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ACT Math : Percentage

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Example Question #1 : Percentage

We asked 1000 people their preferences of movie genres. 7.5% of those asked preferred horror movies, 35% preferred romantic films, 20% preferred dramas and 37.5% preferred comedies. How many people liked horror films?

Possible Answers:

7.5

37.5

750

Correct answer:

Explanation:

People who prefer horror films = 1000 people x 7.5% = 1000 x 0.075 = 75 people

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

There are 20 students in a class. 35 percent of the students in the class are boys. What fraction of the class is girls?

Possible Answers:

$\frac{35}{100}$

$\frac{20}{35}$

$\frac{13}{20}$

$\frac{7}{20}$

$\frac{20}{20}$

Correct answer:

$\frac{13}{20}$

Explanation:

There are 20 total students in the class. 35% of 20 is 7. There are 7 boys in the class.

20-7=13 girls in the class.

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Example Question #3 : Percentage

Which of the following represents $64\%$ as a fraction?

Possible Answers:

$\frac{6}{10}$

$\frac{100}{64}$

$\frac{32}{25}$

$\frac{64}{1000}$

$\frac{16}{25}$

Correct answer:

$\frac{16}{25}$

Explanation:

To represent a percentage as a fraction, keep the percentage in the numerator and put 100 in the denominator.

Therefore:

$64\%$ $=\frac{64}{100}=\frac{32}{50}=\frac{16}{25}$

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Example Question #1 : Percentage

Which of the following fractions is equivalent to $462 \%$

Possible Answers:

$4 \frac{31}{50}$

$4 \frac{18}{25}$

$3 \frac{4}{5}$

$5 \frac{2}{5}$

$3 \frac{18}{25}$

Correct answer:

$4 \frac{31}{50}$

Explanation:

To convert an integer percentage into an improper fraction, set the percentage as a fraction over 100 and simplify as far as you can. At that point, simply convert the improper fraction into a mixed fraction.

$462 \% = \frac{462}{100} = \frac{231}{50} = 4 \frac{31}{50}$

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Example Question #5 : Percentage

A politician promises to spend up to $26.8 \%$ of his budget on improving roads. Which of the following is closest to the fraction of their budget the politician must devote to road improvement?

Possible Answers:

$\frac{67}{250}$

$\frac{45}{193}$

$\frac{123}{250}$

$\frac{12}{37}$

$\frac{77}{177}$

Correct answer:

$\frac{67}{250}$

Explanation:

To convert a decimal percentage into a fraction, first convert it to a decimal:

$26.8 \% = .268$

Now, set ths as a fraction with 1.0 as the denominator (expanding to as many significant digits as you need to line the fraction up):

$26.8 \% = \frac{.268}{1.000} = \frac{268 }{1000}$

Now just reduce your fraction!

$\frac{268}{1000} = \frac{134}{500} = \frac{67}{250}$

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Example Question #6 : Percentage

Convert to a fraction: $(5x) \%$

Possible Answers:

$\frac{5}{x}$

$\frac{50x}{2}$

$\frac{x}{20}$

$\frac{x}{5}$

$\frac{20x}{5}$

Correct answer:

$\frac{x}{20}$

Explanation:

To convert a percentage to a fraction, divide the percentage by 100, then simplify. The presence of a variable does not significantly affect this process.

$(5x) \% = \frac{5x}{100} = \frac{1x}{20} = \frac{x}{20}$

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Example Question #2 : Percentage

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:

75%

15%

50%

35%

45%

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 : Fractions And Percentage

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:

$80\%$

$70\%$

$40\%$

$30\%$

$60\%$

Correct answer:

$70\%$

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:

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

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

300 - 90 = 210

Finally, find what percentage this equals:

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

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Example Question #9 : Percentage

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

Possible Answers:

$30\%$

$25\%$

$7\%$

$2.8\%$

$28\%$

Correct answer:

$28\%$

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 $\frac{7}{25}$ is the numerator of the equivalent fraction whose denominator is 100. In order to convert $\frac{7}{25}$ to a fraction over 100, I need to multiply the numerator and denominator each by 4.

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

Therefore, our answer is 28%.

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

$7\div25=0.28$

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

$0.28=28\%$

With this method, our answer is again 28%.

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Example Question #10 : Percentage

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

Possible Answers:

$300a^{2} \%$

$a^{1.5} \%$

$1.5^a \%$

$150a^{-1} \%$

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

Correct answer:

$150a^{-1} \%$

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.

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

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ACT Math : Percentage

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #1 : Percentage

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

Example Question #3 : Percentage

Example Question #1 : Percentage

Example Question #5 : Percentage

Example Question #6 : Percentage

Example Question #2 : Percentage

Example Question #1 : Fractions And Percentage

Example Question #9 : Percentage

Example Question #10 : Percentage

All ACT Math Resources

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