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ACT Math : Fractions and Percentage

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Example Questions

Example Question #15 : Fractions

is $28 \frac{4}{7} \%$ of . What percent of is ?

Possible Answers:

$525 \%$

$685 \frac{5}{7} \%$

$14 \frac{7}{12} \%$

None of the other choices gives the correct answer.

$19 \frac{1}{21} \%$

Correct answer:

$525 \%$

Explanation:

is $28 \frac{4}{7} \%$ of , so

$6M = \frac{28\frac{4}{7}}{100} \cdot 4N = \frac{28\frac{4}{7} \cdot 7 \cdot 4}{100 \cdot 7} \cdot N = \frac{800}{700 } N = \frac{8}{7}N$

$\frac{8}{7}N = 6M$

$\frac{7}{8} \cdot \frac{8}{7}N =\frac{7}{8} \cdot 6M$

$N =\frac{21}{4} M = 5.25 M$ , or 525% of .

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Example Question #31 : Percents

There are registered students in the math club. Students are deciding what activity they could do for their end of semester event. They have three choices: rock climbing, bowling, or outdoor laser tag. students vote for rock climbing, students vote for bowling, and students vote for outdoor laser tag.

What percent of students did not vote?

Possible Answers:

$0\%$

$14.5\%$

$12.5\%$

$13.5\%$

$11.5\%$

Correct answer:

$12.5\%$

Explanation:

The number of students who did not vote is:

48-14-12-16=6

The percent of students who did not vote is therefore:

$\frac{6}{48}=\frac{1}{8}=0.125$

$12.5\%$ of the students did not vote.

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Example Question #1401 : Act Math

There are 300 students in a math class. $\frac{3}{5}$ of the class consists of boys. How many girls are in the math class?

Possible Answers:

120

180

Correct answer:

120

Explanation:

First, we need to find the fraction of the class that are girls.

$\frac{5}{5}-\frac{3}{5}=\frac{2}{5}$

Next, find the number of students that are female. If we know that there are 300 students total, we can write the following ratio for girls:

$\frac{x}{300}$

Create a proportion.

$\frac{x}{300}=\frac{2}{5}$

Cross multiply and solve for the number of girls, .

$\frac{x}{300}\times\frac{2}{5}$

$5\cdot x=2\cdot300$

5x=600

Divide both sides of the equation by 5.

$\frac{5x}{5}=\frac{600}{5}$

x=120

There are 120 girls in the class.

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Example Question #11 : Fractions And Percentage

Convert $14\%$ to a fraction.

Possible Answers:

$\frac{14}{99}$

$\frac{7}{50}$

$\frac{3}{20}$

$\frac{1}{6}$

$\frac{1}{14}$

Correct answer:

$\frac{7}{50}$

Explanation:

Divide 14 by 100. Simplifying this fraction will give the reduced fractional form of $14\%$ :

$\frac{14}{100}= \frac{7}{50}$

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Example Question #15 : Fractions

percent of percent of the students in a high school take Anglo-Saxon as their first foreign language. What fraction of the students does this represent?

Possible Answers:

$\frac{3}{10}$

$\frac{73}{100}$

$\frac{21}{100}$

$\frac{3}{7}$

$\frac{3}{5}$

Correct answer:

$\frac{21}{100}$

Explanation:

For percentages, remember that the key language is found in the words "is" and "of". "Of" is translated as multiplication, and "is" is translated as equality. Here, we merely need to set up the equation:

0.3 * 0.7 *1=0.21

Notice carefully, we use to represent the $100\%$ of the class. It really is a filler. 0.21 is the same as $\frac{21}{100}$ . This is the answer.

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Example Question #18 : Fractions

If percent of percent of a group of peanuts was processed in Indiana, what fraction of the original amount of peanuts does this group represent?

Possible Answers:

$\frac{5}{8}$

$\frac{3}{20}$

$\frac{3}{8}$

$\frac{4}{5}$

$\frac{3}{10}$

Correct answer:

$\frac{3}{20}$

Explanation:

0.5 * 0.3 *1=0.15

Notice carefully, we use to represent the $100\%$ of the group of peanuts processed anywhere. It really is a filler. 0.15 is the same as $\frac{15}{100}$ . Reduce this by canceling out the common : $\frac{3}{20}$ .

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Example Question #11 : Fractions And Percentage

A stadium holds a total of 13,758 seats. Of that total, 6,732 seats are full with spectators. How many seats, to the nearest percent, are currently full?

Possible Answers:

$43\%$

$44\%$

$49\%$

$39\%$

$51\%$

Correct answer:

$49\%$

Explanation:

To answer this question, we must find the percentage of the amount of seats filled up within the stadium. To find a percentage, there are two steps.

First, you divide the part of the total number by the total number itself (in this case the amount of seats filled divided by the total number of seats). So, for this data:

$\frac{part}{whole} = \frac{6,732}{13,758} = 0.489$

The second step is to multiply your answer by 100 so that it will now be represented as a percentage. So for this data:

$\frac{6,732}{13,758} = 0.489 \cdot 100 = 48.9 %$

The question asked us to round our answer to the nearest whole percent. To do this, we round a number up one place if the last digit is a 5, 6, 7, 8, or 9, and we round it down if the last digit is a 1, 2, 3, or 4. Therefore:

$48.9% \rightarrow 49%$ $48.9 \rightarrow 49$

So our answer for the amount of seats filled within the stadium is $49\%$ .

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ACT Math : Fractions and Percentage

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #15 : Fractions

Example Question #31 : Percents

Example Question #1401 : Act Math

Example Question #11 : Fractions And Percentage

Example Question #15 : Fractions

Example Question #18 : Fractions

Example Question #11 : Fractions And Percentage

All ACT Math Resources

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