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# Subtraction of Integers Help

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By McGraw-Hill Professional
Updated on Sep 21, 2011

## Subtraction of Integers

In arithmetic, subtraction is usually thought of as "taking away." For example, if you have six books on your desk and you take four to class, you have two books left on your desk. The "taking away" concepts work well in arithmetic, but with algebra, a new way of thinking about subtraction is necessary.

In algebra, we think of subtraction as adding the opposite. For example, in arithmetic, 8 – 6 = 2. In algebra, 8 +(–6) = 2. Notice that in arithmetic, we subtract 6 from 8. In algebra, we add the opposite of 6, which is –6, to 8. In both cases, we get the same answer.

To subtract one number from another, add the opposite of the number that is being subtracted .

#### Example 1

Subtract (+12) – (–8).

#### Solution 1

Add +8 (the opposite of –8) to 12 to get 20, as shown.

Hence, (+12) – (–8) = 20.

#### Example 2

Subtract (–6) – (+3).

#### Solution 2

Hence, (–6) – (+3) = –9.

Math Note: Sometimes the answers in subtraction do not look correct, but once you get the opposite, you follow the rules of addition. If the two numbers have like signs, use Rule 1 for addition. If the two numbers have unlike signs, use Rule 2 for addition.

#### Example 3

Subtract (–10) – (–3).

#### Solution 3

Hence, (–10) – (–3)=(–7).

#### Example 4

Subtract (–8) – (–12).

#### Solution 4

Hence, (–8) – (–12)= +4

#### Practice

Subtract:

1. (+10) – (+6)

2. (–3) – (–12)

3. (–7) – (+18)

4. (+15) – (–20)

5. (–8) – (–13)

6. (+9) – (–2)

7. (–11) – (–11)

8. (+14) – (–8)

9. (–5) – (+5)

10. 0 – (–3)

1. +4

2. +9

3. –25

4. +35

5. +5

6. +11

7. 0

8. +22

9. –10

10. +3

More practice problems for this concept can be found at: Integers Practice Test.

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