# ### maths categories

• #### articles (27)

Believe me or not, multiplying (and dividing) by number five and also its decimal multiples is more often needed than you might think. And you don't have always a calculator or at least some paper and 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 and as a middle number of a base of decimal system could play a significant role when we need to estimate something while rounding - if not nearest ten, then at least five for better accuracy, and then to work with this estimated number (to maybe multiply or divide something with it).

Second (very convenient) fact is, that 5 IS made by 2 and 10 - perfect. Let me show you what do I mean:

5 = 10/2

So 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 at the moment easier for me.
Here I'd go for times 10, divide 2:
17 * 5 = 17 * (10/2) = (17 * 10) / 2 = 170 (just "add" one zero) / 2 (applying another mental maths trick where I divide first 100 and then 70 and later will add it together as 50 + 35) = 85

Another example (where I decided to use first dividing by 2 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, so for number 5 (think about it as 5/1) it would be 1/5 then. 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 as the similar parts of previous examples)

How does it work with decimal multiples of 5? Just at the end add zeros/move 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 feling more confident now when it comes to using 5's for multiplying or dividing?