Math CentralQuandaries & Queries


Question from tina, a student:

a girls monthly take home pay is 1932.00. her monthly expenses total 1910.00. What percent of her monthly take home pay are her monthly expenses?

Hi Tina,

A percentage is a fraction which has a denominator of 100. Thus for example $26\%$ is $\large \frac{26}{100}.$ If you have a fraction and you want to express it as a percent you need to find an equivalent fraction with the denominator of $100.$

For example on the small bookshelf in my office I just counted $38$ books and $8$ of them are mathematics text books. What percent of the books on my shelf are mathematics text books?

The fraction of books on my shelf that are mathematics text books is $\large \frac{8}{38}$ so I need to find a fraction, equivalent to $\large \frac{8}{38}$ which has a denominator of $100.$ Thus I need to find $x$ if

\[\frac{x}{100} = \frac{8}{38}\]

To solve for $x,$ multiply each side by $100$ to obtain

\[x = \frac{8}{38} \times 100 = 21.05\]

and hence $21.05\%$ of the books on my shelf are mathematics text books.

I hope this helps,

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