#### 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.

The answer is 20.

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).

We already know that the answer to this is -20.

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

Answers

**Please answer the questions on the exit ticket**

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