ACT Math - Fractions and Percentage

Which of the following fractions is equivalent to

$4 \frac{31}{50}$

$3 \frac{18}{25}$

$5 \frac{2}{5}$

$3 \frac{4}{5}$

$4 \frac{18}{25}$

Explanation

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

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

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

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):

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

A politician promises to spend up to 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?

$\frac{67}{250}$

$\frac{45}{193}$

$\frac{77}{177}$

$\frac{12}{37}$

$\frac{123}{250}$

Explanation

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

Now, set ths as a fraction with 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!

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

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

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):

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

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

55%

45%

5.5%

15%

4.5%

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%

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

55%

45%

5.5%

15%

4.5%

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%

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

$\frac{40M}{3}$

$\frac{15M}{2}$

$\frac{2M}{15}$

$\frac{3M}{40}$

None of the other responses gives a correct answer.

Explanation

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

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

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

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?

7.5

750

37.5

Explanation

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

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

$\frac{40M}{3}$

$\frac{15M}{2}$

$\frac{2M}{15}$

$\frac{3M}{40}$

None of the other responses gives a correct answer.

Explanation

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

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

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

If a dress in a store originally costs $\small $80$ , what does it cost (in dollars) after a $\small 35%$ discount is applied?

$52

$28

$45

$70

$63

Explanation

To find $\small 35%$ of 80, $\small 80\times 0.35=28$ . Next, subtract $\small 80-28=52$ , for $\small $52$ as the final answer.

Fractions and Percentage

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