by “adding the opposite,” so once you can add integers, subtraction follows the same rules.

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