Lesson 19

In previous lessons, students have compared the size of a product to the size of one factor by reasoning about the size of the other factor. They have done this using calculation, area diagrams, and number line diagrams. The goal of this lesson is to use the distributive property to explain why the comparisons work in all cases without calculating. The key observation is that a number greater than 1, such as \(\frac{5}{4}\), can be written as \(1 + \frac{1}{4}\) so multiplying by \(\frac{5}{4}\) increases any number by \(\frac{1}{4}\) of that number. In the same way multiplying by \(\frac{3}{4}\) or \(1 - \frac{1}{4}\) decreases any number by \(\frac{1}{4}\) of that number. 

Activity 1: Compare Fraction Products on the Number Line