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ACT Math : Fractions and Percentage

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Example Question #1 :Fractions

$\frac{5.5}{10}$ is equivalent to what percentage?

Possible Answers:

55%

45%

15%

4.5%

5.5%

Correct answer:

55%

Explanation:

Divide the fraction out to get the decimal

5.5 / 10 = 0.55

To find the percentage, shift the decimal point two to the right = 55%

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Example Question #2 :Fractions

Write $\frac{27}{25}$ as a percent

Possible Answers:

$8\%$

$127\%$

$27\%$

$93\%$

$108\%$

Correct answer:

$108\%$

Explanation:

To find a percent from a fraction you can either divide the number on your calculator and multiply by 100:

$100\cdot\frac{27}{25}=108$

or you can just multiply the numerator and denominator by the same number that makes the denominator equal to 100 (because a % is just #/100):

$\frac{27}{25}\cdot\frac{4}{4}=\frac{108}{100}$

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Example Question #1 :Fractions

One half of a group of professors is made up of mathematicians, and one fourth of the remaining portion is made up of philosophers. The remaining portion is made up of sociologists. If there are 464 professors in the room, how many are sociologists?

Possible Answers:

146

174

110

Correct answer:

174

Explanation:

To begin, remember with percentages that "of" means multiplication and "is" means "equals." Now, we know that one fourth of the remaining half are philosophers. This means that he philosophers really are:

$\frac{1}{4}*\frac{1}{2}=\frac{1}{8}$

So, there are $1-\frac{1}{2}-\frac{1}{8}$ sociologists as a percentage. This is:

$1-\frac{1}{2}-\frac{1}{8}=\frac{8}{8}-\frac{4}{8}-\frac{1}{8}=\frac{3}{8}$

Therefore, $\frac{3}{8}$ ofthe 464 are sociologists, or:

$\frac{3}{8}*464=174$ are sociologists.

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Example Question #4 :Fractions

Convert the following fraction into a percent.

$\frac{2}{5}$

Possible Answers:

$25\%$

$36\%$

$20\%$

$40\%$

Correct answer:

$40\%$

Explanation:

To convert a fraction into a percent, make the denominator 100 and then the numerator will be the percent. Thus,

$\frac{2}{5}*\frac{20}{20}=\frac{40}{100}=40\%$

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Example Question #5 :Fractions

On a 15,000 acre plot of land, there areacres in which deer live. What percentage of the land does this represent? Round to the nearest hundredth.

Possible Answers:

$0.05\%$

$0.01\%$

$0.04\%$

$0.25\%$

$0\%$

Correct answer:

$0.05\%$

Explanation:

For percentages, it is always easiest to translate into language that uses "is" and "of." "Is" means "equals" and "of" means "multiply." So, we have:

What percentage of 15,000 is? This is the same as:

x * 15,000=7

Solving for, you get:

$x=\frac{7}{15000}=0.00046666666667$

Now, as a percent, this is equal to:

$0.00046666666667 * 100= 0.046666666667\%$

Rounding to the nearest hundredth, you have $0.05\%$ .

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Example Question #6 :Fractions

is $8\frac{1}{3} \%$ of, which is 35% of. All three are positive integers. In which range does the smallest possible value of X+Y+Z fall?

Possible Answers:

Between 300 and 400

Between 600 and 700

Between 400 and 500

Between 700 and 800

Between 500 and 600

Correct answer:

Between 300 and 400

Explanation:

is 35% of, so $Y = \frac{35}{100}Z = \frac{7}{20}Z$ .

is $8\frac{1}{3} \%$ of, so $X = \frac{8\frac{1}{3}}{100}Y = \frac{8\frac{1}{3}\times 3}{100 \times 3}Y = \frac{25}{300 }Y = \frac{1}{12}Y$ .

Consequently,

$X = \frac{1}{12}Y = \frac{1}{12} \cdot \frac{7}{20}Z = \frac{7}{240}Z$

The smallest integercan be is 240. If this happens,

$Y = \frac{7}{20}Z = \frac{7}{20} \cdot 240 = 84$

$X = \frac{7}{240} \cdot 240 = 7$

Their sum is

X + Y + Z = 7 + 84 + 240 = 331

The correct choice is that the sum is between 300 and 400.

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Example Question #1 :Fractions And Percentage

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

Possible Answers:

Correct answer:

Explanation:

is $16\frac{2}{3} \%$ ofand $62\frac{1}{2} \%$ 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 #2 :Fractions And Percentage

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

Possible Answers:

$\frac{3M}{40}$

$\frac{40M}{3}$

$\frac{2M}{15}$

$\frac{15M}{2}$

None of the other responses gives a correct answer.

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 #3 :Fractions And Percentage

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

Possible Answers:

The correct answer is not given among the other responses.

$8 \%$

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

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

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

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 #4 :Fractions And Percentage

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

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

Possible Answers:

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

$3,600\%$

The correct answer is not given among the other responses.

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

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

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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ACT Math : Fractions and Percentage

Study concepts, example questions & explanations for ACT Math

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Example Questions

Example Question #1 :Fractions

Example Question #2 :Fractions

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Example Question #5 :Fractions

Example Question #6 :Fractions

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