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 1 Multiplying negative numbers
Use a calculator to find the answers and see if you can spot any patterns that emerge.
| 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
| 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. You can often look for patterns in maths to help you solve problems and help with your 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 2 What happens next?
Use the patterns in Table 2 to predict the answer to the next calculation in each sequence. Then check your predictions using a 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.