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Add Directed Numbers

In this worksheet, students will practise adding directed numbers.

'Add Directed Numbers' worksheet

Key stage:  KS 4

Curriculum topic:  

Curriculum subtopic:  

Difficulty level:  

Worksheet Overview

QUESTION 1 of 10

Most students can tell you the rules of directed numbers (which is just a fancy way of saying positive and negative numbers) but many students struggle when applying these rules. Why? Because the rules differ for addition and subtraction compared with multiplication and division.

 

The rules:

Two positives make a positive.

A positive and a negative makes a negative.

A negative and a positive makes a negative.

Two negatives make a positive.

 

Adding negative numbers:

The thing that students get wrong when they add negative number is that they only affect each other if they are together.

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.

 

Example 1: Work out the value of

3 + - 5

In this question we have a + and a - together, so they will affect each other and will become a negative overall, this means we can rewrite the sum as;

3 - 5

To do this, we can now read from left to right. - 5 means go 5 to the left, so if we start on a number line at 3 and go 5 to the left, we get;

3 - 5 = -2

 

Example 2: Work out the value of

- 2 + - 4

In this question we have a + and a - together, so they will affect each other and will become a negative overall, this means we can rewrite the sum as;

- 2 - 4

To do this, we can now read from left to right. - 4 means go 4 to the left, so if we start on a number line at -2 and go 4 to the left, we get;

-2 - 4 = -6

 

Which operator is the same as + -?

+

-

Work out the answer to the sum

3 - 9

Complete the sentence below

Work out the answer to 4 + - 2

2

-2

Which of the following options is the correct answer to the sum 6 + - 3?

9

-3

3

-9

What is the answer to the sum 5 + - 3?

What is the answer to the sum 7 + - 9?

2

-2

What is the answer to the sum -5 + - 3?

 

Which of the following answers is correct for the sum -6 + - 6?

-12

0

12

Which of the following are correct sums?

Click correct or incorrect for each one.

  • Question 1

Which operator is the same as + -?

CORRECT ANSWER
-
EDDIE SAYS
The trick to remember here is, 'A mix of signs is a minus' + and - together is the same as a single -
  • Question 2

Work out the answer to the sum

3 - 9

CORRECT ANSWER
- 6
-6
EDDIE SAYS
Because we only have one sign, we don't have to worry about changing anything. If you start at 3 on the number line and count 9 to the left (- 9), you will get to -6.
  • Question 3

Complete the sentence below

CORRECT ANSWER
EDDIE SAYS
Remember my little trick, 'A mix of signs makes a minus'. This also tells us that the same signs (either ++ or --) will give a positive. Is this becoming less daunting?
  • Question 4

Work out the answer to 4 + - 2

CORRECT ANSWER
2
EDDIE SAYS
If we look at the signs together, we see that we have a positive and a negative, gives us a negative. The sum can now be rewritten as 4 - 2 which we should be able to (I hope) do in our heads. Simple!
  • Question 5

Which of the following options is the correct answer to the sum 6 + - 3?

CORRECT ANSWER
3
EDDIE SAYS
If we remember our directed number rules, + - is the same as - Therefore, we can rewrite the sum as 6 - 3.
  • Question 6

What is the answer to the sum 5 + - 3?

CORRECT ANSWER
2
EDDIE SAYS
Remember that a plus and a minus together will give a negative.
  • Question 7

What is the answer to the sum 7 + - 9?

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

What is the answer to the sum -5 + - 3?

 

CORRECT ANSWER
-8
EDDIE SAYS
If we deal with the + and - in the middle first (always deal with the signs that are together first). + - gives a - overall, leaving us with - 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 together. 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

Which of the following answers is correct for the sum -6 + - 6?

CORRECT ANSWER
-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 as -6 - 6. Do the two negatives now affect each other? No, because they aren't together. So, start at -6 on the number line and count down 6! You've got this keep going.
  • Question 10

Which of the following are correct sums?

Click correct or incorrect for each one.

CORRECT ANSWER
EDDIE SAYS
They all look like they should give -2, which just goes to show that you should always manually work out the sum rather than relying on gut instinct. 6 + - 4 will give 2 and -3 + -1 will give -4. Well done, that’s another activity completed!
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