Math Background

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 1one-fourth ÷ 2one-half 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.

    1one-fourth ÷ 2one-half = five fourths ÷ five-halves

  • 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 five fourths by the reciprocal of five-halves, two-fifths.)

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

     five fourths ÷ five-halves = five fourths x two-fifths

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

    x two-fifths = five times two over four times five = one-half

    The quotient is one-half.

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

    one-half x 2one-half = one-half x five-halves = five fourths, or 1one-fourth

    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.

Houghton Mifflin Math Grade 5