1.2.6 Double and Half Trick

This trick involves multiplying by a clever version of 1. Let’s look at an example:

15 × 78 =

We can rewrite this as:

2/2 × 15 × 78 = (15 × 2) × (78/2) = 30 × 39 = 1170

So the procedure is you double one of the numbers and half the other one, then multiply. This trick is exceptionally helpful when multiplying by 15 or any two-digit number ending in 5. Another example is:

35 × 42 = 70 × 21 = 1470

It is also good whenever you are multiplying an even number in the teens by another number:

18 × 52 = 9 × 104 = 936

or

14 × 37 = 7 × 74 = 518

The purpose of this trick is to save time on calculations. It is a lot easier to multiply a single-digit number than a two-digit number.

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Problem Set 1.2.6

Practice these problems. Type your answer and press Enter to check: