Fractions as Division
Write the fraction 7/3 as a division equation.
7÷3
Compare the fractions 7/5 and 5/7. Which one is greater? Explain your reasoning.
7/5 is greater because 7/5 is greater than 1, and 5/7 is less than 1.
Solve: 4 × ⅗. Explain how you got your answer.
12/5 or 2 2/5
Explanation vary
The school library has 9 bookshelves, and ⅗ of them contain fiction books. How many bookshelves contain fiction books?
3/5 of 9 = 27/5 = 5 2/5 shelves contain fiction books.
Compare: 2 × (3/5 + 2/10) and 2 × 3/5 + 2 × 2/10. Are they equal?
Yes, they're equal.
A baker has 5 loaves of bread and wants to share them equally among 8 customers. How much bread does each customer get?
The class has 12 pencils to be shared equally among 5 students. How many pencils does each student receive? Express your answer as a fraction.
12÷5 = 12/5 = 2 2/5
Each student will receive 2 pencils.
A soccer team practices ⅔ of an hour each day for 6 days. How many total hours do they practice?
2/3 x 6 = 4 hours
They will practice for a total of 4 hours.
Write a numerical expression for the phrase: "Subtract ⅖ from ¾, then multiply by 6."
(2/5 - 3/4) x 6
Use a tape diagram to model 9 ÷ 4 and express the answer as a mixed number.
Tape Diagram answers vary.
9/4 = 2 1/4
A farmer has 17 gallons of milk and pours them evenly into 6 containers. How many gallons are in each container?
17÷6 = 17/6 = 2 5/6
Each container has 2 5/6 gallons of milk.
Use a tape diagram to solve 5 × ¾.
Answers vary
15/4 = 3 3/4
A container holds 5 gallons of water. If ⅔ of it is used, how many gallons remain?
2/3 of 5 = 10/3 = 3 1/3 is used
5 - 3 1/3 = 1 2/3 gallons are left over.
A school cafeteria orders 5 trays of pizza. Each tray holds ¾ of a pizza. How much total pizza did they order?
5 x 3/4 = 15/4 = 3 3/4pizzas
If 15 apples are shared equally among 6 children, how many apples does each child get? Express your answer as a fraction.
15÷6= 15/6 = 3 1/2
Each child gets 3 1/2 apples.
Draw a model to show 4 ÷ 3 and explain how it represents the fraction.
Answers vary
A recipe calls for ⅖ cup of sugar per batch of cookies. How much sugar is needed for 7 batches?
2/5 x 7 = 14/5 = 2 4/5
2 4/5 cups of sugar are needed for 7 batches of cookies.
Explain why multiplying a whole number by a fraction less than 1 results in a smaller product.
The product is less because one of the factors is a fraction, a part of a whole.
Write a written expression for this numerical expression:
(5 x 3/4) + (2 x 2/5)
The product of 5 and 3/4 plus the product of 2 and 2/5
A teacher divides 10 pounds of clay among 3 students. Write an equation to represent this division and solve.
10 ÷ 3
10/3 = 3 1/3 pounds per student
Which is greater: 5 ÷ 2 or 2 ÷ 5? Use a fraction to explain your reasoning.
5÷2 is greater because the answer will be 5/2, an improper fraction, greater than 1.
2÷5 is less because the answer is 2/5, a proper fraction, less than 1.
Solve: 8 × ⅗. Write the answer as a fraction and a mixed number.
24/5
4 4/5
Which is larger: ⅗ × 12 or 5 × ⅗? Explain your reasoning.
3/5 x 12 is larger because 12 is greater than 5. Both numbers are being multiplied by 3/5.
Write a written expression for this numerical expression:
7- (4 ÷ 3)
7 minus the quotient of 4 and 3