Interpreting Division of a Whole Number by a Fraction

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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Common Core For Grade 6

New York State Common Core Math Module 2, Grade 6, Lesson 2

Lesson 2 Student Outcomes

• Students use visual models such as fraction bars, number lines, and area models to show the quotient of whole numbers and fractions. Students use the models to show the connection between those models and the multiplication of fractions.
• Students understand the difference between a whole number being divided by a fraction and a fraction being divided by a whole number.

NYS Math Module 2 Grade 6 Lesson 2 Examples

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?

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Problem Set
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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