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# But who’s multiplying: Long multiplication

We begin our examination of the multiple methods of multiplication with everyone’s least favourite, long multiplication. In this way, any pair of numbers can be multiplied in a wholly inefficient manner. Here is an example.

 78 × 29 702 + 1560 2262 NEW

We begin by multiplying the first multiplicand by the last digit of the second. Then the first multiplicand is multiplied by each successive digit of the second multiplicand, appending zeroes appropriately to represent multiplication by the tens digit, the hundreds digit, and so on. Finally, the intermediate products are summed.

There is only one advantage to long multiplication: it subdivides the problem into several steps, so that each individual step is much simpler.

But with all these additional steps, the possibility of error is greater. The process also requires quite a bit of paper space, especially for large numbers, and cannot easily be done mentally.

Nonetheless, this is one of the first methods that students tend to learn. But is this how they really should be multiplying numbers? Join us next week to discover an almost identical method that is just a tiny bit better.

 861270 × 9318 6890160 8612700 258381000 + 7751430000 8025313860 NEW

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