   SEARCH HOME Math Central Quandaries & Queries  Question from Kenneth: 16 is 4% of what amount? The answer can be determined by the following unusual manner: 4% = 16 1% = 4 100% = 400 Can the following solutions for the following be determined by using the same type of calculation? 16 is ?% of 400 ? is 4% of 400 I thank you for your reply. Hi Kenneth,

What you did is correct but I think it is advantageous to use a variable, especially for the two questions you asked. In your first example let $X$ be the unknown quantity then you could write your solution as

4% of $X$ = 16
thus 1% of $X$ = 4
and hence 100% of $X$ = 400, or $X = 400.$

Two more observations. Firstly the word "of" in this situation indicates multiplication as in

one half of 50 is $\large \frac12 \normalsize \times 50 = 25$

or

one third of 90 is $\large \frac13 \normalsize \times 90 = 30.$

Secondly "percent" means per 100 so, for example 4% is $\large \frac{4}{100}.$

Back to your question 16 is ?% of 400. You have used "?" for the unknown quantity so I'll stick to that and your question becomes

$16 = \frac{?}{100} \times 400$

or

$16 = ? \times 4 \mbox{ and hence } ? = 4.$

and your second question ? is 4% of 400 becomes

$? = \frac{4}{100} \times 400 = 4 \times 4 = 16.$

I hope this helps,
Penny       * Registered trade mark of Imperial Oil Limited. Used under license. Math Central is supported by the University of Regina and the Imperial Oil Foundation.