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ACT Math : Fractions

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Example Question #1391 : Act Math

is $16\frac{2}{3} \%$ of and $62\frac{1}{2} \%$ of ; all are positive integers. Give the smallest possible value of .

Possible Answers:

Correct answer:

Explanation:

is $16\frac{2}{3} \%$ of and $62\frac{1}{2} \%$ of , so

$A = \frac{16\frac{2}{3} }{100}B = \frac{16\frac{2}{3}\cdot 3 }{100 \cdot 3}B = \frac{50}{300}B = \frac{1}{6} B$ ,

so B = 6A .

$A = \frac{62\frac{1}{2} }{100}C = \frac{62\frac{1}{2} \cdot 2 }{100 \cdot 2}C= \frac{125}{200}C = \frac{5}{8} C$

so $C = \frac{8} {5}A$

must be divisible by 5, so the least possible value is 5 itself.

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Example Question #1392 : Act Math

is $7\frac{1}{2} \%$ of . Which of the following expressions is equal to ?

Possible Answers:

$\frac{2M}{15}$

$\frac{3M}{40}$

$\frac{15M}{2}$

None of the other responses gives a correct answer.

$\frac{40M}{3}$

Correct answer:

$\frac{40M}{3}$

Explanation:

is $7\frac{1}{2} \%$ of , so

$M = \frac{7\frac{1}{2}}{100} \cdot N = \frac{7\frac{1}{2} \cdot 2}{100\cdot 2} \cdot N = \frac{15}{200} N = \frac{3}{40} N$

$N = \frac{40}{3}M = \frac{40M}{3}$

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Example Question #1393 : Act Math

is $15 \frac{5}{8} \%$ of , which is 80% of . What percent of is ?

Possible Answers:

The correct answer is not given among the other responses.

$19\frac{17}{32} \%$

$12\frac{1}{2} \%$

$8 \%$

$5\frac{3}{25} \%$

Correct answer:

The correct answer is not given among the other responses.

Explanation:

is 80% of , so $N = \frac{80 }{100}P = \frac{4}{5}P$ .

Consequently, $P = \frac{5}{4}N$

is $15 \frac{5}{8} \%$ of , so $M = \frac{15 \frac{5}{8} }{100} N = \frac{15 \frac{5}{8} \cdot 8 }{100\cdot 8} N = \frac{5 }{32} N$

Consequently, $N = \frac{32} {5 }M$ .

$P = \frac{5}{4} \cdot\frac{32} {5 }M = \frac{32}{4}M = 8M$ , so

is 800% of . This is not one of the choices.

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Example Question #1 : Fractions And Percentage

is $22\frac{1}{2} \%$ of .

$\frac{2}{M}$ is what percent of $\frac{5}{N}$ ?

Possible Answers:

The correct answer is not given among the other responses.

$177 \frac{7}{9} \%$

$56\frac{1}{4} \%$

$3,600\%$

$277\frac{7}{9} \%$

Correct answer:

$177 \frac{7}{9} \%$

Explanation:

is $22\frac{1}{2} \%$ of , so

$M = \frac{22\frac{1}{2}}{100} N= \frac{22\frac{1}{2}\cdot 2}{100\cdot 2} N= \frac{45}{200 } N= \frac{9}{40} N=\frac{9N}{40}$ ,

$\frac{1}{M} = \frac{40}{9N}$

and

$\frac{2}{M} = \frac{80}{9N}$

The question can be rewritten as

$\frac{80}{9N}$ is what percent of $\frac{5}{N}$ ?

The answer is

$\frac{\frac{80}{9N}}{\frac{5}{N}} \times 100 \%$

$=\left ( \frac{80}{9N} \div \frac{5}{N}} \right ) \times 100 \%$

$=\left ( \frac{80}{9N} \cdot \frac{N}{5} \right ) \times 100 \%$

$= \frac{16}{9 } \times 100 \%$

$= 177 \frac{7}{9} \%$

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Example Question #11 : Fractions

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

Possible Answers:

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

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

None of the other choices gives the correct answer.

$525 \%$

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

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 #16 : How To Find Percentage

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:

$14.5\%$

$13.5\%$

$11.5\%$

$0\%$

$12.5\%$

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 #12 : Fractions

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

Convert $14\%$ to a fraction.

Possible Answers:

$\frac{7}{50}$

$\frac{1}{6}$

$\frac{1}{14}$

$\frac{14}{99}$

$\frac{3}{20}$

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 #14 : 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:

$\frac{3}{10}$

$\frac{21}{100}$

$\frac{3}{5}$

$\frac{73}{100}$

$\frac{3}{7}$

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 #15 : 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:

$\frac{5}{8}$

$\frac{3}{10}$

$\frac{3}{8}$

$\frac{3}{20}$

$\frac{4}{5}$

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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ACT Math : Fractions

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #1391 : Act Math

Example Question #1392 : Act Math

Example Question #1393 : Act Math

Example Question #1 : Fractions And Percentage

Example Question #11 : Fractions

Example Question #16 : How To Find Percentage

Example Question #12 : Fractions

Example Question #11 : Fractions

Example Question #14 : Fractions

Example Question #15 : Fractions

All ACT Math Resources

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