learnbits.app· Geography

Difference: counting on

You learn an easy way to subtract when the two numbers are close together: count on.

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How to work it out

  1. Check if the two numbers are close.
  2. Start at the smaller number and count on to the nearest round number, then to the target.
  3. Add the jumps.

A worked example

502 − 498

  1. Count on from 498 to 500: that is 2.
  2. Count on from 500 to 502: that is 2.
  3. Add the steps: 2 + 2 = 4.
More examples

1005 − 998

  1. Count on from 998 to 1000: that is 2.
  2. Count on from 1000 to 1005: that is 5.
  3. Add the steps: 2 + 5 = 7.

405 − 396

  1. Count on from 396 to 400: that is 4.
  2. Count on from 400 to 405: that is 5.
  3. Add the steps: 4 + 5 = 9.

Try it yourself

  1. 201 − 197 =

  2. 910 − 903 =

Watch out

  • You subtract column by column and swap the digits round: for 502 − 498 you write 196.

    First look at how far apart the numbers are. If they are close together, count on.

Tips

  • If the numbers are close together, counting on is faster than subtracting.
  • The difference stays the same, whichever way you count.

Exceptions

  • If the numbers are far apart, like 900 − 123, counting on is not quicker: subtract step by step instead.

Why it works

For 502 − 498 the column method means exchanging across two columns. But the numbers are only 4 apart. If you count on from 498 to 502, you have it in two small steps. The difference between two numbers is the same, whichever way you look at it.