Intensive SAT MATH
Fraction Word Problems
Fraction Word Problems
Fraction represents how many equal part of things in which you’re interested out of a whole.
 The picture below shows 3 parts of an equal piece of cake that still remain and 1 part of it is removed.
A fraction of the remaining parts is
A fraction of the removed part is
𝑓𝑟𝑎𝑐𝑡𝑖𝑜𝑛 =
𝑃𝑎𝑟𝑡
𝑊ℎ𝑜𝑙𝑒
Types of fraction word problems
1. Find fraction from the given numbers or other fractions
2. Find number from the given fractions
Find Fraction
1. On Monday evening, Channel 2 scheduled 2 hours of situation comedy, 1 hour of news, and 3 hours of movies.
What part of the evening’s programming was devoted to situation comedy?
(A)
(B)
(C)
(D)
(E)
2.1 What part of a yard is 1 ft. and 3 in.?
(1 yard = 3 feet.)
2.2 What part of a gallon is 2 qt. 1 pt.?
(1 gallon = 8 pints, 1 quart = 2 pints)
(A)
(A)
(B)
(B)
(C)
(C)
(D)
(D)
(E)
(E)
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Intensive SAT MATH
Fraction Word Problems
3. An hour-long television program included 20 minutes of commercials. What fraction of the hour-long program was
not commercials?
4. A camp employs 4 men, 6 women, 12 girls and 8 boys. In the middle of the summer, 3 girls are fired and replaced by
women. What fraction of the staff is then made up of women?
(A)
(B)
(C)
(D)
(E)
5. At the beginning of the day, the prices of stocks A and B are the same. At the end of the day, the price of stock A has
increased by of its original price and the price of stock B has decreased by
stock A is what fraction of the price of stock B?
of its original price. The new price of
(A)
(B)
(C)
(D)
(E)
6. There are three times as many students enrolling in scary major as students enrolling in another major at a Monster
University. What part of the students present are the student enrolling in another major?
(A)
(B)
(C)
(D)
(E)
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Intensive SAT MATH
Fraction Word Problems
7. Equal amounts of cake batter are poured into two empty pans of different size so that one pan is full and the
other is full. If all the batter is poured from the pan with larger volume into the smaller pan, what fraction of the
smaller pan is then filled?
8. In an election, of the male voters and of the female voters cast their ballots for candidate A. If the number of female
voters was times the number of male voters, what fraction of the total number of votes cast did candidate A receive?
(A)
(B)
(C)
(D)
(E)
9. Of this year’s graduating seniors at South High, will be going to college. Of these, will go to four-year
colleges, while the rest will be going to two-year colleges. What part of the class will be going to two-year
colleges?
(A)
(B)
(C)
(D)
(E)
10. In a poll, 35 people were in favor of building a new library, 14 people were against it, and 1 person had no opinion.
What fraction of those polled were in favor of building a new library?
(A)
(B)
(C)
(D)
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Intensive SAT MATH
Fraction Word Problems
(E)
11. If a film takes 90 minutes to show, what fraction of the film is competed 15 minutes after it begins?
(A)
(B)
(C)
(D)
(E)
12. In a certain class, 3 out of 24 students are in student organizations. What is the ratio of students in student
organizations to students not in student organizations?
(A)
(B)
(C)
(D)
(E)
13. A student’s grade in a course is determined by 4 quizzes and 1 exam. If the exam counts twice as much as each
of the quizzes, what fraction of the final grade is determined by the exam?
(A)
(B)
(C)
(D)
(E)
14. 800 employees work for the Metropolitan Transportation Company. of these are college graduates, while of
the remainder are high school graduates. What part of the employees never graduated from high school?
(A)
(B)
(C)
(D)
(E)
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Intensive SAT MATH
Fraction Word Problems
15. Half of the women in the Spring Garden Club are over 60 years old. of the remainder are under 40. What part of
the membership is between 40 and 60 years old?
(A)
(B)
(C)
(D)
(E)
16. After doing of the family laundry before breakfast, Mrs. Stefanie did of the remainder before lunch. What part
of the laundry was left for the afternoon?
(A)
(B)
(C)
(D)
(E)
17. On a certain college faculty, of the professions are male, and the ratio of the number of tenured to untenured
profession is 2:5. If of the male professions are tenured, then what fraction of the female professors are untenured?
(A)
(B)
(C)
(D)
(E)
18. On each of the days Monday through Friday, Toni spent 1 hour commuting to work and 1 hour commuting back home.
What fraction of the total number of hours in these five days did she spend commuting?
(A)
(B)
(C)
(D)
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Intensive SAT MATH
Fraction Word Problems
(E)
Find Numbers
1. After Claire has read the first of a book, there are 120 pages left to read. How many pages of the book has Claire
read?
(A) 160
(B) 200
(C) 240
(D) 300
(E) 320
2. After of the people in a room leave, three people enter the same room. The number of people who are now in the
room, assuming no other people enter or leave, is of the original number of people who were in the room. How
many people left the room?
(A) 9
(B) 18
(C) 24
(D) 27
(E) 36
3. If Greg lost 20 pounds, then the ratio of Ted’s weight to Greg’s weight would be . If Ted weighs 180 pounds, what
was Greg’s initial weight?
(A) 115 pounds
(B) 125 pounds
(C) 135 pounds
(D) 145 pounds
(E) 155 pounds
4. At the end of the season, the ratio of the number of games a team has won to the number of games it lost is 4 : 3.
If the team won 12 games and each game played ended in either a win or a loss, how many games did the team play
during the season?
(A) 9
(B) 15
(C) 18
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Intensive SAT MATH
Fraction Word Problems
(D) 21
(E) 24
5. In a list of 100 numbers, the fraction of numbers greater than 15 is
How many numbers in the list are equal to 15?
(A) 10
(B) 24
(C) 49
(D) 55
(E) 74
and the fraction of numbers less than 15 is
6. An item is on sale on Monday at off the list price of dollars. On Friday, the sale price of the item is reduced by
of the current price. What is the number of dollars in the final sale price of the item?
(A)
(B)
(C)
(D)
(E)
7. June gives of her p pencils to Roger and then gives of the pencils that she has left to Maria. In terms of ,
how many pencils does June now have?
(A)
(B)
(C)
(D)
(E)
8. After Arlene pumps gas into the gas tank of her car, the gas gauge moves from exactly full to exactly full. If the
gas costs $1.50 per gallon and Arlene is charged $18.00 for the gas, what is the capacity, in gallons, of the gas tank?
(A) 24
(B) 20
(C) 18
(D) 16
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.
Intensive SAT MATH
Fraction Word Problems
(E) 15
9. At a high school basketball game, of students who attended were seniors, of the other students who attended
were juniors, and the remaining 80 students who attended were all sophomores. How many seniors attended this
game?
(A) 120
(B) 175
(C) 180
(D) 210
(E) 300
10. A water tank is full. After 12 gallons are poured out, the tank is full. When the tank is full, how many gallons of
water does it hold?
(A) 25
(B) 32
(C) 35
(D) 42
(E) 45
11. In a school election, Susan received of the ballots cast, Mary received of remaining ballots, and Bill received
all of the other votes. If Bill received 48 votes, how many votes did Susan receive more than Mary?
(A) 75
(B) 76
(C) 88
(D) 108
(E) 120
12. Doris spent of her savings on a used car, and she spent of her remaining savings on a new carpet. If the
carpet cost her $250, how much were Doris’s original savings?
(A) $1,000
(B) $1,200
(C) $1,500
(D) $2,000
(E) $3,000
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Intensive SAT MATH
Fraction Word Problems
13. In a certain college class, each student received a grade of A, B, C, or D or an “Incomplete”. In this class, of the
students received As, received Bs, received Cs, received Ds. If 3 students received grades of “Incomplete”, how
many students were in the class?
14. The sum of the digits of a two-digit integers is 9. If the ones digit is the tens digit, what is the ones digits?
15. Henry used of the length of a board to make a box and of the original length of the board to repair a step.
The remaining piece of the board was 2 feet long. How many feet long was the original board?
(A) 8
(B) 12
(C) 18
(D) 22
(E) 24
16. Pink paint is made by mixing 5 parts white paint with 1 part red paint. If Joseph uses this method for making pink
paint and he has 3 gallons of white paint and 1 gallon of red, what is the maximum amount of pink paint that Joseph
can make?
(A)
gallons
(B)
gallons
(C)
gallons
(D)
gallons
(E)
gallons
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Intensive SAT MATH
Fraction Word Problems
Ratio of A to B to C
1. The ratio of A to B is a : 8 and the ratio of B to C is 12 : c. If the ratio of A to C is 2 : 1, what is the ratio of a to c?
(A) 2 : 3
(B) 3 : 2
(C) 4 : 3
(D) 3 : 4
(E) 1 : 3
2. Company A, Company B, and Company C are three Internet providers in a certain area of the country. The ratio of
subscribers of A to B to C is 2:5:6. If there are a total of 65,000 subscriptions, how many of the 65,000 use Company A
and Company C?
(A) 55,000
(B) 40,000
(C) 35,000
(D) 30,000
(E) 25,000
3. A school club includes only sophomores, juniors and seniors, in the ratio of 1 : 3 : 2. If the club has 42 members,
how many seniors are in the club?
(A) 6
(B) 7
(C) 12
(D) 14
(E) 21
4. At a college basketball game, the ratio of the number of freshmen who attended to the number of juniors who attended
is 3 : 4. The ratio of the number of juniors who attended to the number of seniors who attended is 7 : 6. What is the ratio
of the number of freshmen to the number of seniors who attended the basketball game?
(A) 7 : 8
(B) 3 : 4
(C) 2 : 3
(D) 1 : 2
(E) 1 : 3
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Intensive SAT MATH
Fraction Word Problems
5. Jars A, B and C each contain 8 marbles. What is the minimum number of marbles that must be transferred among
the jars so that the ratio of the number of marbles in jar A to the number in jar B to the number in jar C is 1 : 2 : 3?
6. A company produces baseballs at 3 different plants: Plant A, Plant B, and Plant C. Doubling Plant A’s production is
equal to of the company’s total production. Doubling Plant B’s production is equal to the company’s total
production. Tripling Plant C’s production is equal to the company’s total production. What is the ratio of Plant A’s
production to Plant B’s production to Plant C’s production?
(A) 1:3:2
(B) 3:1:2
(C) 2:1:3
(D) 1:2:3
(E) 3:2:1
7. Store A, Store B, and Store C sell soccer balls. The ratio of the number of soccer balls sold of A to B is .The ratio of
the number of soccer balls sold of B to C is . If Store C sold 36 soccer balls, how many soccer balls did Store A sell?
(A) 75
(B) 90
(C) 95
(D) 105
(E) 110
8. If cement, gravel, and sand are to be mixed in the ratio of 3:5:7 respectively, and 5 tons of cement are available,
how many tons of the mixture can be made? (Assume that enough gravel and sand are available to use all the
available cement.)
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