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# Multiplication of Integers Help

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By McGraw-Hill Professional
Updated on Sep 21, 2011

## Multiplication of Integers

For multiplication of integers, there are two basic rules:

Rule 1: To multiply two integers with the same signs, i.e., both are positive or both are negative, multiply the absolute values of the numbers and give the answer a + sign .

#### Example 1

Multiply (+8) × (+2).

#### Solution 1

Multiply 8 × 2 = 16. Since both integers are positive, give the answer a + (positive) sign. Hence, (+8) × (+2) = +16.

#### Example 2

Multiply (–9) × (–3).

#### Solution 2

Multiply 9 × 3 = 27. Since both integers are negative, give the answer a + (positive) sign. Hence, (–9) × (–3)= +27.

Rule 2: To multiply two integers with unlike signs, i.e., one integer is positive and one integer is negative, multiply the absolute values of the numbers and give the answer a(negative) sign .

#### Example 3

Multiply (–7) × (+6).

#### Solution 3

Multiply 7 × 6 = 42 and give the answer a – (negative) sign. Hence, (–7) × (+6) = –42.

#### Example 4

Multiply (+9) × (–5).

#### Solution 4

Multiply 9 × 5 = 45 and give the answer a – (negative) sign. Hence, (+9) × (–5) = –45.

Math Note: Multiplication can be shown without a times sign. For example, (–3)(–5) means (–3) ×(–5). Also, a dot can be used to represent multiplication. For example, 5 ·3 ·2 means 5 × 3 × 2.

To multiply three or more non-zero integers, multiply the absolute values and count the number of negative numbers. If there is an odd number of negative numbers, give the answer asign. If there is an even number of negative signs, give the answer a + sign .

#### Example 5

Multiply (–3)(–4)(–2).

#### Solution 5

Multiply 3 × 4 × 2 = 24. Since there are 3 negative numbers, the answer is negative. Hence, (–3)(–4)(–2) = –24.

#### Example 6

Multiply (–5)(+3)(+4)(–2).

#### Solution 6

Multiply 5 ×3 ×4 ×2 = 120. Since there are 2 negative numbers, the answer is positive. Hence, (–5)(+3)(+4)(–2)= +120.

### Multiplication of Integers Practice Problems

#### Practice

Multiply:

1. (–8)(–5)

2. (+6)(–2)

3. (+4)(–6)

4. (–3)(+5)

5. (–4)(+7)

6. (–3)(–4)(+2)

7. (+3)(–2)(–6)(+9)

8. (+10)(+2)(–6)(+9)

9. (+8)(–4)(–3)(+8)(–2)(+6)

10. (–3)(+10)(–8)(–2)(+4)(–3)

#### Answers

1. 40

2. –12

3. 24

4. –15

5. –28

6. 24

7. 324

8. –1080

9. –9216

10. 5760

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

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