Math Background

Lesson: Dividing Fractions
Introducing the Concept

Although students have worked with division in Grade 4, the division of fractions may cause them some confusion. Some students may need additional help dividing fractions using reciprocals.

Materials: none

Preparation: none

Prerequisite Skills and Concepts: Students should have a basic understanding of multiplying fractions and division facts.

Write the following on the board: one-third ÷ one-half.

  • Say: One way to divide with fractions is to use the reciprocal of the divisor. Any two numbers whose product is 1 are reciprocals of each other. The reciprocal of a fraction is the fraction inverted; that is, the numerator and denominator are reversed. When you divide fractions, you rewrite the problem as a multiplication problem using the reciprocal of the divisor.

    Have students determine the reciprocals for the following and explain their thinking.

    1. one-half (two over one, since one-half x two over one = 1)
    2. 1one-third (three-fourths, since 1 one-third = four-thirds and four-thirds x three-fourths = 1)
    3. 5 (one-fifth, since 5 = five over one and five over one x one-fifth = 1)
  • Ask: Suppose you wanted to find the quotient of one-third ÷ one-half. Which fraction is the divisor? (one-half) What is the reciprocal? (two over one)
    Ask a volunteer to write the division on the board.  one-third ÷ one-half = one-third x two over one = two-thirds
  • Ask: Is this answer reasonable? How can you check the answer? (Just as with whole numbers, the product of the quotient and the divisor must equal the dividend. two-thirds x one-half = one-third.)
  • Ask: If the dividend is a proper fraction and the divisor is a proper fraction, will the quotient be greater than or less than the dividend? (greater than)

    You may wish to solve other division problems until you feel that students understand how to use reciprocals when dividing with fractions.


Houghton Mifflin Math Grade 5