Calculating
Connecting addition and subtraction
In this unit you see how addition and subtraction are joined together. They are opposites, so one can undo the other. You use fact families, number bonds and estimating to help you.
Inverse calculations
Addition and subtraction are inverse (opposite) operations. One undoes the other. If 4 + 6 = 10, then the inverse is 10 - 6 = 4. You can read the calculation backwards to find the inverse.
Fact families
Three numbers that go together make a fact family of 4 calculations: 2 additions and 2 subtractions. For 3, 5 and 8: 3 + 5 = 8, 5 + 3 = 8, 8 - 3 = 5 and 8 - 5 = 3.
Number bonds to 10
Number bonds are pairs that add up to a number. The bonds to 10 are 0 and 10, 1 and 9, 2 and 8, 3 and 7, 4 and 6, and 5 and 5. Each bond has an inverse: 6 + 4 = 10 gives 10 - 4 = 6 and 10 - 6 = 4.
Estimate, then check
Round each number to the nearest 10 to estimate an answer. Then you can use the inverse calculation to check. For 42 + 37, estimate 40 + 40 = 80. The real answer is 79, which is close, and 79 - 37 = 42 checks it.
Worked examples
Find the inverse calculation
- Start with the addition 4 + 6 = 10.
- The inverse is a subtraction using the same numbers.
- Read it backwards: take 6 away from 10.
Answer: The inverse of 4 + 6 = 10 is 10 - 6 = 4.
Write a fact family
- The three numbers are 3, 5 and 8.
- The two additions: 3 + 5 = 8 and 5 + 3 = 8.
- The two subtractions: 8 - 3 = 5 and 8 - 5 = 3.
Answer: 3 + 5 = 8, 5 + 3 = 8, 8 - 3 = 5, 8 - 5 = 3
Use a number bond and its inverse
- 6 and 4 make 10, so 6 + 4 = 10.
- The inverse takes a part away from 10.
- So 10 - 4 = 6 and 10 - 6 = 4.
Answer: 6 + 4 = 10, 10 - 4 = 6, 10 - 6 = 4
Estimate and then check
- Round to the nearest 10: 42 to 40 and 37 to 40.
- Estimate: 40 + 40 = 80.
- Work it out: 42 + 37 = 79, then check with the inverse 79 - 37 = 42.
Answer: 42 + 37 = 79 (close to the estimate of 80)
Where you see this in real life
- Checking your change at a shop by adding it back up.
- Using the opposite calculation to make sure a sum is right.
- Filling in a missing number, like 4 + ? = 10.
- Estimating a total quickly before working it out exactly.
Key words
- Inverse
- The opposite operation. Subtraction is the inverse of addition.
- Fact family
- Four calculations made from the same three numbers.
- Number bond
- A pair of numbers that add up to a total, such as 6 and 4 making 10.
- Estimate
- A close answer found by rounding, used to check your work is sensible.
- Round
- To change a number to the nearest 10 to make it easier to work with.