8.4Expressing One Quantity as a Percentage of Another

To express quantity $A$ as a percentage of quantity $B$ , divide $A$ by $B$ and multiply by $100\%$ . The result tells you what fraction of $B$ the quantity $A$ is, expressed out of $100$ .

Express A as a percentage of B

\displaystyle \dfrac{A}{B} \times 100\%

Expressing as a percentage

In a class of $\displaystyle 36$ students, $\displaystyle 27$ passed a math quiz. What percentage of the class passed?

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\displaystyle \text{Percentage who passed}

\displaystyle = \dfrac{27}{36} \times 100\%

\displaystyle = 0.75 \times 100\%

\displaystyle = 75\%

Comparing by percentage

School A has $\displaystyle 480$ students and $\displaystyle 144$ are in sports CCA. School B has $\displaystyle 350$ students and $\displaystyle 91$ are in sports CCA. Which school has a higher percentage of students in sports CCA?

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School A:

\dfrac{144}{480} \times 100\% = 30\%

School B:

\dfrac{91}{350} \times 100\% = 26\%

School A has a higher percentage (

30\% > 26\%

Now you try

A student scored 31 out of 40 on a test. What percentage is that?

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\displaystyle \text{Percentage}

\displaystyle = \dfrac{31}{40} \times 100\%

\displaystyle = 77.5\%

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