ACT Math - How to find a fraction from a 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.

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

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

Convert to a fraction.

$\frac{7}{50}$

$\frac{1}{14}$

$\frac{14}{99}$

$\frac{1}{6}$

$\frac{3}{20}$

Explanation

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

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

There are 20 students in a class. 35 percent of the students in the class are boys. What fraction of the class is girls?

$\frac{20}{20}$

$\frac{7}{20}$

$\frac{35}{100}$

$\frac{20}{35}$

$\frac{13}{20}$

Explanation

There are 20 total students in the class. 35% of 20 is 7. There are 7 boys in the class.

girls in the class.

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?

$\frac{21}{100}$

$\frac{3}{10}$

$\frac{73}{100}$

$\frac{3}{5}$

$\frac{3}{7}$

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:

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

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?

$\frac{3}{20}$

$\frac{4}{5}$

$\frac{5}{8}$

$\frac{3}{8}$

$\frac{3}{10}$

Explanation

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

Which of the following represents as a fraction?

$\frac{16}{25}$

$\frac{100}{64}$

$\frac{64}{1000}$

$\frac{32}{25}$

$\frac{6}{10}$

Explanation

To represent a percentage as a fraction, keep the percentage in the numerator and put in the denominator.

Therefore:

$=\frac{64}{100}=\frac{32}{50}=\frac{16}{25}$

Convert to a fraction:

$\frac{x}{20}$

$\frac{5}{x}$

$\frac{x}{5}$

$\frac{20x}{5}$

$\frac{50x}{2}$

Explanation

To convert a percentage to a fraction, divide the percentage by 100, then simplify. The presence of a variable does not significantly affect this process.

$(5x) % = \frac{5x}{100} = \frac{1x}{20} = \frac{x}{20}$

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?

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 .

How to find a fraction from a percentage

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