ACCUPLACER Arithmetic Quiz: Fraction Word Problems
20 questions · exam conditions
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Fraction Word ProblemsQuestion 1 of 20

A recipe that yields 12 cookies requires 1341 \frac{3}{4} cups of sugar. How many cups of sugar are needed to make 30 cookies?

3123 \frac{1}{2}
3783 \frac{7}{8}
4384 \frac{3}{8}
4124 \frac{1}{2}
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ACCUPLACER Arithmetic Quiz

ACCUPLACER Arithmetic Quiz: Fraction Word Problems

Practice Fraction Word Problems in ACCUPLACER Arithmetic with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Fraction Word Problems, giving you a quick way to practice the rules, question types, and explanations that matter most for ACCUPLACER Arithmetic.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

A recipe that yields 12 cookies requires 1341 \frac{3}{4} cups of sugar. How many cups of sugar are needed to make 30 cookies?

  1. 3123 \frac{1}{2}
  2. 3783 \frac{7}{8}
  3. 4384 \frac{3}{8} (correct answer)
  4. 4124 \frac{1}{2}
Explanation: First, find the scaling factor for the recipe: 3012=52\frac{30}{12} = \frac{5}{2}. Convert the sugar amount to an improper fraction: 134=741 \frac{3}{4} = \frac{7}{4}. Multiply the sugar amount by the scaling factor: 74×52=358\frac{7}{4} \times \frac{5}{2} = \frac{35}{8}. Convert back to a mixed number: 35÷8=435 \div 8 = 4 with a remainder of 3, so the answer is 4384 \frac{3}{8} cups.

Question 2

Three partners, Alex, Beth, and Chandra, invest in a business. Alex invests 14\frac{1}{4} of the total capital, and Beth invests 25\frac{2}{5} of the total capital. What fraction of the capital must Chandra invest?

  1. 320\frac{3}{20}
  2. 35\frac{3}{5}
  3. 1320\frac{13}{20}
  4. 720\frac{7}{20} (correct answer)
Explanation: First, find the total fraction of capital invested by Alex and Beth combined. Find a common denominator for the fractions: 14+25=520+820=1320\frac{1}{4} + \frac{2}{5} = \frac{5}{20} + \frac{8}{20} = \frac{13}{20}. The total capital is represented by 1. To find Chandra's share, subtract the combined share of Alex and Beth from 1: 1−1320=2020−1320=7201 - \frac{13}{20} = \frac{20}{20} - \frac{13}{20} = \frac{7}{20}.

Question 3

A farmer has a 50-pound bag of grain. On Monday, he uses 15\frac{1}{5} of the bag. On Tuesday, he adds 10 more pounds of grain to the bag. On Wednesday, he uses 13\frac{1}{3} of the new total amount in the bag. How many pounds of grain are left?

  1. 251325 \frac{1}{3}
  2. 30
  3. 331333 \frac{1}{3} (correct answer)
  4. 40
Explanation: On Monday, the farmer uses 15×50=10\frac{1}{5} \times 50 = 10 pounds. The amount remaining is 50−10=4050 - 10 = 40 pounds. On Tuesday, he adds 10 pounds, so the new total is 40+10=5040 + 10 = 50 pounds. On Wednesday, he uses 13\frac{1}{3} of this amount: 13×50=503=1623\frac{1}{3} \times 50 = \frac{50}{3} = 16 \frac{2}{3} pounds. The amount left is 50−1623=331350 - 16 \frac{2}{3} = 33 \frac{1}{3} pounds.

Question 4

After a party, 18\frac{1}{8} of a pizza is left. Before the last guest took their slices, there was 12\frac{1}{2} of the pizza remaining. What fraction of the original pizza did the last guest eat?

  1. 16\frac{1}{6}
  2. 58\frac{5}{8}
  3. 12\frac{1}{2}
  4. 38\frac{3}{8} (correct answer)
Explanation: The amount the last guest ate is the difference between the amount of pizza available before they ate and the amount left after they ate. Subtract the final fraction from the starting fraction: 12−18=48−18=38\frac{1}{2} - \frac{1}{8} = \frac{4}{8} - \frac{1}{8} = \frac{3}{8}. The last guest ate 38\frac{3}{8} of the original pizza.

Question 5

An exam is 3 hours long. A student spends 12\frac{1}{2} of the total time on the math section and 25\frac{2}{5} of the remaining time on the science section. How much time, in minutes, is left for the other sections?

  1. 36
  2. 54 (correct answer)
  3. 72
  4. 90
Explanation: First, convert the total time to minutes: 3 hours×60 min/hour=1803 \text{ hours} \times 60 \text{ min/hour} = 180 minutes. Time spent on math: 12×180=90\frac{1}{2} \times 180 = 90 minutes. Remaining time: 180−90=90180 - 90 = 90 minutes. Time spent on science: 25×90=2×18=36\frac{2}{5} \times 90 = 2 \times 18 = 36 minutes. Time left for other sections: 90−36=5490 - 36 = 54 minutes.

Question 6

A container is filled with 6126 \frac{1}{2} gallons of water. Another 3133 \frac{1}{3} gallons are added. If the container's total capacity is 15 gallons, what fraction of the container is now full?

  1. 23\frac{2}{3}
  2. 2945\frac{29}{45}
  3. 12\frac{1}{2}
  4. 5990\frac{59}{90} (correct answer)
Explanation: First, find the total amount of water in the container by adding the two amounts: 612+313=(6+3)+(12+13)=9+(36+26)=9566 \frac{1}{2} + 3 \frac{1}{3} = (6+3) + (\frac{1}{2} + \frac{1}{3}) = 9 + (\frac{3}{6} + \frac{2}{6}) = 9 \frac{5}{6} gallons. Convert this to an improper fraction: 956=5969 \frac{5}{6} = \frac{59}{6}. To find the fraction of the container that is full, divide the amount of water by the total capacity: 596÷15=596×115=5990\frac{59}{6} \div 15 = \frac{59}{6} \times \frac{1}{15} = \frac{59}{90}.

Question 7

Three friends share a pizza. The first friend eats 13\frac{1}{3} of the pizza. The second friend eats 38\frac{3}{8} of what is left. What fraction of the original pizza does the third friend get?

  1. 14\frac{1}{4}
  2. 724\frac{7}{24}
  3. 512\frac{5}{12} (correct answer)
  4. 1724\frac{17}{24}
Explanation: After the first friend eats 13\frac{1}{3}, the amount of pizza remaining is 1−13=231 - \frac{1}{3} = \frac{2}{3}. The second friend eats 38\frac{3}{8} of this remainder, which is 38×23=624=14\frac{3}{8} \times \frac{2}{3} = \frac{6}{24} = \frac{1}{4} of the original pizza. The total eaten by the first two friends is 13+14=412+312=712\frac{1}{3} + \frac{1}{4} = \frac{4}{12} + \frac{3}{12} = \frac{7}{12}. The fraction left for the third friend is 1−712=5121 - \frac{7}{12} = \frac{5}{12}.

Question 8

A library has 120 reference books. It loans out 14\frac{1}{4} of them. Of the books remaining in the library, 23\frac{2}{3} are non-fiction. How many non-fiction books are remaining in the library?

  1. 30
  2. 60 (correct answer)
  3. 80
  4. 90
Explanation: First, calculate the number of books loaned out: 14×120=30\frac{1}{4} \times 120 = 30 books. Then, find the number of books remaining: 120−30=90120 - 30 = 90 books. Finally, calculate the number of non-fiction books among those remaining: 23×90=2×30=60\frac{2}{3} \times 90 = 2 \times 30 = 60. There are 60 non-fiction books remaining.

Question 9

A company's profit was $64,000 in one year. The next year, the profit was 78\frac{7}{8} of the previous year's profit. In the third year, the profit was again 78\frac{7}{8} of the second year's profit. What was the company's profit in the third year?

  1. $49,000 (correct answer)
  2. $56,000
  3. $58,000
  4. $60,000
Explanation: To find the profit in the second year, calculate 78\frac{7}{8} of $64,000: ( \frac{7}{8} \times 64000 = 7 \times 8000 = 56,000 \). To find the profit in the third year, calculate \frac{7}{8}of the second year's profit: \( \frac{7}{8} \times 56000 = 7 \times 7000 =49,000 ).

Question 10

Two runners are in a race that is 10 kilometers long. Runner A has completed 34\frac{3}{4} of the race. Runner B has completed 23\frac{2}{3} of the race. How many more kilometers has Runner A completed than Runner B?

  1. 56\frac{5}{6} (correct answer)
  2. 1
  3. 1161 \frac{1}{6}
  4. 1231 \frac{2}{3}
Explanation: First, find the fraction of the race that separates the two runners: 34−23=912−812=112\frac{3}{4} - \frac{2}{3} = \frac{9}{12} - \frac{8}{12} = \frac{1}{12}. Next, find this fractional distance of the total race length: 112×10 km=1012 km=56\frac{1}{12} \times 10 \text{ km} = \frac{10}{12} \text{ km} = \frac{5}{6} km. So, Runner A is 56\frac{5}{6} of a kilometer ahead of Runner B.

Question 11

A baker made a batch of dough weighing 40 pounds. He used 35\frac{3}{5} of the dough to make loaves of bread. He then used 14\frac{1}{4} of the remaining dough to make dinner rolls. How many pounds of dough were left over?

  1. 4
  2. 12 (correct answer)
  3. 16
  4. 20
Explanation: First, calculate the amount of dough used for bread: 35×40=24\frac{3}{5} \times 40 = 24 pounds. Then, find the amount of dough remaining: 40−24=1640 - 24 = 16 pounds. Next, calculate the amount of dough used for dinner rolls from the remainder: 14×16=4\frac{1}{4} \times 16 = 4 pounds. Finally, subtract the dough used for rolls from the remainder to find the final amount left over: 16−4=1216 - 4 = 12 pounds.

Question 12

A person allocates 14\frac{1}{4} of their monthly income to rent and 15\frac{1}{5} of the remaining amount to groceries. If the person's monthly income is $2,400, how much is spent on groceries?

  1. $360 (correct answer)
  2. $480
  3. $600
  4. $1,080
Explanation: First, calculate the amount spent on rent: ( \frac{1}{4} \times 2400 = 600 \). Next, find the remaining income: \( 2400 - 600=600 = 1800 ). Finally, calculate the amount spent on groceries from the remainder: ( \frac{1}{5} \times 1800 = $360 ).

Question 13

A carpenter has a board of wood that is 15 feet long. He needs to cut as many shelves as possible that are each 2132 \frac{1}{3} feet long. After cutting the maximum number of whole shelves, how much wood, in feet, will be left over?

  1. 37\frac{3}{7}
  2. 14
  3. 6
  4. 1 (correct answer)
Explanation: First, determine how many shelves can be cut by dividing the total length by the shelf length: 15÷213=15÷73=15×37=457=63715 \div 2 \frac{1}{3} = 15 \div \frac{7}{3} = 15 \times \frac{3}{7} = \frac{45}{7} = 6 \frac{3}{7}. This means 6 whole shelves can be cut. Calculate the amount of wood used for these 6 shelves: 6×213=6×73=146 \times 2 \frac{1}{3} = 6 \times \frac{7}{3} = 14 feet. The leftover wood is the original length minus the used length: 15−14=115 - 14 = 1 foot.

Question 14

A driver is on a 240-mile trip. The driver covers 13\frac{1}{3} of the distance before stopping for lunch. After lunch, the driver covers 38\frac{3}{8} of the remaining distance. How many miles are left to complete the trip?

  1. 90
  2. 100 (correct answer)
  3. 140
  4. 160
Explanation: First, calculate the distance covered before lunch: 13×240=80\frac{1}{3} \times 240 = 80 miles. The remaining distance is 240−80=160240 - 80 = 160 miles. After lunch, the driver covers 38\frac{3}{8} of this remainder: 38×160=3×20=60\frac{3}{8} \times 160 = 3 \times 20 = 60 miles. The final remaining distance is 160−60=100160 - 60 = 100 miles.

Question 15

A delivery truck has a weight capacity of 2122 \frac{1}{2} tons. If it is being loaded with crates that each weigh 18\frac{1}{8} of a ton, what is the maximum number of crates that can be loaded onto the truck?

  1. 10
  2. 16
  3. 20 (correct answer)
  4. 24
Explanation: To find the number of crates, divide the total capacity of the truck by the weight of a single crate. First, convert the mixed number to an improper fraction: 212=522 \frac{1}{2} = \frac{5}{2}. Now, perform the division: 52÷18=52×81=402=20\frac{5}{2} \div \frac{1}{8} = \frac{5}{2} \times \frac{8}{1} = \frac{40}{2} = 20. The truck can hold a maximum of 20 crates.

Question 16

A water tank is 34\frac{3}{4} full. After using 16\frac{1}{6} of the water currently in the tank for irrigation, and then adding 45 gallons, the tank becomes 56\frac{5}{6} full. What is the total capacity of the tank?

  1. 180 gallons
  2. 216 gallons (correct answer)
  3. 240 gallons
  4. 270 gallons
Explanation: Let C be the tank's capacity. Initially: 3C4\frac{3C}{4} gallons. After using 16\frac{1}{6} of current water: 3C4−16×3C4=3C4(1−16)=3C4×56=5C8\frac{3C}{4} - \frac{1}{6} × \frac{3C}{4} = \frac{3C}{4}(1 - \frac{1}{6}) = \frac{3C}{4} × \frac{5}{6} = \frac{5C}{8}. After adding 45 gallons: 5C8+45=5C6\frac{5C}{8} + 45 = \frac{5C}{6}. Solving: 45=5C6−5C8=20C−15C24=5C2445 = \frac{5C}{6} - \frac{5C}{8} = \frac{20C - 15C}{24} = \frac{5C}{24}. Therefore: C=45×245=216C = 45 × \frac{24}{5} = 216 gallons. Choice A comes from setting up the equation incorrectly. Choice C results from using 16\frac{1}{6} of total capacity instead of current water. Choice D comes from computational errors in fraction arithmetic.

Question 17

Sarah is reading a book. On Monday, she read 18\frac{1}{8} of the book. On Tuesday, she read 35\frac{3}{5} of what remained. On Wednesday, she read 84 pages, which completed exactly 12\frac{1}{2} of what was left after Tuesday. How many pages are in the entire book?

  1. 480 pages (correct answer)
  2. 560 pages
  3. 672 pages
  4. 720 pages
Explanation: Let P be total pages. After Monday: P−P8=7P8P - \frac{P}{8} = \frac{7P}{8} remains. After Tuesday: 7P8−35×7P8=7P8×25=7P20\frac{7P}{8} - \frac{3}{5} × \frac{7P}{8} = \frac{7P}{8} × \frac{2}{5} = \frac{7P}{20} remains. Wednesday's 84 pages is half of what remained after Tuesday: 84=12×7P20=7P4084 = \frac{1}{2} × \frac{7P}{20} = \frac{7P}{40}. Solving: P=84×407=480P = 84 × \frac{40}{7} = 480 pages. Choice B results from incorrectly calculating Tuesday's remaining fraction. Choice C comes from treating Wednesday's reading as 13\frac{1}{3} instead of 12\frac{1}{2} of remaining. Choice D results from calculation errors in the fraction operations.

Question 18

On Monday, a painter uses 13\frac{1}{3} of a can of paint. On Tuesday, she uses 25\frac{2}{5} of the paint that was remaining in the can. What fraction of the original can of paint is left?

  1. 415\frac{4}{15}
  2. 25\frac{2}{5} (correct answer)
  3. 23\frac{2}{3}
  4. 1115\frac{11}{15}
Explanation: After Monday, the remaining paint is 1−13=231 - \frac{1}{3} = \frac{2}{3} of the can. On Tuesday, she uses 25\frac{2}{5} of this remainder, which is 25×23=415\frac{2}{5} \times \frac{2}{3} = \frac{4}{15} of the original can. The fraction of paint left is the amount after Monday minus the amount used Tuesday: 23−415=1015−415=615=25\frac{2}{3} - \frac{4}{15} = \frac{10}{15} - \frac{4}{15} = \frac{6}{15} = \frac{2}{5}.

Question 19

The perimeter of a rectangular garden is 251225 \frac{1}{2} feet. If the length of the garden is 8148 \frac{1}{4} feet, what is the width of the garden in feet?

  1. 4124 \frac{1}{2} (correct answer)
  2. 8128 \frac{1}{2}
  3. 99
  4. 171417 \frac{1}{4}
Explanation: The perimeter of a rectangle is 2L+2W=P2L + 2W = P. The combined length of the two long sides is 2×814=2×334=664=16122 \times 8 \frac{1}{4} = 2 \times \frac{33}{4} = \frac{66}{4} = 16 \frac{1}{2} feet. Subtract this from the total perimeter to find the combined length of the two widths: 2512−1612=925 \frac{1}{2} - 16 \frac{1}{2} = 9 feet. Since this is the length of two widths, divide by 2 to find the length of one width: 9÷2=4129 \div 2 = 4 \frac{1}{2} feet.

Question 20

In a class of 60 students, 25\frac{2}{5} are in the school band. Of the students in the band, 14\frac{1}{4} play a brass instrument. How many students in the class play a brass instrument?

  1. 6 (correct answer)
  2. 10
  3. 18
  4. 24
Explanation: First, find the number of students in the band: 25×60=2×12=24\frac{2}{5} \times 60 = 2 \times 12 = 24. Next, find the number of these band students who play a brass instrument: 14×24=6\frac{1}{4} \times 24 = 6. Therefore, 6 students play a brass instrument.