Multiply or Divide?
A recipe uses 2/3 cup of sugar per batch. You make 3 batches.
Multiply or divide? Then, find the total amount of sugar.
Multiply.
2/3 × 3
= 2 cups
The trail is 8 miles long. Mai walked 1/4 of the trail.
How many miles did she walk?
2 miles
Three friends equally share 3/6 kg of cherries.
Write a division expression.
3/6 ÷ 3
Match the expression to its value:
1/2 × 8
A) 4 B) 16 C) 1/16
A) 4
A square tile measures 1/2 ft by 1/2 ft.
What is the area?
1/4 square foot
You have 3/4 of a pizza. Each slice is 1/8 of a pizza.
Multiply or divide? How many slices are there?
Divide.
3/4 ÷ 1/8
= 6 slices
Find the value of:
3 × 1/5
3/5
Solve:
3/6 ÷ 3
1/6
Match:
3/4 ÷ 3
A) 1/4 B) 9/4 C) 1/12
A) 1/4
Find the area of a rectangle that is 3/4 ft by 2/3 ft.
1/2 square foot
A container holds 1/2 liter of water. Jada drank 1/4 of the water.
Multiply or divide? How much did she drink?
Multiply.
1/2 × 1/4
= 1/8 liter
Which expression represents 2/3 of 12?
A) 12 ÷ 2/3
B) 2/3 × 12
2/3 × 12.
“Of the whole”
Which situation matches 2/3 ÷ 4?
A) Four groups of 2/3
B) Sharing 2/3 equally among 4
B) Sharing 2/3 equally among 4.
Which two expressions have the same value?
A) 2 × 1/3
B) 1/3 ÷ 2
C) 1/6
Explain.
B and C. Both equal 1/6
Mai says a 1/2 ft by 1/2 ft tile has the same area as a 1 ft by 1 ft tile.
Do you agree or disagree? Why?
Disagree. 1/2 × 1/2 = 1/4, which is smaller than 1
Which expression matches this situation?
“You are sharing 3/5 of a cake equally among 3 people.”
A) 3/5 × 3
B) 3/5 ÷ 3
Explain your choice.
B) 3/5 ÷ 3.
Division because you are sharing the fraction equally
A model shows 3 out of 5 equal sections shaded, and each section represents 1/4 of a whole.
Which expression matches the shaded region?
A) 3/5 × 1/4
B) 1/4 ÷ 3/5
C) 3 × 1/4
D) 5 × 1/4
A) 3/5 × 1/4
A student says:
“To find 1/3 of 3/4, you divide because you’re sharing.”
Do you agree or disagree? Why?
Disagree. In this case, 1/3 of 3/4 is a multiplication problem, but if you are dividing a fraction among people, you divide. The key is to consider whether the problem is asking for a fraction of a quantity or to share it equally.
A student says 15 ÷ 1/3 = 5.
Is the student correct? Explain the error if not.
Incorrect. Dividing a whole number by a fraction increases its value.
A bathroom floor is covered by 12 tiles, each 1/3 ft by 3/4 ft.
What is the total area of the floor?
Area of one tile = 1/4.
Multiply by 12.
Total area = 3 square feet
True or False:
“If a problem says of, you always multiply.”
Defend your answer with an example.
False. “Of” often means multiply, but sharing situations require division.
Example:
“You have 3/4 of a pizza, and you want to share it equally among 3 people.”
Even though the situation involves part of a whole, you divide because you are sharing.
3/4 ÷ 3
Each person gets 1/4 of a pizza.
Create a real-world situation that matches 4 × 3/8, and explain what the product means.
12/8 or 1 and 1/2
Write two different word problems:
• One that matches 3 × 1/4
• One that matches 3/4 ÷ 3
One grouping model: three groups of 1/4. One sharing model: sharing 3/4 among 3 people.
Without calculating, decide which is greater:
3 × 2/5 or 2/5 ÷ 3
Explain how you know.
3 × 2/5 is greater. Dividing by 3 makes the value smaller
For example, 3 × 2/5 = 6/5, and 2/5 ÷ 3 = 2/15.
Explain why multiplying both side lengths by a fraction less than 1 makes the area smaller.
Each side length is scaled down, so the area shrinks even more