Fraction of a Set - ISEE Lower Level Mathematics Achievement

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?
Answer: 36 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.
There are 16 party favors for 4 friends. Each friend gets the same. What fraction is each share?
Answer: $1/4$ 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."
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?
Answer: $9 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: $\$27 - \$18 = \$9$ .
A teacher has 24 pencils. She gives $1/3$ to the class. How many pencils is that?
Answer: 8 pencils 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.
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?
Answer: 12 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 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?
Answer: 60 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?
Answer: 8 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.
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?
Answer: $6.25 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: $\$3.75 + \$2.50 = \$6.25$ .
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?
Answer: 5 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 container holds red, blue, and yellow beads. There are 24 red beads and 30 blue beads. The number of yellow beads is $\frac{1}{3}$ of the total number of red and blue beads combined. How many beads are in the container in total?
Answer: 72 First, find the combined number of red and blue beads: $24 + 30 = 54$ . Next, calculate the number of yellow beads, which is $\frac{1}{3}$ of this sum: $\frac{1}{3} \times 54 = 18$ . Finally, find the total number of beads by adding all three colors together: $54 (red and blue) + 18 (yellow) = 72$ beads.
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?
Answer: 15 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: $\frac{3}{5} \times 25 = 15$ .
A teacher has 24 pencils. She gives 8 pencils to the class. Which fraction of the set is 8?
Answer: $1/3$ 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.
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?
Answer: 25 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: $60 - 35 = 25$ .
There are 16 party favors and 4 friends. What fraction does each friend get?
Answer: $1/4$ 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.
Mr. Jones has a rectangular garden that is 100 square feet. He plants vegetables in $\frac{3}{5}$ 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?
Answer: 15 sq ft First, calculate the area used for vegetables: $\frac{3}{5} \times 100 = 60$ square feet. Next, find the remaining area: $100 - 60 = 40$ 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: $40 - 25 = 15$ square feet.
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?
Answer: 4 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.
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?
Answer: $150 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: $\frac{1}{3} \times \$450 = \$150$ .
In a school play, 12 students are in the chorus. This represents $\frac{2}{7}$ of the total cast. The rest of the cast are actors. How many actors are in the play?
Answer: 30 First, find the total number of students in the cast. If 12 students is $\frac{2}{7}$ of the total, then $\frac{1}{7}$ of the total is $12 \div 2 = 6$ students. The total cast ( $\frac{7}{7}$ ) is $6 \times 7 = 42$ students. To find the number of actors, subtract the number of chorus members from the total cast: $42 - 12 = 30$ actors.
A basket has 12 apples. $1/4$ are taken out. How many apples are removed?
Answer: 3 apples 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.
On a field trip, $\frac{1}{3}$ of the students chose to visit the dinosaur exhibit and $\frac{1}{2}$ chose the space exhibit. The remaining 8 students chose the ocean exhibit. How many students were on the field trip in total?
Answer: 48 First, find the fraction of students who visited the dinosaur or space exhibits by adding the fractions: $\frac{1}{3} + \frac{1}{2} = \frac{2}{6} + \frac{3}{6} = \frac{5}{6}$ . The remaining students represent the fraction $1 - \frac{5}{6} = \frac{1}{6}$ . If 8 students is $\frac{1}{6}$ of the total, then the total number of students is $8 \times 6 = 48$ .

Start this quiz