Videos and solutions to help Grade 6 students learn how to divide a whole number by a fraction using visual models.

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Lessons for Grade 6

Common Core For Grade 6

• Students understand the difference between a whole number being divided by a fraction and a fraction being divided by a whole number.

Example 1:

Group 1: How many half-miles are in miles?

Group 2: How many quarter hours are in hours?

Group 3: How many one-third cups are in cups?

Group 4: How many one-eighth pizzas are in pizzas?

Group 5: How many one-fifths are in wholes?

Write the division
question that was
answered in each model.

What multiplication
question could the model
also answer?

Write the question given
to each group as a
multiplication question.

Example 2

Molly used cups of flour to bake bread. If this was 3/4 of the total amount of flour she started with, what was the original
amount of flour?

a. Create a model to represent what the question is asking for.

b. Explain how you would determine the answer using the model.

Exercises 1–5

1. A construction company is setting up signs on 4 miles of the road. If the company places a sign every 1/8 of a mile,
how many signs will it need?

2. George bought 12 pizzas for a birthday party. If each person will eat 3/8 of a pizza, how many people can George
feed with pizzas?

3. The Lopez family has adopted miles of trail on the Erie Canal. If each family member cleans up 3/4 of a mile, how
many family members will be needed to clean the adopted section?

4. Margo is freezing 8 cups of strawberries. If this is 2/3 of the total strawberries that were picked, how many cups of
strawberries did Margo pick?

5. Regina is chopping up wood. She has chopped 10 logs so far. If the 10 logs represent 5/8 of all the logs that need to
be chopped, how many logs need to be chopped in all?

Rewrite each problem as a multiplication question. Model the answer.

1. Nicole has used 6 feet of ribbon. This represents 3/8 of the total amount of ribbon she started with. How much ribbon did Nicole have at the start?

2. A boy scout has 3 meters of rope. He cuts the rope into cords 3/5 m long. How many cords will he make?

3. 12 gallons of water fill a tank to 3/4 capacity.

a. What is the capacity of the tank?

b. If the tank is then filled to capacity, how many half-gallon bottles can be filled with water in the tank?

4. Hunter spent 2/3 of his money on a video game before spending half of his remaining money on lunch. If his lunch costs $10, how much money did he have at first?

5. Students were surveyed about their favorite colors. 1/4 of the students preferred red, 1/8 of the students preferred blue, and 3/5 of the remaining students preferred green. If 15 students preferred green, how many students were surveyed?

6. Mr. Scruggs got some money for his birthday. He spent 1/5 of it on dog treats. Then, he divided the remainder equally among his 3 favorite charities.

a. What fraction of his money did each charity receive?

b. If he donated $60 to each charity, how much money did he received for his birthday?

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