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ACT Math : How to find percentage from a fraction

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Example Questions

Example Question #1 : How To Find Percentage From A Fraction

Luke went to the grocery store. It took him 15 minutes to drive to the store from his house, 30 minutes to shop, 5 minutes to put groceries in his car, and 20 minutes to drive home due to traffic.

What percentage of the trip did Luke spend inside his car?

Possible Answers:

45%

15%

50%

75%

35%

Correct answer:

50%

Explanation:

You take 15 + 20 = 35 minutes as total time spent in the car.

Then, you take 15 + 20 + 5 + 30 = 70 minutes as total trip time.

We take (35/70) x 100% = 50%

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Example Question #1 : How To Find Percentage From A Fraction

There are 300 sandwiches at a company-wide picnic. If half of the sandwiches are tuna, and the provider mistakenly uses expired tuna in three-fifths of those sandwiches, what percentage of total sandwiches still remain edible?

Possible Answers:

$30\%$ $\displaystyle 30\%$

$40\%$ $\displaystyle 40\%$

$80\%$ $\displaystyle 80\%$

$70\%$ $\displaystyle 70\%$

$60\%$ $\displaystyle 60\%$

Correct answer:

$70\%$ $\displaystyle 70\%$

Explanation:

This multi-part question makes use of both fractions and percentages, as well as some tricky language if you are not paying close attention.

First off, determine what three-fifths of the 150 tuna sandwiches is:

$150 \cdot (\frac{3}{5}) = 90$ $\displaystyle 150 \cdot (\frac{3}{5}) = 90$

Now, refer back to the question, which asks how many TOTAL sandwiches (tuna and non-tuna) still remain edible. This is simple arithmetic.

$\displaystyle 300 - 90 = 210$

Finally, find what percentage this equals:

$\frac{210}{300} = 0.7=70\%$ $\displaystyle \frac{210}{300} = 0.7=70\%$

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Example Question #2 : How To Find Percentage From A Fraction

Express the fraction $\frac{7}{25}$ $\displaystyle \frac{7}{25}$ as a percentage.

Possible Answers:

$25\%$ $\displaystyle 25\%$

$30\%$ $\displaystyle 30\%$

$2.8\%$ $\displaystyle 2.8\%$

$28\%$ $\displaystyle 28\%$

$7\%$ $\displaystyle 7\%$

Correct answer:

$28\%$ $\displaystyle 28\%$

Explanation:

Converting a fraction to a percentage can be done in two ways. The first way involves recalling that a percent is just a fraction of 100 (per cent). Therefore, the percent equivalent to $\frac{7}{25}$ $\displaystyle \frac{7}{25}$ is the numerator of the equivalent fraction whose denominator is 100. In order to convert $\frac{7}{25}$ $\displaystyle \frac{7}{25}$ to a fraction over 100, I need to multiply the numerator and denominator each by 4.

$\frac{7}{25}\cdot \frac{4}{4}=\frac{28}{100}$ $\displaystyle \frac{7}{25}\cdot \frac{4}{4}=\frac{28}{100}$

Therefore, our answer is 28%.

The other approach is to convert the fraction to a decimal first by dividing 7 by 25.

$7\div25=0.28$ $\displaystyle 7\div25=0.28$

To convert a decimal to a percent, just shift the decimal point two places to the right.

$0.28=28\%$ $\displaystyle 0.28=28\%$

With this method, our answer is again 28%.

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Example Question #1 : How To Find Percentage From A Fraction

Convert to a percentage: $\frac{3a}{2a^2}$ $\displaystyle \frac{3a}{2a^2}$

Possible Answers:

$a^{1.5} \%$ $\displaystyle a^{1.5} \%$

$1.5^a \%$ $\displaystyle 1.5^a \%$

$300a^{2} \%$ $\displaystyle 300a^{2} \%$

$150a^{-1} \%$ $\displaystyle 150a^{-1} \%$

$\frac{3^a}{2^a} \%$ $\displaystyle \frac{3^a}{2^a} \%$

Correct answer:

$150a^{-1} \%$ $\displaystyle 150a^{-1} \%$

Explanation:

Despite the presence of a variable, the rule remains the same: To convert a fraction to a percentage, multiply the numerator by 100 and solve the fraction.

$\frac{3a}{2a^2} = (\frac{300a}{2a^2}) = 150a^{-1} \%$ $\displaystyle \frac{3a}{2a^2} = (\frac{300a}{2a^2}) = 150a^{-1} \%$

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Example Question #11 : Percentage

A politician promises to spend a minimum of $\frac{3}{8}$ $\displaystyle \frac{3}{8}$ of his budget on improving roads. What is the minimum percent of the budget that must be spent on roads to keep this promise?

Possible Answers:

$37.5 \%$ $\displaystyle 37.5 \%$

$47 \%$ $\displaystyle 47 \%$

$32.5 \%$ $\displaystyle 32.5 \%$

$23.8 \%$ $\displaystyle 23.8 \%$

$35.5 \%$ $\displaystyle 35.5 \%$

Correct answer:

$37.5 \%$ $\displaystyle 37.5 \%$

Explanation:

To find a percentage from a fraction, multiply the numerator by 100 $\displaystyle 100$, then solve the fraction.

$\frac{3}{8} = (\frac{3 \cdot 100}{8}) \% = \frac{300}{8} \% = 37.5 \%$ $\displaystyle \frac{3}{8} = (\frac{3 \cdot 100}{8}) \% = \frac{300}{8} \% = 37.5 \%$

Thus, the politician must spend at least $37.5 \%$ $\displaystyle 37.5 \%$ of the budget on roads.

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Example Question #3 : How To Find Percentage From A Fraction

Convert to a percentage: $\frac{2}{5} + \frac{13}{15}$ $\displaystyle \frac{2}{5} + \frac{13}{15}$

Round to the nearest integer.

Possible Answers:

$157 \%$ $\displaystyle 157 \%$

$145 \%$ $\displaystyle 145 \%$

$127 \%$ $\displaystyle 127 \%$

$172 \%$ $\displaystyle 172 \%$

$148 \%$ $\displaystyle 148 \%$

Correct answer:

$127 \%$ $\displaystyle 127 \%$

Explanation:

We can solve this problem either by adding the two fractions and then converting to a percentage, or by converting each fraction to a percentage before adding them. We'll use the first method in this case:

$\frac{2}{5} + \frac{13}{15} = \frac{6}{15} + \frac{13}{15} = \frac{19}{15}$ $\displaystyle \frac{2}{5} + \frac{13}{15} = \frac{6}{15} + \frac{13}{15} = \frac{19}{15}$

Now, just as before, multiply our numerator by 100 $\displaystyle 100$ and solve the fraction:

$\frac{19}{15} = \left (\frac{1900}{15} \right ) \% \approx 127 \%$ $\displaystyle \frac{19}{15} = \left (\frac{1900}{15} \right ) \% \approx 127 \%$

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ACT Math : How to find percentage from a fraction

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #1 : How To Find Percentage From A Fraction

Example Question #1 : How To Find Percentage From A Fraction

Example Question #2 : How To Find Percentage From A Fraction

Example Question #1 : How To Find Percentage From A Fraction

Example Question #11 : Percentage

Example Question #3 : How To Find Percentage From A Fraction

All ACT Math Resources

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