# Add Directed Numbers

In this worksheet, students will apply the rules related to positive and negative numbers to work out answers to addition 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 > adding 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 affect each other because they're together.

However, in the sum -3 + 6, the signs would not affect 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: 3 + - 5

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

They will become a negative overall.

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

As 5 is larger than 3, our answer will be less than 0 and a negative number.

If we picture a number line and start at 3, we then need to move 5 to the left to reach -2

e.g. Work out the value of: - 2 + - 4

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

They will become a negative overall.

This means we can rewrite the sum as: - 2 - 4

If we picture a number line and start at -2, we then need to move 4 to the left to reach -6

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

Which operator is the same as + -?

+

-

x

Work out the answer to the sum:

3 - 9

If your answer is a negative, do not use a space between the number and the sign e.g. -99 rather than - 99.

Complete the sentence to summarise the relationship between different combinations of + and - signs.

What is the answer to the sum below?

4 + - 2

2

-2

Which of the options is the correct answer to the sum below?

6 + - 3

9

-3

3

-9

Work out:

5 + - 3

If your answer is a negative, do not use a space between the number and the sign e.g. -99 rather than - 99.

What is the answer to the sum below?

7 + - 9

2

-2

14

What is the answer to the sum below?

-5 + - 3

If your answer is a negative, do not use a space between the number and the sign e.g. -99 rather than - 99.

What is the correct answer to the sum below?

-6 + - 6

-12

0

12

Which of the sums below have been answered correctly?

• Question 1

Which operator is the same as + -?

-
EDDIE SAYS
The trick to remember here is: "A mix of signs results in a minus overall". When you see a + and a - next to each other in a sum, it is the same as having just a -.
• Question 2

Work out the answer to the sum:

3 - 9

If your answer is a negative, do not use a space between the number and the sign e.g. -99 rather than - 99.

- 6
-6
EDDIE SAYS
We don't need to worry about changing any of the operators here, as we just have one present. 9 is larger than 3, so we know our answer will be less than 0 and a negative number. Imagine you are starting at 3 on a number line, and counting 9 steps to the left. What number will you reach?
• Question 3

Complete the sentence to summarise the relationship between different combinations of + and - signs.

EDDIE SAYS
Remember our little phrase from Q1? "A mix of signs makes a minus overall." This also tells us that the same signs (either ++ or --) will both give a positive. That may seems strange with two negatives, but this is the rule we need to remember and apply.
• Question 4

What is the answer to the sum below?

4 + - 2

2
EDDIE SAYS
If we look at the signs next to each other, we see that we have a positive and a negative. This results in a negative overall. Our sum can now be rewritten as: 4 - 2 This is much simpler to calculate, isn't it?
• Question 5

Which of the options is the correct answer to the sum below?

6 + - 3

3
EDDIE SAYS
If we recall our directed number rules: + - is the same as -. Therefore, we can rewrite 6 + - 3 as 6 - 3. The answer to this simple sum is 3.
• Question 6

Work out:

5 + - 3

If your answer is a negative, do not use a space between the number and the sign e.g. -99 rather than - 99.

2
EDDIE SAYS
Remember that a plus and a minus sign together will give a minus overall. 5 + - 3 = 5 - 3 = 2
• Question 7

What is the answer to the sum below?

7 + - 9

-2
EDDIE SAYS
It's a common mistake to say 2 here. However, don't forget that if you are subtracting a number which is bigger than the first one, you'll get a negative answer because you're going further left of zero on the number line. 7 + - 9 = 7 - 9 = -2
• Question 8

What is the answer to the sum below?

-5 + - 3

If your answer is a negative, do not use a space between the number and the sign e.g. -99 rather than - 99.

-8
EDDIE SAYS
Always deal with the signs that are together before calculating anything. If we deal with the + and - in the middle first . we know that + - gives a - overall. So our sum -5 + - 3 = - 5 - 3 Does the negative at the start affect the one in the middle? No, because it isn't next to the other ones and they only impact one another if they are directly next to each other. We can now just start at -5 and count down 3 to get -8. Don't be tempted to say -2 - that's what you'd get if you added the 3.
• Question 9

What is the correct answer to the sum below?

-6 + - 6

-12
EDDIE SAYS
Always remember to deal with the signs in the middle that are together first. Our rules tell us we can rewrite this sum as: -6 - 6 Do the two negatives now affect each other? No, because they are not directly next to each other. So, start at -6 on your mental number line and count down 6 to the left. Hopefully you reached -12, rather than returning to 0. If you thought it was 0, you moved the wrong way on the number line and added instead of subtracting.
• Question 10

Which of the sums below have been answered correctly?

EDDIE SAYS
These sums all have the same answer! This just goes to show that you should always manually work out the sum, rather than relying on gut instinct. For the first option, 3 + - 5 > 3 - 5 = -2, so this is correct. For the second option, 6 + - 4 > 6 - 4 = 2, so the answer of -2 is incorrect. For the third option, -3 + - 1 > -3 - 1 = -4, so the answer of -2 is also incorrect here. Great work on completing another activity! Why not move on to practise other computations with directed numbers, such as subtraction, division or multiplication?
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