# Subtract Directed Numbers

In this worksheet, students will apply the rules related to positive and negative numbers to work out answers to subtraction sums.

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

You may remember the rules of directed numbers (which is just a fancy way of saying positive and negative numbers), but find them trickier to apply.

This is very common and many students feel this way.

Why?

Because the rules differ for addition and subtraction, compared with multiplication and division.

The Rules:

Two positive symbols make a positive overall.

A positive and a negative symbol make a negative overall.

A negative and a positive symbol make a negative overall.

Two negative symbols make a positive overall.​

The Exception > subtracting negative numbers:

The complication comes when adding negative numbers.

They only affect each other if the signs are positioned next to each other.

So in the sum 3 - - 5, the signs would impact each other because they're together.

However, in the sum -3 - 6, the signs would not impact each other as they are not together.

Let's put these rules into context with some examples now.

e.g. Work out the value of: 6 - + 2

In this question we have a + and a - together, so they will affect each other.

They will become a negative overall.

So we can rewrite the sum as: 6 - 2

If we picture a mental number line, to take 2 from 6, we move 2 spaces to the left on the number line to arrive at: 4

e.g. Work out the value of: - 3 - - 5

In this question we have a - and a - together, so they will affect each other and become a positive overall.

However, the - at the start of the sum is on its own so does not need to be changed at all.

This means we can rewrite the sum as: - 3 + 5

Start at -3 on your mental number line and move 5 spaces to the right (as this is an addition sum) to reach: 2

In this activity, you will apply the rules related to positive and negative numbers to work out answers to subtraction sums.

Which symbol is the same as - + in a calculation?

+

-

÷

Complete the sentence below to summarise a rule about directed numbers.

+

-

÷

Work out the answer to:

4 - 8

Work out the answer to the sum:

3 - - 5

Which is the correct answer to the calculation below?

-2 - - 3

1

-1

5

-5

Work out the answer to:

6 - + 4

Work out the answer to:

3 - - 9

Work out the answer to:

- 6 - - 8

What is the answer to the sum below?

-6 - - 6

-12

12

0

For each of the expressions below, select if a correct answer has been reached.

• Question 1

Which symbol is the same as - + in a calculation?

-
EDDIE SAYS
Remember our rules for directed numbers: "A mix of signs makes a minus overall." If the symbols are alike they always result in a + overall, whilst the opposite is true if they are not alike.
• Question 2

Complete the sentence below to summarise a rule about directed numbers.

EDDIE SAYS
Two of any symbol (either ++ or --) will make a positive (+) overall. Remember this important fact to help you in the rest of this activity.
• Question 3

Work out the answer to:

4 - 8

-4
- 4
EDDIE SAYS
This question tests your use of a number line here. If you start at 4 and take away 8 (move to the left), what number do you get to? You will reach -8 not 0. If you got to 0, you moved right rather than left which meant that you added the numbers, rather than subtracting. Hopefully, this is beginning to make more sense now.
• Question 4

Work out the answer to the sum:

3 - - 5

8
EDDIE SAYS
Remember the rules for directed number: Two negatives next to each other make a positive. We can now rewrite our original expression as: 3 + 5 That's much easier to calculate, isn't it?
• Question 5

Which is the correct answer to the calculation below?

-2 - - 3

1
EDDIE SAYS
Lots of negatives in this one! Just take it slowly... The two negatives that are together make a positive overall: - 2 + 3 We now need to start at -2 on our mental number line and move 3 to the right, as we are adding. -2 + 3 = 1
• Question 6

Work out the answer to:

6 - + 4

2
EDDIE SAYS
What do you get if you have a negative and a positive together? That results in a negative. If we rewrite our original calculation, we get: 6 - 4 = 2
• Question 7

Work out the answer to:

3 - - 9

12
EDDIE SAYS
Two negatives next to each other? That'll be a positive. If we rewrite our calculation, we have: 3 + 9 = 12
• Question 8

Work out the answer to:

- 6 - - 8

2
EDDIE SAYS
Two negatives will always give us a positive, but only if they're directly next to each other. The two negatives in the middle of this sum will make a positive overall, but the one at the start won't affect this. We can now rewrite the question as: -6 + 8 = 2
• Question 9

What is the answer to the sum below?

-6 - - 6

0
EDDIE SAYS
As always, we need to combine the negatives that are together. We will now have: - 6 + 6 When we add, we move to the right on our mental number line, so we will get back to 0 with this sum.
• Question 10

For each of the expressions below, select if a correct answer has been reached.

EDDIE SAYS
Did you use the rules for directed numbers to help you? The sums can be rewritten as: 3 - 5 = -2 (Correct) -6 + 2 = -4 is the answer here (Incorrect) 4 + 3 = 7 is the answer here (Incorrect) Great job! Why not move on to revise multiplying or dividing directed numbers now?
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