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Subtracting Reverses

What's a reverse? A reverse is a number written backwards from another number. So, 256 is the reverse of 652. There is a neat little trick dealing with the subtraction of reverses.


1 Method with Nines

When you subtract two three-digit reverses, a pattern emerges with the difference. The difference is usually a three-digit answer, except in one case, where it is the number 99.

  • The first digit of the difference is the difference in the hundreds places, minus 1.
  • The center digit is 9.
  • The last digit is the number you need to add to the first digit of the difference to get 9.



764 - 467 =

The first digit is the difference in the hundreds place, minus 1: 7 - 4 - 1 = 2.

The center digit is 9.

The last digit is the number you add to the first digit to get 9, or 9 - 2 = 7.

Therefore, 764 - 467 = 297.



423 - 324 =

The first digit is the difference in the hundreds place, minus 1: 4 - 3 - 1 = 0. Since it's 0, you don't write anything.

The center digit is 9.

The last digit is 9 - 0 = 9.

Thus, 423 - 324 = 99.

Also, watch out for problems where you are subtracting a smaller number minus a larger number. The process is the same, using the bigger number as your starting point. Don't forget to put a negative sign on the answer.



357 - 753 =

You have to think of this one backwards. You still subtract the hundreds places, minus 1: 7 - 3 - 1 = 3.

The center number is 9.

9 - 3 = 6.

Therefore, 357 - 753 = -396. Don't forget the negative.

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