Short-Cut Math

The 370 − 37 is, of course, 37 × (10 − 1) instead of 37 × 9.

By adding an amount 10 one number and subtracting an equal amount from a second number, the sum of the two numbers remains the same.

Either way, the answer is the same.

To multiply 64 by 25, for instance, you can divide 64 by 4 (= 16) and multiply by 100 (just add two zeros), and there’s your answer: 1,600.

Take 28 × 15, for instance.

If you halve 28 (= 14) and double 15 (= 30), you change the problem to 14 × 30 which, as you can see, is an easy 420—the same answer you will get by multiplying 28 by 15.

If you halve 28 (= 14) and double 15 (= 30), you change the problem to 14 × 30 which, as you can see, is an easy 420—the same answer you will get by multiplying 28 by 15.

It’s not always the size of a number that makes it difficult to handle but the KIND of number it is. You know, of course, that it’s much easier to multiply by 10 than by 9 even though 10 is the larger number. However, the “difficult” number 9 can be changed into two “easy” numbers, 10 minus 1, which equal 9. Therefore, to multiply a number by 9, you can multiply by 10 (simply add a zero to the number) and subtract the number, thus: 37 × 9 = 370 − 37 = 333.

They’re inexpensive, easily carried, never need a battery, and give you a record of what you did so the work can be checked.

For example, to find the sum of 29 and 36, you can add 1 to 29 and subtract 1 from 36 so that the problem becomes 30 + 35; you can see at once that the answer is 65.

You can apply the same principle to multiplying.