In earlier lessons, students learned to multiply fractions. In this lesson, they use that knowledge to learn the property of the reciprocal of a fraction.
The reciprocal of a fraction is the fraction that, when multiplied by the original fraction, results in a product of one.
This means that reciprocal fractions are any two fractions that have a product of one.
For a given fraction, the reciprocal fraction has a numerator that is the same as the denominator or the original fraction and a denominator that is the same as the numerator of the original fraction.
In this lesson students create fractions that are reciprocals of a given fraction.
In the prior lesson, students learn the definition of a reciprocal. In this lesson, they apply that knowledge to learn to divide fractions.
Using arrays to represent fractions, division of fractions is illustrated as a process of finding a missing factor. Students learn that the fraction needed to find the known product is the reciprocal of the original fraction. This is the basis for defining the division of fractions as multiplying the fraction that represents the dividend by the inverse of the fraction that represents the divisor.
In the last lesson, students learned to divide fractions. In this lesson they learn to divide mixed numbers.
The first step is to convert the mixed numbers to improper fractions. The last step is to divide these fractions.