Students explore methods of dividing a fraction by a unit fraction.
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 means finding the number of fifths in . In this lesson, students will see that this is × 5.
Students learn and apply several methods for dividing a fraction by a unit fraction, such as .
- Model . Change the model and the fractions in the problem to twelfths: . 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 × 4 fourths in . This is the same as using the multiplicative inverse.
- Rewrite both fractions so they have a common denominator: . 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