Students extend multiplication and division of whole numbers to multiply fractions by fractions and divide a whole number and a unit fraction.
Unit Narrative
In this unit, students find the product of two fractions, divide a whole number by a unit fraction, and divide a unit fraction by a whole number.
Previously, students made sense of multiplication of a whole number and a fraction in terms of the side lengths and area of a rectangle. In this unit, students make sense of multiplication of two fractions the same way. Students interpret area diagrams with two unit fractions for their side lengths, a unit fraction and a non-unit fraction, and then two non-unit fractions.
Through repeated reasoning, students notice regularity in the value of the product (MP8). They generalize that it can be found by multiplying the numerators and multiplying the denominators of the factors:
For example, is because there are equal parts in the whole square and parts are shaded.
Next, students make sense of division situations and expressions that involve a whole number and a unit fraction. They recall that division can be understood in terms of finding the number of equal-size groups or finding the size of each group.
For instance, students interpret to mean finding the size of one part if is split into 4 equal parts, and to mean finding how many
