How do you do multiplication without a calculator or long multiplication?

Answer 1

I round one of the numbers (usually the larger one but either one works) up or down to the nearest number that is easy to multiply in my head.

Like this:

423 x 12

Becomes:

425 x 12

Then I would say that if 425 x 12 = ___, then 850 x 6 = ____ too.

Because 850 = 425 x 2 and 6 = 12 / 2

And if 850 x 6 = ____, then 1700 X 3 = ____ also.

1700 x 3 = (1000 x 3) + (700 x 3) = 3000 + 2100 = 5100

So, 425 x 12 = 5100. But, we started with 423 not 425.

(425 x 12) - ((425-423) x 12) = 423 x 12

425 - 423 = 2

So, we need to multiply the difference (2) by 12 and subtract that from the 5100 to get the real answer.

2 x 12 = 24

5100 - 24 = 5100 - 25 + 1 = 5076

423 x 12 = 5076 Ta Da!

Another way, is to break one into easy to use numbers (12 is good for this) and skip the rounding step. But, sometimes there is no easy split (3746 x 5317) and then the rounding works better. But, here is the split method (I also used it above.)

423 x 12 = (423 x 10) + 423 x 2

423 x 10 = 4230 and 423 x 2 = 846

4230 + 846 = 5076

With practice you will get faster at this and you will even be able to hold a conversation while doing the math. Then everyone will think you are a genius!