Liam is reading a book that has 120 pages. He has read (\frac{2}{5}) of the book. How many pages does he have left to read?
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ISEE Lower Level Mathematics Achievement Quiz
Practice Fraction Of A Set in ISEE Lower Level Mathematics Achievement with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.
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Liam is reading a book that has 120 pages. He has read (\frac{2}{5}) of the book. How many pages does he have left to read?
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 Mathematics Achievement.
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.
Liam is reading a book that has 120 pages. He has read (\frac{2}{5}) of the book. How many pages does he have left to read?
Explanation: First, find the number of pages Liam has read. Multiply the total number of pages by the fraction he has read: (\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 = 72) pages. Alternatively, find the fraction of the book left to read: (1 - \frac{2}{5} = \frac{3}{5}). Then, calculate this fraction of the total pages: (\frac{3}{5} \times 120 = 72) pages.
A farm has 80 animals. (\frac{3}{8}) of the animals are chickens and (\frac{1}{5}) of the animals are cows. How many more chickens than cows are on the farm?
Explanation: First, calculate the number of chickens: (\frac{3}{8} \times 80 = 3 \times 10 = 30) chickens. Next, calculate the number of cows: (\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 = 14).
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?
Explanation: First, find the number of quarters: (\frac{3}{8} \times 40 = 15) quarters. The value of the quarters is (15 \times 0.25=3.75). Next, find the number of dimes. The rest of the coins are dimes, so (40 - 15 = 25) dimes. The value of the dimes is (25 \times 0.10=2.50). Finally, add the values together to find the total value of the collection: (3.75+2.50 = $6.25).
At a park, (\frac{1}{2}) of the people are children and (\frac{1}{5}) are teenagers. The rest are adults. If there are 12 more children than teenagers, how many adults are at the park?
Explanation: Let T be the total number of people. The difference in the fraction of children and teenagers is (\frac{1}{2} - \frac{1}{5} = \frac{5}{10} - \frac{2}{10} = \frac{3}{10}). This difference represents 12 people, so (\frac{3}{10}T = 12). To find the total T, first find what (\frac{1}{10}T) is: (12 \div 3 = 4). Then the total T is (4 \times 10 = 40) people. The fraction of adults is (1 - (\frac{1}{2} + \frac{1}{5}) = 1 - \frac{7}{10} = \frac{3}{10}). The number of adults is (\frac{3}{10}) of the total: (\frac{3}{10} \times 40 = 12).
A tailor cuts a piece of ribbon for a project. First, she cuts off (\frac{1}{5}) of the original length. Then, she cuts off (\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?
Explanation: First, find the total fraction of the ribbon that was cut off. Since both fractions are of the original length, add them together: (\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 - \frac{7}{10} = \frac{3}{10}). This remaining (\frac{3}{10}) is equal to 18 inches. If (\frac{3}{10}) of the length is 18 inches, then (\frac{1}{10}) of the length is (18 \div 3 = 6) inches. The original length ((\frac{10}{10})) is (6 \times 10 = 60) inches.
A party punch is made by mixing grape juice, apple juice, and sparkling water. In a 36-ounce pitcher of punch, (\frac{4}{9}) is grape juice and (\frac{1}{3}) is apple juice. The rest is sparkling water. How many ounces of sparkling water are in the pitcher?
Explanation: Calculate the amount of grape juice: (\frac{4}{9} \times 36 = 16) ounces. Calculate the amount of apple juice: (\frac{1}{3} \times 36 = 12) ounces. The total amount of juice is (16 + 12 = 28) ounces. To find the amount of sparkling water, subtract the juice amount from the total: (36 - 28 = 8) ounces. Alternatively, add the fractions (\frac{4}{9} + \frac{1}{3} = \frac{7}{9}). The remaining fraction for water is (1 - \frac{7}{9} = \frac{2}{9}). Then (\frac{2}{9} \times 36 = 8) ounces.
A garden has 72 flowers. One-third of the flowers are tulips and (\frac{1}{6}) are daffodils. The rest of the flowers are roses. How many roses are in the garden?
Explanation: First, find the number of tulips: (\frac{1}{3} \times 72 = 24). Then, find the number of daffodils: (\frac{1}{6} \times 72 = 12). The total number of tulips and daffodils is (24 + 12 = 36). To find the number of roses, subtract this sum from the total number of flowers: (72 - 36 = 36). So, there are 36 roses.
A teacher has 24 pencils. She gives 8 pencils to the class. Which fraction of the set is 8?
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.
There are 16 party favors for 4 friends. Each friend gets the same. What fraction is each share?
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."
There are 16 party favors and 4 friends. What fraction does each friend get?
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.
A teacher has 24 pencils. 1/3 go to the class. What is 1/3 of 24?
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.
A basket has 12 apples. 1/4 are taken out. How many apples are removed?
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.
In a collection of 60 trading cards, (\frac{1}{4}) are holographic and (\frac{1}{3}) are rare. If none of the cards are both holographic and rare, how many cards in the collection are neither?
Explanation: This is a multi-step problem. First, find the number of holographic cards: (\frac{1}{4} \times 60 = 15). Next, find the number of rare cards: (\frac{1}{3} \times 60 = 20). Add these amounts together to find the total number of special cards: (15 + 20 = 35). Finally, subtract this from the total number of cards to find how many are neither: (60 - 35 = 25).
Maya received $36 for her monthly allowance. She spent (\frac{1}{4}) of it on a movie ticket. Then, she spent (\frac{2}{3}) of the remaining money on a book. How much money did she have left?
Explanation: First, calculate the cost of the movie ticket: (\frac{1}{4} \times 36=9). Next, find the amount of money remaining after buying the ticket: (36−9 = 27\). Then, calculate the cost of the book, which is \(\frac{2}{3}\) of the remaining money: \(\frac{2}{3} \times 27 = 18\). Finally, subtract the cost of the book from the money she had left to find the final amount: \(27 - 18=9).
In a survey of 48 students, (\frac{5}{8}) said their favorite sport was soccer. Of the remaining students, (\frac{2}{3}) said their favorite sport was basketball. How many students chose basketball?
Explanation: First, find the number of students who chose soccer: (\frac{5}{8} \times 48 = 30). Next, find the number of remaining students: (48 - 30 = 18). The number of students who chose basketball is (\frac{2}{3}) of this remainder: (\frac{2}{3} \times 18 = 12).
A school's goal for a fundraiser is to raise $450. After the first week, they have raised (\frac{2}{3}) of their goal. How much more money do they need to raise to meet their goal?
Explanation: There are two ways to solve this. First method: calculate the amount raised so far: (\frac{2}{3} \times 450=300). Then subtract this from the goal: (450−300 = 150\). 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).
A large pizza was cut into 12 equal slices. Ethan ate (\frac{1}{4}) of the pizza, and Olivia ate (\frac{1}{3}) of the pizza. How many slices were left?
Explanation: First, find the number of slices Ethan ate: (\frac{1}{4} \times 12 = 3) slices. Next, find the number of slices Olivia ate: (\frac{1}{3} \times 12 = 4) slices. The total number of slices eaten is (3 + 4 = 7). To find the number of slices left, subtract the number eaten from the total number of slices: (12 - 7 = 5).
A teacher has 24 pencils. She gives 1/3 to the class. How many pencils is that?
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 by dividing 24 by 3. The correct choice is C because 24 ÷ 3 = 8, so the teacher gives 8 pencils to the class. Choice A (6 pencils) would be 1/4 of 24, while choice D (12 pencils) would be 1/2 of 24. To help students: Reinforce that the denominator tells us how many equal groups to make. Use manipulatives like counters to physically divide sets into equal groups and see the fraction in action.
A bag contains 50 marbles. There are 10 red marbles and 15 blue marbles. Of the remaining marbles, (\frac{3}{5}) are green. How many green marbles are in the bag?
Explanation: First, find the total number of red and blue marbles: (10 + 15 = 25). Next, find the number of remaining marbles by subtracting the red and blue marbles from the total: (50 - 25 = 25). Finally, calculate the number of green marbles by finding (\frac{3}{5}) of the remaining marbles: (\frac{3}{5} \times 25 = 15).
In a class of 32 students, (\frac{3}{4}) of them take the bus to school. Of the students who take the bus, (\frac{1}{6}) get off at the first stop. How many students get off at the first stop?
Explanation: First, find the number of students who take the bus: (\frac{3}{4} \times 32 = 24) students. Next, find the number of these students who get off at the first stop by calculating (\frac{1}{6}) of the bus riders: (\frac{1}{6} \times 24 = 4) students.