Believe it or not, multiplying (and dividing) by the number five and also its decimal multiples is needed more often than you might think. And you don't always have a calculator or at least some paper and a pen with you, so that's when you use mental maths.

First of all, after multiplying/dividing by 2 and 10, 5 is one of the easiest other numbers to multiply/divide with. As a middle number of a base-10 decimal system, it could play a significant role when we need to estimate something while rounding – if not to the nearest ten, then at least to the nearest five for better accuracy, and then to work with this estimated number (to maybe multiply or divide something with it).

A second (very convenient) fact is that 5 is made by 2 and 10 – perfect! Let me show you what I mean:

5 = 10 / 2 (not exactly rocket science, but hold on...)

So, if I want to multiply 17 * 5:

17 * 5 = 17 * (10 / 2)

I could either first multiply by 10 and then divide by 2, or vice versa (divide by 2 and then multiply by 10), whichever seems easier for me at the moment.

Here, I'd go for "times 10, then divide by 2":

17 * 5 = 17 * (10 / 2) = (17 * 10) / 2 = 170 (just "add" one zero) / 2 (applying another mental maths trick where I divide 100 first and then 70, and later add them together as 50 + 35) = 85

Another example (where I decided to use dividing by 2 first and then multiplying by 10):

540 * 5 = 540 * (10 / 2) = (540 / 2) * 10 = (using another mental maths trick as described above: 250 + 20) 270 * 10 = 2700

In terms of dividing, it's good to know and use the fact that dividing by a number is the same as multiplying by its inverse value (a reciprocal). So, for the number 5 (think about it as 5/1), its inverse would be 1/5. Therefore, if 5 = 10 / 2:

1/5 = 2/10

Just briefly, all has been described and explained above, here we just change what we multiply and divide with:

17 / 5 = 17 * (1/5) = 17 * (2/10) = (17 * 2) / 10 = 34 / 10 = 3.4

or

540 / 5 = 540 * (1/5) = 540 * (2/10) = (540 / 10) * 2 = 54 * 2 = 108 (solved as 100 + 8, similar to the parts of previous examples where I was split-subtracting)

How does it work with decimal multiples of 5? Just at the end, add zeros/move the decimal point as needed (thinking that 50 = 5 * 10, etc.):

If 17 * 5 = 85, then 17 * 50 = 850.

or

If 540 / 5 = 108, then 540 / 500 = 1.08.

And that's the whole trick! Are you feeling more confident now when it comes to using 5s for multiplying or dividing?