Addition & Subtraction Tricks
Subtracting from 1000 – Nines and a Ten
Subtracting from 1000 usually needs lots of borrowing. This trick avoids it entirely.
This page explains the rule, shows why it works, and walks through worked examples. Then you can try it yourself and check your understanding with practice questions. Use the previous and next links at the bottom to move through the tricks in order.
The rule
The Rule: To subtract a number from 1000, subtract each digit from 9, except the last digit, which you subtract from 10.
Why it works
Why It Works: 999 is an unusually forgiving number to subtract from, because every single one of its digits is a 9 — so subtracting any digit from 9 never requires borrowing from the next column. Subtracting from 1000 is really just subtracting from 999 and then adding back the 1 you “borrowed” to make 999 in the first place. That extra +1 is exactly what happens when the very last digit is subtracted from 10 instead of from 9.
Formal Proof (for advanced learners)
For a three-digit number n with digits d₂d₁d₀: 1000 − n = (999 − n) + 1. Since every digit of 999 is 9, computing 999 − n digit-by-digit never requires borrowing (each digit of n is at most 9), giving digits (9−d₂), (9−d₁), (9−d₀). Adding the final +1 to the units column is equivalent to computing (10−d₀) for the last digit instead of (9−d₀) — exactly the stated rule.
Examples
- 1000 − 356 → 9−3=6, 9−5=4, 10−6=4: 644.
- 1000 − 472 → 9−4=5, 9−7=2, 10−2=8: 528.
- 1000 − 89 → treat as 089: 9−0=9, 9−8=1, 10−9=1: 911.
Step by step
Example A: 1000 − 423
- First two digits, each taken from 9: 9 − 4 = 5 and 9 − 2 = 7.
- The last digit is taken from 10: 10 − 3 = 7.
- Put them together: 577.
Example B: 1000 − 78
- Write 78 with a leading zero so it has three digits: 078.
- First two digits, each taken from 9: 9 − 0 = 9 and 9 − 7 = 2.
- The last digit is taken from 10: 10 − 8 = 2.
- Put them together: 922.
Try it yourself
Now it is your turn. A new random question appears each time. Type your answer in the box and press Check Answer. If you are right, we show how the trick got you there, step by step. If you are not, you will see the full working two ways, the shortcut and the usual method, so you can spot exactly where your answer differed. Press New Question as often as you like: a few quick rounds is the best way to make the trick feel automatic.
Practice questions
Have a go on paper first, then tap Show answer to check your method.
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Work out 1000 − 234.
Show answer
766. First two digits, each taken from 9: 9 − 2 = 7 and 9 − 3 = 6. The last digit is taken from 10: 10 − 4 = 6. Put them together: 766.
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Work out 1000 − 567.
Show answer
433. First two digits, each taken from 9: 9 − 5 = 4 and 9 − 6 = 3. The last digit is taken from 10: 10 − 7 = 3. Put them together: 433.
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Work out 1000 − 845.
Show answer
155. First two digits, each taken from 9: 9 − 8 = 1 and 9 − 4 = 5. The last digit is taken from 10: 10 − 5 = 5. Put them together: 155.
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Work out 1000 − 91.
Show answer
909. Write 91 with a leading zero so it has three digits: 091. First two digits, each taken from 9: 9 − 0 = 9 and 9 − 9 = 0. The last digit is taken from 10: 10 − 1 = 9. Put them together: 909.
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A stadium has 1000 seats and 618 are taken. How many seats are empty?
Show answer
382. First two digits, each taken from 9: 9 − 6 = 3 and 9 − 1 = 8. The last digit is taken from 10: 10 − 8 = 2. Put them together: 382.
Tips and watch-outs
- If the number ends in zeros, leave them as zeros and use “10 minus” on the last non-zero digit: 1000 − 350 = 650.
- For short numbers, add leading zeros first: 89 becomes 089.