## Lesson: Dividing Fractions Developing the Concept

After students understand how to divide fractions and are comfortable with the idea of reciprocals, you can present a division problem using mixed numbers.

Materials: none

Preparation: none

Prerequisite Skills and Concepts: Students should be able to model and divide with fractions using reciprocals and improper fractions. They should also know the division facts.

Write the expression 1 ÷ 2 on the board.

• Say: You know how to divide fractions. Now let's divide mixed numbers.
• Ask: What is the first thing you need to do before you can divide?
Guide students to see that they need to change the mixed numbers to improper fractions before they can divide. Ask a volunteer to write the improper fractions on the board.

1 ÷ 2 = ÷

• Ask: We have a division problem with fractions. What do we do next to divide fractions?
(Rewrite the division problem as a multiplication problem by multiplying by the reciprocal of , .)

If necessary, have a volunteer explain how to find the reciprocal of . Write it on the board.

÷ = x

Guide students as they multiply by first finding common factors and then writing the answer in simplest form.

x = =

The quotient is .

• Ask: How can you check your work? (Use multiplication to check division. You can multiply the quotient, , by the divisor, 2. The result should be the dividend, 1.)

x 2 = x = , or 1

Repeat the activity by using fractions, fractions and mixed numbers, and only mixed numbers in the division problems.

Wrap-Up and Assessment Hints
To assess students' progress, divide the class into two groups. Have each student write a division problem using mixed numbers similar to those in the problems you have presented. Have groups exchange papers and check each other's work. If some students still have difficulty, have them work in small groups, or pair them with a student who has mastered the skill. Encourage them to model the division first and then divide by using pencil and paper.