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# Multiplying and Dividing Integers

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## Paula Holmgren

on 17 September 2014

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#### Transcript of Multiplying and Dividing Integers

Multiplying and Dividing Integers
Example 1
We will start by trying to work out the answer to 5 × (-4).

First of all, think about the sum 5 × 4.

This is the same as 4 + 4 + 4 + 4 + 4, which gives 20.

In the same way, the sum 5 × (-4) can be written (-4) + (-4) + (-4) + (-4) + (-4), which gives -20.
We can see from this that:
We can see from this that:
5 × 4 (a positive number multiplied by a positive number) gives 20 (a positive answer).
5 × (-4) (a positive number multiplied by a negative number) gives -20 (a negative answer).

Conclusion
Multiplying and dividing using Integers
In this section we look at how to multiply and divide when both negative and positive numbers are involved.

Rules for Multiplication and Division
We can summaries the rules for multiplying and dividing two numbers as follows:
Rules:
If the signs are the same (both positive or both negative), the answer will be positive.
If the signs are different (one positive and one negative), the answer will be negative
Example 2
Now we will work out the answer to
(-4) × 5.

Multiplications work both ways round, for example 3 × 4 is the same as 4 × 3.

In the same way, (-4) × 5 must be the same as 5 × (-4).

Example 3
Work out the answer to (-4) × (-5).

We start by doing the multiplication without the signs: 4 × 5 = 20.

The table above tells us that a negative number multiplied by a negative number gives a positive answer.

We can now see that the answer to (-4) × (-5) must be 20.

Now we can see that:
(-4) × 5 (a negative number multiplied by a positive number) gives -20 (a negative answer).

Practice Problems
Example Questions
In each question below, you should start by multiplying or dividing the numbers as normal, ignoring the signs.
You should then work out whether the answer is positive or negative using the rules given above.
(a) 5 × (-7)
(b) (-3) × 4
(c) (-3) × (-5)
(d) 20 ÷ (-4)
(e) (-14) ÷ 2
(f) (-12) ÷ (-3)

(a) 5 × (-7) =
-35

(b) (-3) × 4 =
-12
(c) (-3) × (-5) =
15
(d) 20 ÷ (-4) =
-5
(e) (-14) ÷ 2 =
-7
(f) (-12) ÷ (-3) =
4