Solve tricky calculations by rounding to an easier number
Numbers such as 18, 29, 39, and 98 are close to round numbers. That makes them easier to work with than they may first appear.
Take 18 + 17. Adding 17 to 18 may not feel obvious, but adding 17 to 20 is easier. Add 2 to turn 18 into 20, calculate 20 + 17, then subtract the extra 2. The final answer is still exactly the same. This method is called compensation.
Turn 18 into 20, then remove the extra 2
Each circle counts as one. The two orange circles make 18 into 20. After adding 17, remove those same two circles to get the correct answer.
How to calculate 18 + 17 in your head
Change 18 to the easier number 20. Then make sure the extra 2 does not stay in your answer.
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Round 18 up to 20
18 + 2 = 20
Twenty is easier to add to than 18. The calculation now contains 2 more than it should.
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Do the easier addition
20 + 17 = 37
Now the addition is simpler: 20 + 17 = 37.
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Remove the extra 2
37 − 2 = 35
The question started with 18, not 20. Remove the extra 2, and the correct answer is 35.
More addition examples
Look for a number close to 10, 20, 30, 100, or another round number. Use that easier number, then reverse the small change you made.
67 + 29
= 96
198 + 46
= 244
52 + 39
= 91
The same idea works for subtraction
When you subtract a little too much, add the extra amount back.
83 − 39
= 44
152 − 98
= 54
704 − 297
= 407
How to keep the answer correct
Compare the original number with the round number you used. Then reverse that small change.
You made a number in an addition larger
Subtract the extra amount48 became 50, so subtract 2
You made a number in an addition smaller
Add the missing amount52 became 50, so add 2
You subtracted a larger number
Add back what you subtracted too much39 became 40, so add 1
Now try 64 + 29
64 + 29 = ?
Replace 29 with a nearby round number. What extra amount will you need to remove?
Show the answer Hide the answer
Use 64 + 30 = 94, then subtract the extra 1. So 64 + 29 = 93.
When this strategy is useful
This method is useful whenever one number is close to a round number that is easier to calculate with.
Add prices
For $4.98 + $2.40, think $5.00 + $2.40 − $0.02.
Compare totals
For 198 + 305, think 200 + 305 − 2 and see 503 quickly.
Try the method while you play
Look for numbers close to a multiple of 10. Calculate with the round number, then reverse the small change you made.
Questions about compensation
What is compensation in maths?
Compensation means replacing a number with a nearby number that is easier to use, then reversing the small change so the answer stays correct.
When should I use the compensation strategy?
Use it when a number is close to 10, 20, 30, 100, or another round number. If changing the number makes the calculation harder to follow, use a different method.
Does compensation change the answer?
No. You reverse the small change before finishing, so the answer remains exactly the same.