ISEE Lower Level Quiz: Fraction Word Problems
19 questions · exam conditions
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Fraction Word ProblemsQuestion 1 of 19

In a bag of fruit, 23\frac{2}{3} of the fruits are apples. The rest are oranges and pears. There are 6 oranges, which is 12\frac{1}{2} of the number of non-apple fruits. How many total fruits are in the bag?

18 fruits
24 fruits
30 fruits
36 fruits
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ISEE Lower Level Quiz

ISEE Lower Level Quiz: Fraction Word Problems

Practice Fraction Word Problems in ISEE Lower Level 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 ISEE Lower Level.

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

In a bag of fruit, 23\frac{2}{3} of the fruits are apples. The rest are oranges and pears. There are 6 oranges, which is 12\frac{1}{2} of the number of non-apple fruits. How many total fruits are in the bag?

  1. 18 fruits
  2. 24 fruits
  3. 30 fruits
  4. 36 fruits (correct answer)
Explanation: First, find the total number of non-apple fruits. Since 6 oranges make up 12\frac{1}{2} of the non-apple fruits, the total number of non-apple fruits is 6×2=126 \times 2 = 12. Next, determine what fraction of the total fruits are non-apples. If 23\frac{2}{3} are apples, then 1−23=131 - \frac{2}{3} = \frac{1}{3} of the fruits are non-apples. We know that this 13\frac{1}{3} is equal to 12 fruits. To find the total number of fruits, solve 13×Total=12\frac{1}{3} \times \text{Total} = 12. The total is 12÷13=12×3=3612 \div \frac{1}{3} = 12 \times 3 = 36.

Question 2

A container holds 2 gallons of juice. Sara pours out 14\frac{1}{4} of the juice. Then she and her two friends share the remaining juice equally. How many gallons of juice does each person get?

  1. 14\frac{1}{4} gallon
  2. 12\frac{1}{2} gallon (correct answer)
  3. 34\frac{3}{4} gallon
  4. 23\frac{2}{3} gallon
Explanation: First, calculate the amount of juice poured out: 14×2=12\frac{1}{4} \times 2 = \frac{1}{2} gallon. Next, find the amount of juice remaining: 2−12=1122 - \frac{1}{2} = 1\frac{1}{2} gallons. Sara and her two friends make a total of 3 people. They share the remaining juice equally, so divide the remaining amount by 3: 112÷3=32÷3=32×13=36=121\frac{1}{2} \div 3 = \frac{3}{2} \div 3 = \frac{3}{2} \times \frac{1}{3} = \frac{3}{6} = \frac{1}{2} gallon. Each person gets 12\frac{1}{2} gallon of juice.

Question 3

At a certain school, 35\frac{3}{5} of the students are girls. Of the girls, 14\frac{1}{4} have brown hair. What fraction of the students at the school are girls who do NOT have brown hair?

  1. 320\frac{3}{20} of the students
  2. 25\frac{2}{5} of the students
  3. 920\frac{9}{20} of the students (correct answer)
  4. 34\frac{3}{4} of the students
Explanation: First, determine the fraction of girls who do not have brown hair. If 14\frac{1}{4} of the girls have brown hair, then 1−14=341 - \frac{1}{4} = \frac{3}{4} of the girls do not. Next, find what fraction this group represents of the entire school. Since girls make up 35\frac{3}{5} of the school, multiply this by the fraction of girls without brown hair: 35×34=920\frac{3}{5} \times \frac{3}{4} = \frac{9}{20}. Thus, 920\frac{9}{20} of the students are girls without brown hair.

Question 4

A library had 60 visitors one morning. Of these visitors, 23\frac{2}{3} were adults. Later, 14\frac{1}{4} of the adults who were there in the morning left. How many adults were still in the library?

  1. 10 adults
  2. 15 adults
  3. 30 adults (correct answer)
  4. 40 adults
Explanation: First, find the initial number of adults: 23×60=40\frac{2}{3} \times 60 = 40 adults. Next, find the number of adults who left: 14×40=10\frac{1}{4} \times 40 = 10 adults. Finally, subtract the number of adults who left from the initial number of adults to find how many remain: 40−10=3040 - 10 = 30 adults.

Question 5

A recipe for soup requires 23\frac{2}{3} cup of carrots and a recipe for stew requires 34\frac{3}{4} cup of carrots. If you make half of the soup recipe and a full stew recipe, how many total cups of carrots do you need?

  1. 1112\frac{1}{12} cups (correct answer)
  2. 1 cup
  3. 57\frac{5}{7} cup
  4. 1512\frac{5}{12} cups
Explanation: When you encounter fraction word problems involving recipes, focus on identifying what portions of each recipe you're making, then carefully add the amounts together. First, determine how many carrots you need for each recipe. The soup recipe calls for 23\frac{2}{3} cup, but you're only making half the recipe, so you need 12×23=26=13\frac{1}{2} \times \frac{2}{3} = \frac{2}{6} = \frac{1}{3} cup. The stew recipe requires 34\frac{3}{4} cup, and you're making the full recipe, so you need 34\frac{3}{4} cup. Now add these amounts: 13+34\frac{1}{3} + \frac{3}{4}. To add fractions, find a common denominator. The least common multiple of 3 and 4 is 12. Convert both fractions: 13=412\frac{1}{3} = \frac{4}{12} and 34=912\frac{3}{4} = \frac{9}{12}. Adding gives you 412+912=1312=1112\frac{4}{12} + \frac{9}{12} = \frac{13}{12} = 1\frac{1}{12} cups. Looking at the wrong answers: Choice B (1 cup) results from incorrectly adding 13+34\frac{1}{3} + \frac{3}{4} without finding a proper common denominator. Choice C (57\frac{5}{7} cup) comes from adding the numerators and denominators incorrectly (1+33+4\frac{1+3}{3+4}). Choice D (15121\frac{5}{12} cups) happens if you forget to take half of the soup recipe and use the full 23\frac{2}{3} cup instead. Remember to read recipe problems carefully—always check whether you're making full or partial recipes before calculating ingredient amounts. Convert to common denominators methodically to avoid arithmetic errors.

Question 6

A large truck is carrying a load of bricks that weighs 34\frac{3}{4} of a ton. A smaller truck is carrying a load that is 23\frac{2}{3} as heavy as the large truck's load. What is the weight, in tons, of the smaller truck's load?

  1. 112\frac{1}{12} of a ton
  2. 1512\frac{5}{12} tons
  3. 118\frac{1}{8} tons
  4. 12\frac{1}{2} of a ton (correct answer)
Explanation: When you see a problem involving fractions of quantities, you need to multiply fractions to find "a fraction of" something. Here, you're looking for what 23\frac{2}{3} of 34\frac{3}{4} ton equals. To find 23\frac{2}{3} of 34\frac{3}{4} ton, multiply the fractions: 23×34=2×33×4=612=12\frac{2}{3} \times \frac{3}{4} = \frac{2 \times 3}{3 \times 4} = \frac{6}{12} = \frac{1}{2}. The smaller truck's load weighs 12\frac{1}{2} ton. Answer choice A (112\frac{1}{12} ton) represents a common error where students subtract the fractions instead of multiplying: 34−23=912−812=112\frac{3}{4} - \frac{2}{3} = \frac{9}{12} - \frac{8}{12} = \frac{1}{12}. This makes no sense logically since the smaller truck should carry a substantial portion of the larger truck's load. Answer choice B (15121\frac{5}{12} tons) results from adding the fractions: 34+23=912+812=1712=1512\frac{3}{4} + \frac{2}{3} = \frac{9}{12} + \frac{8}{12} = \frac{17}{12} = 1\frac{5}{12}. This also doesn't match the problem's requirement. Answer choice C (1181\frac{1}{8} tons) might come from incorrectly calculating 23×34\frac{2}{3} \times \frac{3}{4} and getting a mixed number, but this exceeds the original load weight, which is impossible. Remember: when you see "is ab\frac{a}{b} as heavy as" or similar language, you're multiplying fractions. The key phrase "as heavy as" signals multiplication, not addition or subtraction.

Question 7

A baker starts with a 10-pound bag of flour. He uses 14\frac{1}{4} of the bag for bread. He then uses 13\frac{1}{3} of the remaining flour for muffins. How many pounds of flour are left in the bag?

  1. 2 12\frac{1}{2} pounds
  2. 4 16\frac{1}{6} pounds
  3. 5 pounds (correct answer)
  4. 7 12\frac{1}{2} pounds
Explanation: First, calculate the flour used for bread: 14×10=104=2.5\frac{1}{4} \times 10 = \frac{10}{4} = 2.5 pounds. Then, find the amount of flour remaining: 10−2.5=7.510 - 2.5 = 7.5 pounds. Next, calculate the flour used for muffins, which is 13\frac{1}{3} of the remaining amount: 13×7.5=2.5\frac{1}{3} \times 7.5 = 2.5 pounds. Finally, subtract the flour used for muffins from the amount that was remaining: 7.5−2.5=57.5 - 2.5 = 5 pounds. There are 5 pounds of flour left.

Question 8

At a concert, 15\frac{1}{5} of the attendees are children. Of the adults, the number of women is three times the number of men. If there are 120 men at the concert, how many people are at the concert in total?

  1. 600 people (correct answer)
  2. 500 people
  3. 480 people
  4. 720 people
Explanation: This problem tests your ability to work with fractions and proportional relationships by building up from given information to find a total. Start with what you know: there are 120 men at the concert. Since the number of women is three times the number of men, there are 3×120=3603 \times 120 = 360 women. This means there are 120+360=480120 + 360 = 480 adults total. Now use the fraction information. If 15\frac{1}{5} of attendees are children, then 45\frac{4}{5} must be adults. Since you found there are 480 adults, you can set up the equation: 45×total=480\frac{4}{5} \times \text{total} = 480. Solving for the total: total=480×54=600\text{total} = 480 \times \frac{5}{4} = 600 people. Looking at the wrong answers: Choice B (500) likely comes from incorrectly assuming adults make up 45\frac{4}{5} of 500, but 45×500=400≠480\frac{4}{5} \times 500 = 400 \neq 480. Choice C (480) is the trap of giving just the number of adults instead of the total attendees. Choice D (720) might result from incorrectly thinking children are 14\frac{1}{4} of the total instead of 15\frac{1}{5}, or from calculation errors with the ratios. The correct answer is A (600 people). Strategy tip: In multi-step fraction problems, always work backwards from concrete numbers to check your answer. Here, verify: 15×600=120\frac{1}{5} \times 600 = 120 children, and 600−120=480600 - 120 = 480 adults, which matches what you calculated.

Question 9

A recipe that makes 1 dozen cookies requires 34\frac{3}{4} cup of flour. If Sarah wants to make 16 cookies, how much flour will she need?

  1. 12\frac{1}{2} cup
  2. 1 cup (correct answer)
  3. 1 14\frac{1}{4} cups
  4. 1 12\frac{1}{2} cups
Explanation: First, determine what fraction of the recipe Sarah is making. A dozen is 12 cookies. Sarah is making 16 cookies, so she is making 1612\frac{16}{12} of the recipe. This fraction simplifies to 43\frac{4}{3}. Next, multiply the amount of flour by this fraction: 34×43=1212=1\frac{3}{4} \times \frac{4}{3} = \frac{12}{12} = 1. Sarah will need 1 cup of flour.

Question 10

A painter used 13\frac{1}{3} of a can of paint for a wall. He then used 12\frac{1}{2} of the remaining paint for a door. What fraction of the original can of paint is left?

  1. 16\frac{1}{6} of the can
  2. 14\frac{1}{4} of the can
  3. 13\frac{1}{3} of the can (correct answer)
  4. 56\frac{5}{6} of the can
Explanation: First, find the fraction of paint remaining after painting the wall: 1−13=231 - \frac{1}{3} = \frac{2}{3}. Next, find the amount of paint used for the door, which is 12\frac{1}{2} of the remaining 23\frac{2}{3}: 12×23=26=13\frac{1}{2} \times \frac{2}{3} = \frac{2}{6} = \frac{1}{3}. The amount of paint left is the amount that remained after painting the wall minus the amount used for the door: 23−13=13\frac{2}{3} - \frac{1}{3} = \frac{1}{3}. So, 13\frac{1}{3} of the original can is left.

Question 11

After selling 25\frac{2}{5} of his comic books, Leo has 18 comic books left. How many comic books did he have originally?

  1. 27 comic books
  2. 30 comic books (correct answer)
  3. 36 comic books
  4. 45 comic books
Explanation: If Leo sold 25\frac{2}{5} of his comic books, the fraction he has left is 1−25=351 - \frac{2}{5} = \frac{3}{5}. The problem states that this remaining fraction is equal to 18 comic books. So, 35\frac{3}{5} of the original total is 18. To find the original total, we can set up the equation 35×Total=18\frac{3}{5} \times \text{Total} = 18. Solving for the total gives Total=18÷35=18×53=6×5=30\text{Total} = 18 \div \frac{3}{5} = 18 \times \frac{5}{3} = 6 \times 5 = 30. Leo originally had 30 comic books.

Question 12

A spool contains a ribbon that is 5125\frac{1}{2} yards long. If the ribbon is cut into shorter pieces that are each 14\frac{1}{4} of a yard long, how many full pieces can be cut?

  1. 20 pieces
  2. 21 pieces
  3. 22 pieces (correct answer)
  4. 23 pieces
Explanation: To find the number of pieces, divide the total length of the ribbon by the length of each piece. First, convert the mixed number to an improper fraction: 512=1125\frac{1}{2} = \frac{11}{2}. Now, divide 112\frac{11}{2} by 14\frac{1}{4}: 112÷14=112×41=442=22\frac{11}{2} \div \frac{1}{4} = \frac{11}{2} \times \frac{4}{1} = \frac{44}{2} = 22. Therefore, 22 full pieces can be cut.

Question 13

A carpenter has a board that is 12 feet long. He needs to cut it into shelves that are each 2142\frac{1}{4} feet long. How many full shelves can he cut from the board?

  1. 4 shelves
  2. 5 shelves (correct answer)
  3. 6 shelves
  4. 27 shelves
Explanation: To find the number of shelves, divide the total length of the board by the length of one shelf. First, convert the mixed number to an improper fraction: 214=942\frac{1}{4} = \frac{9}{4}. Now, divide 12 by 94\frac{9}{4}: 12÷94=12×49=48912 \div \frac{9}{4} = 12 \times \frac{4}{9} = \frac{48}{9}. To find how many full shelves can be cut, convert the improper fraction to a mixed number: 489=539=513\frac{48}{9} = 5\frac{3}{9} = 5\frac{1}{3}. This means he can cut 5 full shelves and will have a piece of wood left over.

Question 14

A large water jug holds 6 liters. A small cup holds 38\frac{3}{8} of a liter. How many full cups can be filled from the jug?

  1. 2 14\frac{1}{4} cups
  2. 24 cups
  3. 18 cups
  4. 16 cups (correct answer)
Explanation: When you see a question asking "how many full cups can be filled," you're dealing with a division problem where you need to find how many smaller units fit into a larger unit. To solve this, divide the total amount of water by the capacity of each cup: 6÷386 \div \frac{3}{8}. When dividing by a fraction, multiply by its reciprocal instead: 6×836 \times \frac{8}{3}. This gives you 6×83=483=16\frac{6 \times 8}{3} = \frac{48}{3} = 16 full cups. Let's examine why the other answers are incorrect. Choice A (2¼ cups) likely comes from incorrectly multiplying 6×38=188=2146 \times \frac{3}{8} = \frac{18}{8} = 2\frac{1}{4}, but this tells you how much water would be in 6 cups, not how many cups you can fill. Choice B (24 cups) might result from confusing the fraction and thinking each cup holds 14\frac{1}{4} liter, leading to 6÷14=246 \div \frac{1}{4} = 24. Choice C (18 cups) could come from multiplying 6 by the numerator 3, ignoring the denominator entirely. Remember: when a problem asks "how many of X fit into Y," you're dividing Y by X. The key trap here is remembering to flip and multiply when dividing by fractions, and being careful not to multiply when you should divide. Always check if your answer makes sense—16 cups holding 38\frac{3}{8} liter each should give you close to 6 liters total.

Question 15

Mr. Chen owns a 10-acre plot of land. He divides the entire plot into smaller lots that each measure 25\frac{2}{5} of an acre. How many smaller lots can he create?

  1. 4 lots
  2. 20 lots
  3. 25 lots (correct answer)
  4. 50 lots
Explanation: To find the number of smaller lots, divide the total area of the land by the area of each lot. The calculation is 10÷2510 \div \frac{2}{5}. To divide by a fraction, multiply by its reciprocal: 10×52=502=2510 \times \frac{5}{2} = \frac{50}{2} = 25. He can create 25 lots.

Question 16

Jamal had $48. He spent 13\frac{1}{3} of his money on a video game. He then spent 14\frac{1}{4} of the money that was left on a snack. How much money does Jamal have now?

  1. $20
  2. $24 (correct answer)
  3. $32
  4. $36
Explanation: First, calculate the cost of the video game: (\frac{1}{3} \times 48=48 = 16). Next, find the amount of money remaining after buying the game: (48−48 - 16 = 32\). Then, calculate the cost of the snack, which is \frac{1}{4}of the remaining money: \(\frac{1}{4} \times32 = 8\). Finally, subtract the cost of the snack from the amount that was remaining to find the final amount: \(32 - 8=8 = 24).

Question 17

A fuel tank is 34\frac{3}{4} full and contains 120 gallons of fuel. What is the volume of fuel in the tank when it is 12\frac{1}{2} full?

  1. 60 gallons
  2. 160 gallons
  3. 90 gallons
  4. 80 gallons (correct answer)
Explanation: When you encounter fraction word problems involving capacity, your goal is to find the total capacity first, then calculate what any other fraction would contain. Since the tank is 34\frac{3}{4} full and contains 120 gallons, you can set up the equation: 34×total capacity=120\frac{3}{4} \times \text{total capacity} = 120. To find the total capacity, divide 120 by 34\frac{3}{4}, which is the same as multiplying by 43\frac{4}{3}: 120×43=160120 \times \frac{4}{3} = 160 gallons total capacity. Now that you know the tank holds 160 gallons when completely full, you can find how much it contains when 12\frac{1}{2} full: 12×160=80\frac{1}{2} \times 160 = 80 gallons. Looking at the wrong answers: Choice A (60 gallons) represents a common error where students incorrectly think that half of 34\frac{3}{4} full would be half of 120 gallons. Choice B (160 gallons) is the total tank capacity, not the amount when half full. Choice C (90 gallons) might result from incorrectly calculating 34\frac{3}{4} of 120 gallons, then adding or subtracting incorrectly. The correct answer is D (80 gallons). Strategy tip: In fraction capacity problems, always work backwards to find the total capacity first. Once you have that key piece of information, you can calculate any other fractional amount. Don't try to work directly from one fraction to another—you'll likely make calculation errors.

Question 18

Maria spent 13\frac{1}{3} of her money on a book and 12\frac{1}{2} of her remaining money on a snack. If she has $6.00 left, how much money did she start with?

  1. $18.00 (correct answer)
  2. $24.00
  3. $30.00
  4. $36.00
Explanation: Work backwards from the final amount. The $6.00 she has left is the amount after spending 12\frac{1}{2} of her money on a snack, which means 6.00 is the other \(\frac{1}{2}\). So, before buying the snack, she had \(6.00 \times 2 = $12.00). This $12.00 was the amount remaining after she spent 13\frac{1}{3} of her original money on a book. This means the $12.00 represents 1−13=231 - \frac{1}{3} = \frac{2}{3} of her starting money. To find the starting amount, solve the equation (\frac{2}{3} \times \text{Start} = 12.00\). So, \(\text{Start} = 12.00 \div \frac{2}{3} = 12.00×32=12.00 \times \frac{3}{2} = 18.00).

Question 19

A rectangular garden is 4124\frac{1}{2} meters long and 2232\frac{2}{3} meters wide. If 13\frac{1}{3} of the garden's area is planted with tomatoes, what is the area of the section with tomatoes?

  1. 4 square meters (correct answer)
  2. 8 square meters
  3. 12 square meters
  4. 16 square meters
Explanation: First, calculate the total area of the garden by multiplying its length and width. Convert the mixed numbers to improper fractions: 412=924\frac{1}{2} = \frac{9}{2} and 223=832\frac{2}{3} = \frac{8}{3}. The area is 92×83=726=12\frac{9}{2} \times \frac{8}{3} = \frac{72}{6} = 12 square meters. Next, find the area planted with tomatoes, which is 13\frac{1}{3} of the total area: 13×12=4\frac{1}{3} \times 12 = 4. The area with tomatoes is 4 square meters.