Fractions and Percentage

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ACT Math › Fractions and Percentage

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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.

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

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

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

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!

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

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!

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

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

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.

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

$150a^{-1} %$

$a^{1.5} %$

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

$300a^{2} %$

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.

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

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

$150a^{-1} %$

$a^{1.5} %$

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

$300a^{2} %$

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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