Fractions and Percentage - ACT Math
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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?
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?
People who prefer horror films = 1000 people x 7.5% = 1000 x 0.075 = 75 people
People who prefer horror films = 1000 people x 7.5% = 1000 x 0.075 = 75 people
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There are 20 students in a class. 35 percent of the students in the class are boys. What fraction of the class is girls?
There are 20 students in a class. 35 percent of the students in the class are boys. What fraction of the class is girls?
There are 20 total students in the class. 35% of 20 is 7. There are 7 boys in the class.
girls in the class.
There are 20 total students in the class. 35% of 20 is 7. There are 7 boys in the class.
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Which of the following represents 
as a fraction?
Which of the following represents
To represent a percentage as a fraction, keep the percentage in the numerator and put 
in the denominator.
Therefore:
To represent a percentage as a fraction, keep the percentage in the numerator and put
Therefore:
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Which of the following fractions is equivalent to 
Which of the following fractions is equivalent to
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.
To convert an integer percentage into an improper fraction, set the percentage as a fraction over
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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?
A politician promises to spend up to
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):
Now just reduce your fraction!
To convert a decimal percentage into a fraction, first convert it to a decimal:
Now, set ths as a fraction with
Now just reduce your fraction!
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Convert to a fraction: 
Convert to a fraction:
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.
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.
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Convert the following to a percentage.
Convert the following to a percentage.
To convert a fraction into a percentage, simply simplify the fraction into a decimal and multiply by 100.
To convert a fraction into a percentage, simply simplify the fraction into a decimal and multiply by 100.
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The girl's tennis team decided to do multiple fundraisers to raise enough to buy new equipment for next season. The following is a table of 4 of the fundraisers they did and the fraction of the total funds each raised.
The last fundraiser they did earned them the final 
they needed. What percent of the total funds raised did the last fundraiser raise?
The girl's tennis team decided to do multiple fundraisers to raise enough to buy new equipment for next season. The following is a table of 4 of the fundraisers they did and the fraction of the total funds each raised.
The last fundraiser they did earned them the final
The question asks to find what percent the last fundraiser makes up of the total funds raised. The information that's given is how much that last fundraiser made and what fraction the other fundraisers made.
This problem may be solved without the amount of money the last fundraiser raised. The reason is that we know that only 5 fundraisers were done. We're given what the fraction of the other fundraisers were.
If we were to add all the fractions together, including the last fundraiser, the sum of all would equal 1.
Fractions are another version of decimals but also another version of percentages. Percentages are essentially a prettier way of showing parts (or fractions) of a whole, which would be 100%. In the case of fractions, this is the same logic, which is why when all the fractions are summed, they equal 1. This 1 represents 100%.
Upon using lowest common denominators, adding the fractions together, and solving for x, x is calculated to be 
We've almost obtained the final answer. Now it's just a matter of converting this fraction into a percent. As mentioned previously, fractions are another version of decimals. Think of decimals as being the middle conversion between fractions and percents. All that needs to be done to a decimal to turn it in to a percent is to multiply it by 100. For instance, .50 becomes 50%. Conversely, .50 is the same as 
in fraction form. Therefore, one half is 50%.
In order to solve for x in percent, the same conversion must be done.
The question asks to find what percent the last fundraiser makes up of the total funds raised. The information that's given is how much that last fundraiser made and what fraction the other fundraisers made.
This problem may be solved without the amount of money the last fundraiser raised. The reason is that we know that only 5 fundraisers were done. We're given what the fraction of the other fundraisers were.
If we were to add all the fractions together, including the last fundraiser, the sum of all would equal 1.
Fractions are another version of decimals but also another version of percentages. Percentages are essentially a prettier way of showing parts (or fractions) of a whole, which would be 100%. In the case of fractions, this is the same logic, which is why when all the fractions are summed, they equal 1. This 1 represents 100%.
Upon using lowest common denominators, adding the fractions together, and solving for x, x is calculated to be
We've almost obtained the final answer. Now it's just a matter of converting this fraction into a percent. As mentioned previously, fractions are another version of decimals. Think of decimals as being the middle conversion between fractions and percents. All that needs to be done to a decimal to turn it in to a percent is to multiply it by 100. For instance, .50 becomes 50%. Conversely, .50 is the same as
In order to solve for x in percent, the same conversion must be done.
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If a dress in a store originally costs 
, what does it cost (in dollars) after a 
discount is applied?
If a dress in a store originally costs
To find 
of 80, 
. Next, subtract 
, for 
as the final answer.
To find
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Luke went to the grocery store. It took him 15 minutes to drive to the store from his house, 30 minutes to shop, 5 minutes to put groceries in his car, and 20 minutes to drive home due to traffic.
What percentage of the trip did Luke spend inside his car?
Luke went to the grocery store. It took him 15 minutes to drive to the store from his house, 30 minutes to shop, 5 minutes to put groceries in his car, and 20 minutes to drive home due to traffic.
What percentage of the trip did Luke spend inside his car?
You take 15 + 20 = 35 minutes as total time spent in the car.
Then, you take 15 + 20 + 5 + 30 = 70 minutes as total trip time.
We take (35/70) x 100% = 50%
You take 15 + 20 = 35 minutes as total time spent in the car.
Then, you take 15 + 20 + 5 + 30 = 70 minutes as total trip time.
We take (35/70) x 100% = 50%
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There are 300 sandwiches at a company-wide picnic. If half of the sandwiches are tuna, and the provider mistakenly uses expired tuna in three-fifths of those sandwiches, what percentage of total sandwiches still remain edible?
There are 300 sandwiches at a company-wide picnic. If half of the sandwiches are tuna, and the provider mistakenly uses expired tuna in three-fifths of those sandwiches, what percentage of total sandwiches still remain edible?
This multi-part question makes use of both fractions and percentages, as well as some tricky language if you are not paying close attention.
First off, determine what three-fifths of the 150 tuna sandwiches is:
Now, refer back to the question, which asks how many TOTAL sandwiches (tuna and non-tuna) still remain edible. This is simple arithmetic.
Finally, find what percentage this equals:
This multi-part question makes use of both fractions and percentages, as well as some tricky language if you are not paying close attention.
First off, determine what three-fifths of the 150 tuna sandwiches is:
Now, refer back to the question, which asks how many TOTAL sandwiches (tuna and non-tuna) still remain edible. This is simple arithmetic.
Finally, find what percentage this equals:
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Express the fraction 
as a percentage.
Express the fraction
Converting a fraction to a percentage can be done in two ways. The first way involves recalling that a percent is just a fraction of 100 (per cent). Therefore, the percent equivalent to 
is the numerator of the equivalent fraction whose denominator is 100. In order to convert 
to a fraction over 100, I need to multiply the numerator and denominator each by 4.
Therefore, our answer is 28%.
The other approach is to convert the fraction to a decimal first by dividing 7 by 25.
To convert a decimal to a percent, just shift the decimal point two places to the right.
With this method, our answer is again 28%.
Converting a fraction to a percentage can be done in two ways. The first way involves recalling that a percent is just a fraction of 100 (per cent). Therefore, the percent equivalent to
Therefore, our answer is 28%.
The other approach is to convert the fraction to a decimal first by dividing 7 by 25.
To convert a decimal to a percent, just shift the decimal point two places to the right.
With this method, our answer is again 28%.
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A politician promises to spend a minimum of 
of his budget on improving roads. What is the minimum percent of the budget that must be spent on roads to keep this promise?
A politician promises to spend a minimum of
To find a percentage from a fraction, multiply the numerator by 
, then solve the fraction.
Thus, the politician must spend at least 
of the budget on roads.
To find a percentage from a fraction, multiply the numerator by
Thus, the politician must spend at least
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Convert to a percentage: 
Round to the nearest integer.
Convert to a percentage:
Round to the nearest integer.
We can solve this problem either by adding the two fractions and then converting to a percentage, or by converting each fraction to a percentage before adding them. We'll use the first method in this case:
Now, just as before, multiply our numerator by 
and solve the fraction:
We can solve this problem either by adding the two fractions and then converting to a percentage, or by converting each fraction to a percentage before adding them. We'll use the first method in this case:
Now, just as before, multiply our numerator by
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Convert to a percentage: 
Convert to a percentage:
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.
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.
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Convert 
to a fraction.
Convert
Divide 14 by 100. Simplifying this fraction will give the reduced fractional form of 
:
Divide 14 by 100. Simplifying this fraction will give the reduced fractional form of
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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?
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?
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:
The second step is to multiply your answer by 100 so that it will now be represented as a percentage. So for this data:
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:
So our answer for the amount of seats filled within the stadium is 
.
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:
The second step is to multiply your answer by 100 so that it will now be represented as a percentage. So for this data:
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:
So our answer for the amount of seats filled within the stadium is
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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?
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 
. This is the answer.
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
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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?
If
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 group of peanuts processed anywhere. It really is a filler. 
is the same as 
. Reduce this by canceling out the common 
: 
.
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
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There are 
students in a math class. 
of the class consists of boys. How many girls are in the math class?
There are
First, we need to find the fraction of the class that are girls.
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:
Create a proportion.
Cross multiply and solve for the number of girls, 
.
Divide both sides of the equation by 5.
There are 120 girls in the class.
First, we need to find the fraction of the class that are girls.
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:
Create a proportion.
Cross multiply and solve for the number of girls, 
Divide both sides of the equation by 5.
There are 120 girls in the class.
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