 # Multiply and Divide Directed Numbers

In this worksheet, students will practise multiplying and dividing positive and negative numbers, applying the rules related to directed numbers accurately. Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   Pearson Edexcel, OCR, Eduqas, AQA

Curriculum topic:   Number, Number Operations and Integers

Curriculum subtopic:   Structure and Calculation, Calculations with Integers

Difficulty level:   ### QUESTION 1 of 10

When we are adding or subtracting negative numbers, we only need to combine the signs if they are directly next to each other in the equation.

When we are multiplying or dividing directed numbers, the signs do not have to be together, just present in the same calculation.

The Rules:

Two positive symbols make a positive symbol overall.

A positive and negative symbol make a negative symbol overall.

A negative and positive symbol make a negative symbol overall.

Two negative symbols make a positive symbol overall.

What to do when multiplying or dividing:

1) Multiply or divide the numbers first as normal;

2) Deal with the signs afterwards.

Let's put these rules and this process into practice with some examples.

e.g. Calculate 6 x -3

If any of the numbers do not have a sign, we need to assume it is a positive number.

This means we can rewrite our sum as: +6 x -3

1) Multiply the numbers first as normal: 6 x 3 = 18

2) Deal with the signs afterwards: + and - makes a - overall

+6 x -3 = -18

e.g. Calculate -15 ÷ -5

1) Divide the numbers first as normal: 15 ÷ 5 = 3

2) Deal with the signs afterwards: - and - makes a + overall

15 ÷ 5 = +3

We don't put the sign with the answer if it's a positive number, so our answer should be: 15 ÷ 5 = 3

In this activity, you will practise multiplying and dividing positive and negative numbers, applying the rules related to directed numbers accurately.

You can always return to this page to review the rules if you need to at any point in this activity - good luck!

Complete the sentence below to summarise one element of the rules related to directed numbers

3 x -5

-16 ÷ 2

-5 x -5

For the directed number calculations below, select if they have been performed correctly or not.

Imagine your friend is working out:

-5 x -3

Some of the lines in their working are incorrect.

Select the lines which have errors.

5 x 3 = 15

- x - = -

-5 x -3 = -15

-9 ÷ -4

"Two negatives always make a positive."

In what circumstances is this statement true?

Always

Sometimes

Never

-10 x -3 ÷ -2

(-3)2

• Question 1

Complete the sentence below to summarise one element of the rules related to directed numbers

EDDIE SAYS
This is the key difference between adding or subtracting directed numbers, and multiplying or dividing them. When we are multiplying or dividing, the signs do not have to be directly next to each other, they just need to be present in the same equation. Remember this important fact to be successful in the rest of this activity.
• Question 2

3 x -5

-15
- 15
EDDIE SAYS
Following the rules, as we discussed, is what's going to help you. 1) Multiply the numbers first as normal 3 x 5 = 15 2) Deal with the signs next A + and a - become a - overall Then you add the minus sign back into your answer to arrive at -15. Is combining the rules and the process starting to make sense now?
• Question 3

-16 ÷ 2

-8
- 8
EDDIE SAYS
We need to treat a division sum just the same as a multiplication. Again, apply the rules we discussed in the Introduction. 1) Multiply the numbers first 16 ÷ 2 = 8 2) Deal with the signs next A - and a + becomes a - overall So our final answer is -8.
• Question 4

-5 x -5

25
+25
EDDIE SAYS
This is the style of question that can catch students out - it requires you to think carefully and systematically. 1) Multiply the numbers first 5 x 5 = 25 2) Deal with the signs next A - and a - become a + overall This may seem like the opposite of what should happen, but you need to be sure to stick to the rules! This means our answer is +25, which we just write as 25 to be totally accurate.
• Question 5

For the directed number calculations below, select if they have been performed correctly or not.

EDDIE SAYS
• Question 6

Imagine your friend is working out:

-5 x -3

Some of the lines in their working are incorrect.

Select the lines which have errors.

- x - = -
-5 x -3 = -15
EDDIE SAYS
The second line should read - x - = + This would mean the third line should have the answer +15 If your friend made this mistake in an exam, they would lose a mark for the initial mistake with the signs, but they wouldn't lose the answer mark as they have followed through with their working. This is really important to remember for your own exams!
• Question 7

-9 ÷ -4

2.25
EDDIE SAYS
This is another thing examiners love to do, grouping together different topics into one question. Our rules still apply: 1) Divide as normal first 9 ÷ 4 = 2.25 2) Deal with the signs next - ÷ - = + Don't let the decimal trip you up - you can just complete the question as normal.
• Question 8

"Two negatives always make a positive."

In what circumstances is this statement true?

Sometimes
EDDIE SAYS
Let's look at this and eliminate some options. It may help to try this out with actual numbers to test the theory. If we want to eliminate an option, we just have to give one example that shows it isn't true. We know that multiplying two negatives gives a positive so we can eliminate 'Never' as the correct answer. We know that -3 -4 won't end up as a positive, so we can then eliminate 'Always'. This means that 'Sometimes' is the correct answer. If two negative signs are directly next to each other in an addition or subtraction sum or present in a multiplication or division sum, then the outcome will be positive overall. However, if two negatives are present in an addition or subtraction sum but not directly next to each other, then the output will not necessarily be positive overall. A tricky one there!
• Question 9

-10 x -3 ÷ -2

-15
- 15
EDDIE SAYS
Does it matter that we have three numbers here? No! Just split it into two parts and use our steps and rules. First, we deal with the first two numbers: -10 x -3 = 30 Then we can divide this answer by -2: 30 ÷ -2 = -15
• Question 10

(-3)2

9
EDDIE SAYS
This is the question style that catches students out - the most common wrong answer to this is -9. We must think what the question requires: (-3)2 means -3 x -3 We know that two negatives multiplied together will give a positive. So our answer should be 9. Great work on completing this activity! Hopefully you are a professional at applying the rules and our process now. Why not try another directed numbers activity if you would like some more practice?
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