Fractions of a Quantity
Question:
A class has 24 students. 1/3 of the students bring lunch from home. How many students bring lunch?
8 students
Liam has 30 cookies. He gives 1/5 of them to his brother. How many cookies does Liam have left?
24 cookies
A movie lasts 2 hours. You have watched 3/4 of the movie. How much time is left?
Answer: 1/2 hour, or 30 minutes
Sofia has $60. She spends 1/3 of her money on a book.
How much money does she have left?
$40
A student says:
“If 1/4 of 20 is 5, then 1/4 of 40 must also be 5.”
Is the student correct?
Answer: No. 1/4 of 40 = 10.
Question:
A class has 24 students. 1/3 of the students bring lunch from home. How many students bring lunch?
24 pumpkins
A baker has 6 pounds of flour. She uses 2/3 of it to make bread.
How many pounds of flour does she have left?
2 pounds
A runner completes a race in 1 1/2 hours. The first part of the race takes 1/3 hour.
How much time is spent on the rest of the race?
1 1/6 hours
A student has $80. They spend 1/4 of their money on lunch and 1/5 of the remaining money on a game.
How much money is left?
$48
Answer: No. 1/4 of 40 = 10.
A student has 36 stickers and gives away 1/3 of them. The student says they have 12 stickers left.
Do you agree?
Answer: No.
1/3 of 36 = 12 stickers given away.
36 − 12 = 24 stickers left
A farmer has 40 pumpkins. He sells 3/5 of them. How many pumpkins does he sell?
1/2 of a garden
A ribbon is 12 yards long. Maya uses 1/3 of it for a project and then uses 1/4 of the remaining ribbon for another project.
How many yards of ribbon are left?
6 yards
Emma spends 2/5 of an hour reading and 1/4 of an hour drawing.
How much total time does she spend on these activities?
13/20 hour, or 39 minutes
A family has $240 for a trip. They spend 3/8 of the money on food. They then spend 1/4 of the remaining money on souvenirs.
How much money remains?
$112.50
Question:
A student has $100. They spend 1/4 of their money, then spend 1/4 of the remaining money.
The student says they spent 1/2 of their original money.
Are they correct?
Answer: No.
First: 1/4 of $100 = $25
Remaining: $75
Then: 1/4 of $75 = $18.75
Total spent = $43.75, not $50.
A garden is planted with vegetables. 3/4 of the garden contains vegetables, and 2/3 of the vegetable section is planted with tomatoes.
What fraction of the entire garden is planted with tomatoes?
20 markers
A farmer has 5 1/2 acres of land. He uses 2/5 of the land for corn. He uses 1/3 of the remaining land for pumpkins.
How many acres are still unused?
2 3/10
A bike ride takes 1 hour 30 minutes. The first loop takes 1/3 of the total time, and the second loop takes 2/5 of the total time.
How long does the final loop take?
24 minutes
A teacher has $150 to spend on classroom supplies. She spends 2/5 of the money on notebooks and 1/3 of the remaining money on pencils.
How much money does she have left?
$60
A student says:
“If I spend 1/3 of my money and then spend 1/3 of what is left, I have spent 2/3 of my money.”
Is this correct? Explain.
Answer: No.
For example, start with $90:
1/3 of $90 = $30
Remaining = $60
1/3 of $60 = $20
Total spent = $50.
So the student spent 5/9 of the original amount, not 2/3.
A school has 360 students. 2/5 of the students participate in sports. Of those students, 3/4 play team sports.
How many students play team sports?
216
A farmer has 5 1/2 acres of land. He uses 2/5 of the land for corn. He uses 1/3 of the remaining land for pumpkins.
How many acres are still unused?
108 notebooks
Question:
A hiking trail is 10 1/2 miles long. A group completes 2/3 of the trail in the morning. In the afternoon, they complete 3/4 of the distance they had left.
How many miles do they still need to hike?
7/8 mile
A student spends 1/4 of their money on a game and 1/3 of the remaining money on a book. After those purchases, they have $30 left.
How much money did the student have at the beginning?
$6
A student has some money. They spend 1/3 of it on a toy. Then they spend 1/4 of the remaining money on a gift. They have $30 left.
How much money did they start with?
Answer: $60
Work backward:
After spending 1/4 of the remaining money, they have 3/4 left.
If 3/4 = $30:
$30 ÷ 3 × 4 = $40
So $40 was left after buying the toy.
That $40 represents 2/3 of the original amount.
$40 ÷ 2 × 3 = $60