What is Multiplication?

Can be a tricky question, this.

Primary schoolchildren are taught that it is repeated addition, which makes a lot of sense.

4 x 4 =

4 + 4 + 4 + 4 =

16

Four lots of four/groups of/sets of.

But multiplication is also a scaling quantity. It ratchets things up massively quickly. If you type 2x2 into your calculator, then keep multiplying every answer by 2, the calculator will quickly run out of digits. To compare this with addition misses the point that multiplication is the centre of all geometric operations.

It does through the squaring and cubing and so on effect. If you take four centimetres, and for each of these four, you add another four, you get 4 x 4. It is known as squaring because the Greeks used to see it geometrically as the way to find the area of a square. For each centimetre across, there are four up (and vice versa).

x² is a powerful, recurring idea, which has its role in pretty much the entire universe. (E = mc²)

It's also worth noting the effect of multiplication by a fractional quantity.

4 x 1/4 will obviously increase the fraction, but it will have a decreasing effect on the whole number. Unlike multiplication by two whole numbers, where the answer is greater than either, in this operation, the answer will always be smaller than one of the inputted values.