   SEARCH HOME Math Central Quandaries & Queries  Question from Richard, a parent: I need to find the calculation to answer this; I have the figure 379.28, how do I extract 14% from this figure to extract 17.5% I div by 6.714, however i cannot find the formula on how to do this an extract 14% We have two responses for you.

Richard,

you need to be careful and try to understand what 'percent of' means rather than look for a formula in each and every case.

'Percent of' means 'one-hundredths of'. Thus

5% of 379.28 mean (5/100) (379.28) = 18.964;
10% of 379.28 mean (10/100) (379.28) = 37.928;
17.5% of 379.28 mean (17.5/100) (379.28) = 66.374, etc.

I'm guessing that's what you mean by 'extracting' 17.5%; the language is vague because when I first read it I wondered if you meant what was left when you take 17.5 of it away and wasn't sure until I noticed
your 'formula'. Be careful with the division also; you said that extracting 17.5% corresponded to using the formula divide by 6.717 when in fact it is closer to dividing by 5.714. Don't use messy division when multiplication is available. Don't say 'percent', always say 'percent of' and it will remind you that you are taking some number of hundredths of something; you'll find that easier.

Penny

Hi Richard. I think you meant to write 5.714 is related to 17.5%

Here's what is happening:

379.28 x 17.5%
= 379.28 x (17.5 / 100)
= 379.28 x (1 / 5.714)
= 379.28 / 5.714

So with 14% you do the same thing. But the question becomes this:

14 / 100 = 1 / f

multiply both sides by f and we get this:

f x ( 14 / 100 ) = 1

now multiply both sides by the reciprocal of what is in parentheses:

f x (14 / 100) x (100 / 14) = 1 x (100 / 14)

and simplify:

f = 100 / 14

in my calculator that means

f = 7.143

In fact, you can convert any percentage to this decimal method by
dividing the percentage into 100.

So 379.28 x 14% = 379.28 / 7.143.

Stephen La Rocque.>     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.