Adding and Subtracting Integers

What You Will Learn

• Add integers with the same or different signs.
• Subtract positive and negative integers.
• Use a number line to understand movement in both directions.
• Rewrite subtraction as addition of the opposite number.
• Solve everyday problems involving positive and negative values.

1. Quick Review: What Are Integers?

Integers are whole numbers, their negative opposites and zero. They do not include fractions or decimal parts.

Positive integers are greater than zero. Negative integers are less than zero. Zero is neither positive nor negative.

Numbers become greater as you move to the right and smaller as you move to the left.

2. Add Integers with the Same Sign

When two integers have the same sign, add their absolute values and keep their common sign.

Worked example: −8 + (−5)

1. Both numbers are negative.
2. Add their absolute values: 8 + 5 = 13.
3. Keep the negative sign.

Answer: −13.

3. Add Integers with Different Signs

When the signs are different, subtract the smaller absolute value from the larger absolute value. Keep the sign of the number with the larger absolute value.

Worked example: 9 + (−4)

1. The absolute values are 9 and 4.
2. Subtract: 9 − 4 = 5.
3. Since 9 has the larger absolute value and is positive, the answer is positive.

Answer: 5.

Worked example: −11 + 6

Subtract 6 from 11 to get 5. The negative number has the larger absolute value, so the answer is −5.

4. Use a Number Line for Addition

Start at the first number. For a positive number, move right. For a negative number, move left.

Example: 2 + (−5)

1. Start at 2.
2. Adding −5 means move 5 places to the left.
3. You land on −3.

Answer: −3. A number line is especially helpful when you are learning the meaning of negative values.

5. Subtracting an Integer

Subtraction can be rewritten as addition of the opposite. Change the subtraction sign to addition, then change the sign of the number being subtracted.

Worked example 1: 7 − 10

Rewrite as 7 + (−10). The signs are different, and 10 has the larger absolute value. The answer is −3.

Worked example 2: 5 − (−3)

Rewrite as 5 + 3. Subtracting a negative is the same as adding its positive opposite. The answer is 8.

Worked example 3: −4 − 6

Rewrite as −4 + (−6). Add 4 and 6 and keep the negative sign. The answer is −10.

Worked example 4: −4 − (−6)

Rewrite as −4 + 6. The signs differ; 6 has the larger absolute value, so the answer is 2.

6. A Simple Sign Guide

7. Integer Calculations in Everyday Life

Temperature

The temperature is −3°C in the morning. It rises by 8°C. The new temperature is −3 + 8 = 5°C.

Money

Your account balance is −$12. You deposit $20. The new balance is −12 + 20 = $8.

Elevation

A diver is 6 metres below sea level (−6 m) and descends another 4 metres. The new position is −6 + (−4) = −10 m.

Change in temperature

The temperature changes from 4°C to −2°C. The change is −2 − 4 = −6°C, a drop of 6 degrees.

8. Common Mistakes to Avoid

9. Practice Exercises

Try these questions before revealing the answers.

1. −5 + (−7)
2. 12 + (−8)
3. −9 + 4
4. 6 − (−3)
5. −2 − 7
6. −4 − (−9)
7. The temperature is −6°C and rises by 11°C. What is the new temperature?
8. A lift is on floor 3 and travels down 7 floors. Which floor does it reach?

10. Test Your Understanding

Select one answer for each question, then choose Check Answers. Each question is worth one point.

11. Free Printable Worksheet

Print this worksheet or save it as a PDF for extra practice.

12. Lesson Summary

• For two integers with the same sign, add their absolute values and keep the sign.
• For different signs, subtract the smaller absolute value from the larger and keep the sign of the larger absolute value.
• Rewrite subtraction as addition of the opposite number.
• Use a number line to understand movement left and right.
• Check that your answer makes sense in the original situation.

Continue Learning

• Grade 6: Integers and the Number Line
• Grade 7: How to Solve Two-Step Equations
• Grade 7 Maths Learning Path