Math CentralQuandaries & Queries


Question from Jayda, a student:

how go you change a mixed number into a percent

Ex. 3 3/4

Hi Jayda,

A percent is "the numerator of a fraction which has 100 as the denominator". Let me unpack that with some examples.

\[17\% = \frac{17}{100} = 0.17.\]

I wrote 17% as 17 over 100 and then expressed it as a decimal. What if you start with a fraction, for example $\frac{2}{5}?$ To express this fraction with 100 as its denominator you need to multiply the numerator and denominator by 20 and hence

\[\frac{2}{5} = \frac{2 \times 20}{5 \times 20} = \frac{40}{100} = 0.40 = 40\%.\]

You don't always get integers, for example with $\frac13$ you need to multiply the numerator and denominator by $\frac{100}{3}$ to get

\[\frac{1}{3} = \frac{1 \times \frac{100}{3}}{3 \times \frac{100}{3}} = \frac{\frac{100}{3}}{100}= \frac{33.33}{100} = 33.33\%\]

where I wrote the decimal fraction to two places.

What about a mixed number? First express it as an improper fraction and then proceed as I did above. Thus for $1 \frac12$ I get

\[1 \frac{1}{2} = \frac{3}{2} = \frac{3 \times 50}{2 \times 50} = \frac{150}{100} = 1.5 = 150\%\]

I hope this helps.

Write back if yo need more assistance,

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