Topic 2 of 8
Step 3: Adding and subtracting to 20
Fact families: addition and subtraction as opposites
Step 3 · Adding and subtracting to 20 topics
Adding and subtracting undo each other. Three numbers make a family of four facts, and an addition fact you know answers a subtraction.
One family, four facts
The numbers 3, 5 and 8 belong together: 3 and 5 make 8. They give four facts, two adding and two subtracting.
| Adding | Subtracting |
|---|---|
| 3 + 5 = 8 | 8 − 5 = 3 |
| 5 + 3 = 8 | 8 − 3 = 5 |
The biggest number, the whole, comes first when you subtract and last when you add.
Subtracting by thinking of adding
A subtraction asks for a missing part. 13 − 8 asks: 8 and what make 13? If you know 8 + 5 = 13, then 13 − 8 = 5.
Example: Think addition
Find 15 − 7.
- Think: 7 + ? = 15.
- 7 + 8 = 15.
- So 15 − 7 = 8.
Answer8
This is often quicker than counting back, especially when you take away a big number.
The equal sign
The equal sign, =, means "is the same amount as". It does not mean "the answer comes next". 9 = 4 + 5 is true, and so is 4 + 5 = 6 + 3, because both sides make 9.
Example: True or false
Is 7 + 2 = 10 − 1 true?
- Work out the left side: 7 + 2 = 9.
- Work out the right side: 10 − 1 = 9.
- Both sides are 9.
AnswerTrue
Example: A missing number
Find the missing number: 6 + _ = 14.
- Think: 14 − 6.
- 6 + 4 = 10, then 4 more makes 14, so 8 more in all.
Answer8
Try it yourself
Work each one on paper first, then open the answer to check.
Write the fact family for 4, 6 and 10.
Show answer
4 + 6 = 10, 6 + 4 = 10, 10 − 6 = 4, 10 − 4 = 6.
You know 9 + 3 = 12. What is 12 − 9?
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3.
Find 16 − 9 by thinking of adding.
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7, because 9 + 7 = 16.
Is 5 + 5 = 4 + 6 true or false?
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True: both sides are 10.
8 + _ = 13
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5.
_ − 4 = 7
Show answer
11, because 7 + 4 = 11.