ISEE Lower Level Quiz: Fraction Of A Set
20 questions · exam conditions
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Fraction Of A SetQuestion 1 of 20

A tailor cuts a piece of ribbon for a project. First, she cuts off 15\frac{1}{5} of the original length. Then, she cuts off 12\frac{1}{2} of the original length. After these two cuts, 18 inches of ribbon are left. What was the original length of the ribbon in inches?

36
45
60
90
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ISEE Lower Level Quiz

ISEE Lower Level Quiz: Fraction Of A Set

Practice Fraction Of A Set 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 Of A Set, 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

A tailor cuts a piece of ribbon for a project. First, she cuts off 15\frac{1}{5} of the original length. Then, she cuts off 12\frac{1}{2} of the original length. After these two cuts, 18 inches of ribbon are left. What was the original length of the ribbon in inches?

  1. 36
  2. 45
  3. 60 (correct answer)
  4. 90
Explanation: First, find the total fraction of the ribbon that was cut off. Since both fractions are of the original length, add them together: 15+12=210+510=710\frac{1}{5} + \frac{1}{2} = \frac{2}{10} + \frac{5}{10} = \frac{7}{10}. The fraction of the ribbon that is left is 1−710=3101 - \frac{7}{10} = \frac{3}{10}. This remaining 310\frac{3}{10} is equal to 18 inches. If 310\frac{3}{10} of the length is 18 inches, then 110\frac{1}{10} of the length is 18÷3=618 \div 3 = 6 inches. The original length (1010\frac{10}{10}) is 6×10=606 \times 10 = 60 inches.

Question 2

A party punch is made by mixing grape juice, apple juice, and sparkling water. In a 36-ounce pitcher of punch, 49\frac{4}{9} is grape juice and 13\frac{1}{3} is apple juice. The rest is sparkling water. How many ounces of sparkling water are in the pitcher?

  1. 8 (correct answer)
  2. 12
  3. 16
  4. 28
Explanation: Calculate the amount of grape juice: 49×36=16\frac{4}{9} \times 36 = 16 ounces. Calculate the amount of apple juice: 13×36=12\frac{1}{3} \times 36 = 12 ounces. The total amount of juice is 16+12=2816 + 12 = 28 ounces. To find the amount of sparkling water, subtract the juice amount from the total: 36−28=836 - 28 = 8 ounces. Alternatively, add the fractions 49+13=79\frac{4}{9} + \frac{1}{3} = \frac{7}{9}. The remaining fraction for water is 1−79=291 - \frac{7}{9} = \frac{2}{9}. Then 29×36=8\frac{2}{9} \times 36 = 8 ounces.

Question 3

There are 16 party favors and 4 friends. What fraction does each friend get?

  1. 1/21/2
  2. 1/31/3
  3. 1/41/4 (correct answer)
  4. 1/51/5
Explanation: This question tests ISEE Lower Level students on finding a fraction of a set or group. The concept involves understanding fractions as parts of a set and applying simple division to find the part. In this scenario, we need to determine what fraction each friend gets when 16 party favors are shared equally among 4 friends. The correct choice is C because each friend gets 16 ÷ 4 = 4 favors, which is 4/16 = 1/4 of the total. Choice A (1/2) would mean each friend gets 8 favors, while choice B (1/3) would require 3 friends. To help students: Emphasize that equal sharing creates fractions, where the number of people becomes the denominator. Practice problems where students identify both the number of items per person and the fraction of the whole.

Question 4

In a survey of 48 students, 58\frac{5}{8} said their favorite sport was soccer. Of the remaining students, 23\frac{2}{3} said their favorite sport was basketball. How many students chose basketball?

  1. 6
  2. 12 (correct answer)
  3. 18
  4. 32
Explanation: First, find the number of students who chose soccer: 58×48=30\frac{5}{8} \times 48 = 30. Next, find the number of remaining students: 48−30=1848 - 30 = 18. The number of students who chose basketball is 23\frac{2}{3} of this remainder: 23×18=12\frac{2}{3} \times 18 = 12.

Question 5

A container holds red, blue, and yellow beads. There are 24 red beads and 30 blue beads. The number of yellow beads is 13\frac{1}{3} of the total number of red and blue beads combined. How many beads are in the container in total?

  1. 18
  2. 54
  3. 64
  4. 72 (correct answer)
Explanation: First, find the combined number of red and blue beads: 24+30=5424 + 30 = 54. Next, calculate the number of yellow beads, which is 13\frac{1}{3} of this sum: 13×54=18\frac{1}{3} \times 54 = 18. Finally, find the total number of beads by adding all three colors together: 54(redandblue)+18(yellow)=7254 (red and blue) + 18 (yellow) = 72 beads.

Question 6

On a field trip, 13\frac{1}{3} of the students chose to visit the dinosaur exhibit and 12\frac{1}{2} chose the space exhibit. The remaining 8 students chose the ocean exhibit. How many students were on the field trip in total?

  1. 24
  2. 40
  3. 48 (correct answer)
  4. 56
Explanation: First, find the fraction of students who visited the dinosaur or space exhibits by adding the fractions: 13+12=26+36=56\frac{1}{3} + \frac{1}{2} = \frac{2}{6} + \frac{3}{6} = \frac{5}{6}. The remaining students represent the fraction 1−56=161 - \frac{5}{6} = \frac{1}{6}. If 8 students is 16\frac{1}{6} of the total, then the total number of students is 8×6=488 \times 6 = 48.

Question 7

Mr. Jones has a rectangular garden that is 100 square feet. He plants vegetables in 35\frac{3}{5} of the garden. In the remaining section, he plants flowers in an area of 25 square feet. How much of the garden is left unplanted?

  1. 15 sq ft (correct answer)
  2. 25 sq ft
  3. 35 sq ft
  4. 40 sq ft
Explanation: First, calculate the area used for vegetables: 35×100=60\frac{3}{5} \times 100 = 60 square feet. Next, find the remaining area: 100−60=40100 - 60 = 40 square feet. Within this remaining 40 sq ft area, he plants 25 sq ft of flowers. To find the unplanted area, subtract the flower area from the remaining area: 40−25=1540 - 25 = 15 square feet.

Question 8

A box contains 48 crayons. 13\frac{1}{3} are in the red family, and 14\frac{1}{4} are in the blue family. Of the crayons that are not in the red or blue families, 12\frac{1}{2} are green. How many crayons are green?

  1. 10 (correct answer)
  2. 12
  3. 16
  4. 20
Explanation: First, find the number of red crayons: 13×48=16\frac{1}{3} \times 48 = 16. Second, find the number of blue crayons: 14×48=12\frac{1}{4} \times 48 = 12. Third, find the total of red and blue crayons: 16+12=2816 + 12 = 28. Fourth, find the number of remaining crayons: 48−28=2048 - 28 = 20. Finally, find the number of green crayons, which is half of the remainder: 12×20=10\frac{1}{2} \times 20 = 10.

Question 9

Liam is reading a book that has 120 pages. He has read 25\frac{2}{5} of the book. How many pages does he have left to read?

  1. 24
  2. 48
  3. 72 (correct answer)
  4. 80
Explanation: First, find the number of pages Liam has read. Multiply the total number of pages by the fraction he has read: 25×120=2405=48\frac{2}{5} \times 120 = \frac{240}{5} = 48 pages. The question asks for the number of pages left to read, so subtract the pages read from the total: 120−48=72120 - 48 = 72 pages. Alternatively, find the fraction of the book left to read: 1−25=351 - \frac{2}{5} = \frac{3}{5}. Then, calculate this fraction of the total pages: 35×120=72\frac{3}{5} \times 120 = 72 pages.

Question 10

Sarah has a collection of 40 coins. Three-eighths of the coins are quarters, and the rest are dimes. What is the total value of Sarah's coin collection?

  1. $3.75
  2. $6.25 (correct answer)
  3. $4.00
  4. $10.00
Explanation: First, find the number of quarters: 38×40=15\frac{3}{8} \times 40 = 15 quarters. The value of the quarters is (15 \times 0.25=0.25 = 3.75). Next, find the number of dimes. The rest of the coins are dimes, so 40−15=2540 - 15 = 25 dimes. The value of the dimes is (25 \times 0.10=0.10 = 2.50). Finally, add the values together to find the total value of the collection: (3.75+3.75 + 2.50 = $6.25).

Question 11

A farm has 80 animals. 38\frac{3}{8} of the animals are chickens and 15\frac{1}{5} of the animals are cows. How many more chickens than cows are on the farm?

  1. 14 (correct answer)
  2. 16
  3. 30
  4. 46
Explanation: First, calculate the number of chickens: 38×80=3×10=30\frac{3}{8} \times 80 = 3 \times 10 = 30 chickens. Next, calculate the number of cows: 15×80=16\frac{1}{5} \times 80 = 16 cows. The question asks for how many more chickens there are than cows, so find the difference: 30−16=1430 - 16 = 14.

Question 12

At a park, 12\frac{1}{2} of the people are children and 15\frac{1}{5} are teenagers. The rest are adults. If there are 12 more children than teenagers, how many adults are at the park?

  1. 8
  2. 12 (correct answer)
  3. 20
  4. 40
Explanation: Let T be the total number of people. The difference in the fraction of children and teenagers is 12−15=510−210=310\frac{1}{2} - \frac{1}{5} = \frac{5}{10} - \frac{2}{10} = \frac{3}{10}. This difference represents 12 people, so 310T=12\frac{3}{10}T = 12. To find the total T, first find what 110T\frac{1}{10}T is: 12÷3=412 \div 3 = 4. Then the total T is 4×10=404 \times 10 = 40 people. The fraction of adults is 1−(12+15)=1−710=3101 - (\frac{1}{2} + \frac{1}{5}) = 1 - \frac{7}{10} = \frac{3}{10}. The number of adults is 310\frac{3}{10} of the total: 310×40=12\frac{3}{10} \times 40 = 12.

Question 13

A garden has 72 flowers. One-third of the flowers are tulips and 16\frac{1}{6} are daffodils. The rest of the flowers are roses. How many roses are in the garden?

  1. 12
  2. 24
  3. 36 (correct answer)
  4. 48
Explanation: First, find the number of tulips: 13×72=24\frac{1}{3} \times 72 = 24. Then, find the number of daffodils: 16×72=12\frac{1}{6} \times 72 = 12. The total number of tulips and daffodils is 24+12=3624 + 12 = 36. To find the number of roses, subtract this sum from the total number of flowers: 72−36=3672 - 36 = 36. So, there are 36 roses.

Question 14

A teacher has 24 pencils. She gives 8 pencils to the class. Which fraction of the set is 8?

  1. 1/21/2
  2. 1/31/3 (correct answer)
  3. 1/41/4
  4. 1/51/5
Explanation: This question tests ISEE Lower Level students on finding a fraction of a set or group. The concept involves understanding fractions as parts of a set and applying simple division to find the part. In this scenario, 8 pencils out of 24 total are given away, and we need to identify what fraction 8 represents. The correct choice is B because 8 is 1/3 of 24 (since 24 ÷ 3 = 8, or 8 × 3 = 24). Choice A (1/2) would be 12 pencils, while choice C (1/4) would be 6 pencils. To help students: Emphasize checking fractions by multiplying - if 8 is 1/3 of the total, then 8 × 3 should equal 24. Practice identifying fractions from given parts and wholes to strengthen understanding of the relationship.

Question 15

There are 16 party favors for 4 friends. Each friend gets the same. What fraction is each share?

  1. 1/21/2
  2. 1/41/4 (correct answer)
  3. 1/31/3
  4. 1/51/5
Explanation: This question tests ISEE Lower Level students on finding a fraction of a set or group. The concept involves understanding fractions as parts of a set and applying simple division to find the part. In this scenario, 16 party favors are shared equally among 4 friends, so each gets 16 ÷ 4 = 4 favors. The correct choice is B because each friend's share of 4 favors represents 4/16 = 1/4 of the total. Choice A (1/2) would mean each friend gets 8 favors, while choice C (1/3) would work if there were only 3 friends. To help students: Connect division problems to fractions by showing that equal sharing creates fractional parts. Practice converting between "each person gets X items" and "each person gets 1/Y of the total."

Question 16

A teacher has 24 pencils. 1/31/3 go to the class. What is 1/31/3 of 24?

  1. 3
  2. 8 (correct answer)
  3. 12
  4. 21
Explanation: This question tests ISEE Lower Level students on finding a fraction of a set or group. The concept involves understanding fractions as parts of a set and applying simple division to find the part. In the given scenario, we need to calculate 1/3 of 24 pencils, which means dividing 24 by 3. The correct choice is B because 24 ÷ 3 = 8, so 1/3 of 24 equals 8. Choice A (3) might come from using the denominator as the answer, while choice C (12) would be 1/2 of 24. To help students: Emphasize the division process - divide the total by the denominator to find the fraction's value. Practice with different numbers and encourage students to verify by multiplying their answer by the denominator to get back to the original number.

Question 17

A basket has 12 apples. 1/41/4 are taken out. How many apples are removed?

  1. 2 apples
  2. 3 apples (correct answer)
  3. 4 apples
  4. 6 apples
Explanation: This question tests ISEE Lower Level students on finding a fraction of a set or group. The concept involves understanding fractions as parts of a set and applying simple division to find the part. In the given scenario, we need to calculate 1/4 of 12 apples, which means dividing 12 by 4. The correct choice is B because 12 ÷ 4 = 3, so 3 apples are removed from the basket. Choice A (2 apples) might result from incorrect division, while choices C and D represent other fractions of 12. To help students: Emphasize that finding a fraction of a number means dividing by the denominator. Practice with visual models like drawing circles to represent apples and grouping them into fourths.

Question 18

In a collection of 60 trading cards, 14\frac{1}{4} are holographic and 13\frac{1}{3} are rare. If none of the cards are both holographic and rare, how many cards in the collection are neither?

  1. 15
  2. 20
  3. 25 (correct answer)
  4. 35
Explanation: This is a multi-step problem. First, find the number of holographic cards: 14×60=15\frac{1}{4} \times 60 = 15. Next, find the number of rare cards: 13×60=20\frac{1}{3} \times 60 = 20. Add these amounts together to find the total number of special cards: 15+20=3515 + 20 = 35. Finally, subtract this from the total number of cards to find how many are neither: 60−35=2560 - 35 = 25.

Question 19

Maya received $36 for her monthly allowance. She spent 14\frac{1}{4} of it on a movie ticket. Then, she spent 23\frac{2}{3} of the remaining money on a book. How much money did she have left?

  1. $3
  2. $9 (correct answer)
  3. $18
  4. $27
Explanation: First, calculate the cost of the movie ticket: (\frac{1}{4} \times 36=36 = 9). Next, find the amount of money remaining after buying the ticket: (36−36 - 9 = 27\). Then, calculate the cost of the book, which is \frac{2}{3}of the remaining money: \(\frac{2}{3} \times27 = 18\). Finally, subtract the cost of the book from the money she had left to find the final amount: \(27 - 18=18 = 9).

Question 20

A school's goal for a fundraiser is to raise $450. After the first week, they have raised 23\frac{2}{3} of their goal. How much more money do they need to raise to meet their goal?

  1. $150 (correct answer)
  2. $225
  3. $300
  4. $200
Explanation: There are two ways to solve this. First method: calculate the amount raised so far: (\frac{2}{3} \times 450=450 = 300). Then subtract this from the goal: (450−450 - 300 = 150\). Second method: find the fraction of the money they still need to raise: 1 - \frac{2}{3} = \frac{1}{3}. Then calculate that fraction of the total goal: \(\frac{1}{3} \times 450 = $150).