# 1 Multiplication and division with negative numbers

To get a feel for negative numbers, last week you used a number line and also learned how to carry out addition and subtraction involving negative numbers. Now you’re going to turn your attention to multiplication and division. First, you’ll work through a calculator exploration to investigate what happens when you multiply by negative numbers.

## Activity _unit9.1.1 Activity 1 Multiplying negative numbers

Copy Table 1 onto a piece of paper. Then use a calculator to find the answers and see if you can spot any patterns that emerge.

### Table _unit9.1.1 Table 1 Multiplying negative numbers (to complete)

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

2 × 4 | 2 × (–4) | |||

1 × 4 | 1 × (–4) | |||

0 × 4 | 0 × (–4) | |||

(–1) × 4 | (–1) × (–4) | |||

(–2) × 4 | (–2) × (–4) | |||

(–3) × 4 | (–3) × (–4) |

### Answer

#### Table _unit9.1.2 Table 2 Multiplying negative numbers (to complete)

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

2 × 4 | 8 | 2× (–4) | –8 | |

1 × 4 | 4 | 1 × (–4) | –4 | |

0 × 4 | 0 | 0 × (–4) | 0 | |

(–1) × 4 | –4 | (–1) × (–4) | 4 | |

(–2) × 4 | –8 | (–2) × (–4) | 8 | |

(–3) × 4 | –12 | (–3) × (–4) | 12 |

You can probably see that in the first answer column, the numbers are going down by 4 each time. In the second answer column, the numbers are increasing by 4 each time.

See if you can use this observation with the next activity. We often look for patterns in maths to help us to solve problems and help with our understanding of any underlying rules that there may be. Seeing a pattern to help you with the next activity should also help you with your understanding of any rules that are developed.

## Activity _unit9.1.2 Activity 2 What happens next?

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

- a.The next calculation in the first column will be (–4) × 4.

### Answer

The next number in the sequence –4, –8 and –12 is –16.

On the calculator, as expected, (–4) × 4 = –16.

- b.The next calculation in the third column will be (–4) × (–4).

### Answer

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

On the calculator, again as expected, (–4) × (–4) = 16.

Now you’ll look at some rules to help you remember this pattern.