Fractions - ACT Math
Card 0 of 2070
Hannah can travel to her destination in one of two ways: she can drive due north for 36 miles, then due west for 44 miles, traveling an average of 65 miles per hour. Or she can drive directly to the destination, heading northwest, traveling an average of 40 miles per hour. What is the difference, to the nearest minute, between the two routes?
Hannah can travel to her destination in one of two ways: she can drive due north for 36 miles, then due west for 44 miles, traveling an average of 65 miles per hour. Or she can drive directly to the destination, heading northwest, traveling an average of 40 miles per hour. What is the difference, to the nearest minute, between the two routes?
Remember that distance = rate x time
For the first route, we can set up an equation where the total distance (36 + 44) equals the rate (65 mph) multiplied by the time:
36 +44 = 65t
80 = 65t
t = 80/65 = 1.23 hrs = 1 hr, 14 min
To find the time taken for the second route, we first figure out the distance traveled by using the Pythagorean Theorem.
We know that the "legs" of the right triangle are 44 and 36, where the hypotenuse is the straightline distance (northwest), directly to the destination:
a2+b2=c2
442+362=c2
3232=c2
c=56.85
56.85=40t
56.85/40=t
t=1.42 hrs=1 hr, 25 min
1 hr. 25 min. – 1 hr. 14 min. = 11 min.
Remember that distance = rate x time
For the first route, we can set up an equation where the total distance (36 + 44) equals the rate (65 mph) multiplied by the time:
36 +44 = 65t
80 = 65t
t = 80/65 = 1.23 hrs = 1 hr, 14 min
To find the time taken for the second route, we first figure out the distance traveled by using the Pythagorean Theorem.
We know that the "legs" of the right triangle are 44 and 36, where the hypotenuse is the straightline distance (northwest), directly to the destination:
a2+b2=c2
442+362=c2
3232=c2
c=56.85
56.85=40t
56.85/40=t
t=1.42 hrs=1 hr, 25 min
1 hr. 25 min. – 1 hr. 14 min. = 11 min.
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A motorcycle on a full tank of gas travels 478 miles. If a full tank of gas is 12 gallons, and gas costs $4.25 per gallon, what is the approximate miles per gallon rating of the motorcycle, and how much will a full tank of gas cost?
A motorcycle on a full tank of gas travels 478 miles. If a full tank of gas is 12 gallons, and gas costs $4.25 per gallon, what is the approximate miles per gallon rating of the motorcycle, and how much will a full tank of gas cost?
To calculate miles per gallon of gas, we take the 478 miles the motorcycle travels and divide it by the amount of gallons in a full tank of gas, 12 gallons. 478/12 = 39.83, or 39.8 when rounded to the tenths place
For the price, we take the 12 gallons and multiply it by the amount that one gallon costs, $4.25. (12)(4.25) = 51
To calculate miles per gallon of gas, we take the 478 miles the motorcycle travels and divide it by the amount of gallons in a full tank of gas, 12 gallons. 478/12 = 39.83, or 39.8 when rounded to the tenths place
For the price, we take the 12 gallons and multiply it by the amount that one gallon costs, $4.25. (12)(4.25) = 51
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A car averages 31 miles per gallon. Currently, gas costs $3.69 per gallon. About how much would it cost in gas for this car to travel 3,149 miles?
A car averages 31 miles per gallon. Currently, gas costs $3.69 per gallon. About how much would it cost in gas for this car to travel 3,149 miles?
First we determine how many gallons it will take to travel 3,149 miles with this particular car: 3,149/31=101.58 gallons. The cost of gas per gallon= $3.69, therefore 101.58x$3.69= $374.83.
First we determine how many gallons it will take to travel 3,149 miles with this particular car: 3,149/31=101.58 gallons. The cost of gas per gallon= $3.69, therefore 101.58x$3.69= $374.83.
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Max drives his car at a constant rate of 25 miles per hour. At this rate, many minutes will it take him to drive 15 miles?
Max drives his car at a constant rate of 25 miles per hour. At this rate, many minutes will it take him to drive 15 miles?
We know that it takes Max an hour to drive 25 miles. We also know that there are 60 minutes in an hour. Using this information we can create the following ratio:
We are trying to calculate the the amount of time it will take to drive 15 miles. Let's create a proportion and use a variable for the unknown time.
Cross-multiply and solve for the time.
We know that it takes Max an hour to drive 25 miles. We also know that there are 60 minutes in an hour. Using this information we can create the following ratio:
We are trying to calculate the the amount of time it will take to drive 15 miles. Let's create a proportion and use a variable for the unknown time.
Cross-multiply and solve for the time.
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A motorcycle averages 47 miles per gallon. If gas costs $4.13 per gallon, how much gas money is needed for a 1,457 mile road trip?
A motorcycle averages 47 miles per gallon. If gas costs $4.13 per gallon, how much gas money is needed for a 1,457 mile road trip?
We divide 1,457 miles by 47 miles per gallon to find that 31 gallons of gas are needed for the road trip.
We then multiply the gallons of gas by the cost per gallon to find:
31 x 4.13 = 128.03
We divide 1,457 miles by 47 miles per gallon to find that 31 gallons of gas are needed for the road trip.
We then multiply the gallons of gas by the cost per gallon to find:
31 x 4.13 = 128.03
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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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Simplify:
Simplify:
Begin by multiplying all of your decimal fractions by 
:
Simplify:
Now perform the multiplication:
The easiest thing to do next is to subtract 
from 
:
Next, convert 
into the fraction 
:
Now, the common denominator can be 
:
Simplify:
Begin by multiplying all of your decimal fractions by
Simplify:
Now perform the multiplication:
The easiest thing to do next is to subtract
Next, convert
Now, the common denominator can be
Simplify:
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Convert 0.825 into a fraction.
Convert 0.825 into a fraction.
0.825 in fraction form is 
. Simplifying the fraction equals 
.
0.825 in fraction form is
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If 
, 
can equal which of the following?
If
Convert all of the fractions to decimals. Thus, x is contained within the range of 0.33 < x < 0.76. The answers choices become 1/4 = 0.25, 4/12 = 0.33, 2/5 = 0.4, and 5/16 = 0.3125, respectively. Therefore, the only answer which is within the desired range is 2/5.
Convert all of the fractions to decimals. Thus, x is contained within the range of 0.33 < x < 0.76. The answers choices become 1/4 = 0.25, 4/12 = 0.33, 2/5 = 0.4, and 5/16 = 0.3125, respectively. Therefore, the only answer which is within the desired range is 2/5.
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Find the sum of the following:
Find the sum of the following:
To get the decimal from a fraction, divide the numerator by the denominator
To get the decimal from a fraction, divide the numerator by the denominator
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When 5/11 is written as a decimal, what is the 100th digit to the right of the decimal point?
When 5/11 is written as a decimal, what is the 100th digit to the right of the decimal point?
When 5 is divided by 11, the decimal is 0.45 repeating, with a 5 in the hundreths place. The key here is to recognize that 100 is an even number, and the 5 in 0.45 is two places to the right of the decimal point (2 also being an even number).
When 5 is divided by 11, the decimal is 0.45 repeating, with a 5 in the hundreths place. The key here is to recognize that 100 is an even number, and the 5 in 0.45 is two places to the right of the decimal point (2 also being an even number).
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Find the sum to the nearest hundredth:
Find the sum to the nearest hundredth:
1. Convert the fractions to decimals by division:
2. Add the corresponding whole numbers to the decimals:
3. Add the two decimals:
1. Convert the fractions to decimals by division:
2. Add the corresponding whole numbers to the decimals:
3. Add the two decimals:
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