# 5.3 Multiplication and Division with Negative Numbers

Multiplying and dividing with negative numbers is an important skill to possess. Let’s go through a calculator exploration to investigate what happens when you multiply by negative numbers.

## Calculator Exploration—Multiplication with Negative Numbers

The calculator can be accessed on the left-hand side bar under Toolkit.

### Activity: Multiplying Negative Numbers

Copy the following tables into your notebook. Then use the calculator to find the answers and see if you can spot any patterns that emerge.

Calculation | Answer | Calculation | Answer | |
---|---|---|---|---|

#### Discussion

Take your time, and remember to enclose each negative number in parentheses.

#### Answer

Calculation | Answer | Calculation | Answer | |
---|---|---|---|---|

8 | ^{−}8 | |||

4 | ^{−}4 | |||

0 | 0 | |||

^{−}4 | 4 | |||

^{−}8 | 8 | |||

^{−}12 | 12 |

In the first solutions column, the numbers are going down by four each time, and in the second solutions column, the numbers are increasing by four each time.

### Activity: What Happens Next?

Use the patterns in the tables to predict the answer to the next calculation in each sequence. Then, check your predictions using the calculator.

(a)

#### Discussion

What number comes next in the sequence of answers?

#### Answer

(a) The next number in the sequence ^{−}4, ^{−}8, ^{−}12 is ^{−}16 and on the calculator .

(b)

#### Answer

(b) The next number in the sequence 4, 8, 12 is 16 and .

Now we’ll see if we can write some rules to help us remember this pattern.

5.2.9 Calculator Exploration—Negative Numbers