# Division of a Fraction by a Fraction

Videos and solutions to help Grade 6 students use visual models such as fraction bars and area models to show the division of fractions by fractions with common denominators and different denominators.

### New York State Common Core Math Grade 6, Module 2, Lesson 3

Lesson 3 Student Outcomes

• Students use visual models such as fraction bars and area models to show the division of fractions by fractions with common denominators.
• Students make connections to the multiplication of fractions. In addition, students understand that the division of fractions require students to ask, “How many groups of the divisor are in the dividend?” to get the quotient.

Lesson 3 Classwork
Lesson 3 Opening Exercise
Draw a model to represent 12 ÷ 3.
How could we reword this question?
If we divide 12 into three groups of equal size, what is the size of each group?
If we divide 12 into groups of size 3, how many groups would we have?
If I have 12 chickens and I put 3 chickens in each cage, how many cages will I need?
If I have 12 flowers and I place 3 flowers in each vase, how many vases will I need?

Example 1
Draw a model to show the division problem.
8/9 ÷ 2/9

Example 2
Draw a model to show the division problem.
9/12 ÷ 3/12

Example 3
Draw a model to show the division problem.
7/9 ÷ 3/9

Exercises 1–6
For the following exercises, rewrite the division problem. Then be sure to draw a model to support your answer.

1. How many fourths are in three fourths?
How are Example 2 and Exercise 1 similar?
How are the divisors and dividends related?
What conclusions can you draw from these observations?
2. 4/5 ÷ 2/5
3. 9/4 ÷3/4
4. 7/8 ÷ 2/8
5. 13/10 ÷ 2/10
6. 11/9 ÷ 3/9

Lesson 3 Exit Ticket

1. 9/4 ÷ 3/4
2. 7/3 ÷ 2/3

Problem Set
For the following exercises, rewrite the division expression in unit form. Then, find the quotient. Draw a model to support your answer.

1. 4/5 ÷ 1/5
2. 8/9 ÷ 4/9
3. 11/4 ÷ 3/4
4. 13/5 ÷ 4/5

Rewrite the division expression in unit form, and find the quotient.
5. 10/3 ÷ 2/3
6. 8/5 ÷ 3/5
7. 12/7 ÷ 12/7
Represent the division expression using unit form. Find the quotient. Show all necessary work.
8. A runner is 7/8 mile from the finish line. If she can travel 3/8 mlie per minute, how long will it take her to finish the race?
9. An electrician has 4.1 meters of wire.
a. How many strips 7/10 m long can he cut?
b. How much wire will he have left over?
10. Saeed bought 21 1/2 lb. of ground beef. He used 1/4 of the beef to make tacos and 2/3 of the remainder to make quarter-pound burgers. How many burgers did he make?
11. A baker bought some flour. He used 2/5 of the flour to make bread and used the rest to make batches of muffins. If he used 16 lb. of flour making bread and 2/3 lb. for each batch of muffins, how many batches of muffins did he make?

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations. 