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Instructor Overview

Students explore methods of dividing a fraction by a unit fraction.

Key Concepts

In this lesson and in Lesson 5, students explore dividing a fraction by a fraction.

In this lesson, we focus on the case in which the divisor is a unit fraction. Understanding this case makes it easier to see why we can divide by a fraction by multiplying by its reciprocal. For example, finding 34÷15 means finding the number of fifths in 34. In this lesson, students will see that this is 34 × 5.

Students learn and apply several methods for dividing a fraction by a unit fraction, such as 23÷14.

  • Model 23. Change the model and the fractions in the problem to twelfths: 812÷312. Then find the number of groups of 3 twelfths in 8 twelfths. This is the same as finding 8 ÷ 3.
  • Reason that since there are 4 fourths in 1, there must be 23 × 4 fourths in 23. This is the same as using the multiplicative inverse.
  • Rewrite both fractions so they have a common denominator: 23÷14=812÷312. The answer is the quotient of the numerators. This is the numerical analog to modeling.

Goals and Learning Objectives

  • Use models and other methods to divide fractions by unit fractions