1.1 Investigating multiplication by a negative number
It’s time to turn your observations from the previous activities into some useful mathematical rules to go with the ones that you already have for negative numbers from Week 7. This is an important part of problem solving in many different situations, not just in maths.
Activity 3 Being a mathematical detective
Use the results from the Table 2 (repeated below) to complete the following statements.
| 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 |
- a.If you multiply a negative number by a positive number, the answer is …
Answer
If you multiply a negative number by a positive number, the answer is negative: (–) × (+) = (–).
You can extend this rule a little. The order of the numbers doesn’t matter, so multiplying a positive number by a negative number also gives a negative answer.
- b.If you multiply a negative number by a negative number, the answer is …
Answer
If you multiply a negative number by a negative number, the answer is positive: (–) × (–) = (+).
Both of the rules in this activity also work for division! Try dividing 20 by (–5), and (–20) by (–5) to confirm that this is the case.
Now you have these rules, it is helpful for your understanding to look a bit closer at what is actually happening.