Succeed with maths – Part 1

Start this free course now. Just create an account and sign in. Enrol and complete the course for a free statement of participation or digital badge if available.

Free course

# 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

Timing: Allow approximately 10 minutes

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 1 Multiplying negative numbers (to complete)

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)

#### 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 2 What happens next?

Timing: Allow approximately 5 minutes

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.

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).

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.

Skip Your course resources
SWMB_1

### Take your learning further

Making the decision to study can be a big step, which is why you'll want a trusted University. The Open University has 50 years’ experience delivering flexible learning and 170,000 students are studying with us right now. Take a look at all Open University courses.

If you are new to University-level study, we offer two introductory routes to our qualifications. You could either choose to start with an Access module, or a module which allows you to count your previous learning towards an Open University qualification. Read our guide on Where to take your learning next for more information.

Not ready for formal University study? Then browse over 1000 free courses on OpenLearn and sign up to our newsletter to hear about new free courses as they are released.

Every year, thousands of students decide to study with The Open University. With over 120 qualifications, we’ve got the right course for you.

Request an Open University prospectus371