Lesson 19 Compare to 1

- Let’s explain what happens when we multiply a fraction by a fraction greater than, less than, or equal to 1.

Warm-up What Do You Know About …?

What do you know about $\frac{15}{14} \times \frac{23}{30}$ ?

Activity 1 Compare Fraction Products on the Number Line

Match the expressions and number lines that show the same value.
- $\frac{2}{5} \times \frac{4}{3}$
- $\frac{3}{4} \times \frac{5}{2}$
- $\frac{4}{3} \times \frac{5}{2}$
- $(1 + \frac{1}{3}) \times \frac{5}{2}$
- $(1 - \frac{3}{5}) \times \frac{4}{3}$
- $(1 - \frac{1}{4}) \times \frac{5}{2}$
A
B
C
Choose one of the expressions from each set and explain whether the value is greater than or less than the second factor.

Activity 2 True Statement

Problem 1

Rewrite each expression as a sum or difference of 2 products.

$(1 - \frac{2}{5}) \times \frac{4}{7}$
$(1 + \frac{1}{5}) \times \frac{4}{7}$
$(1 - \frac{3}{8}) \times \frac{4}{7}$
$(1 + \frac{1}{8}) \times \frac{4}{7}$

Problem 2

Fill in each blank with $<$ or $>$ to make the inequality true.

$(1 - \frac{2}{5}) \times \frac{4}{7}$ $\frac{4}{7}$
$(1 + \frac{1}{5}) \times \frac{4}{7}$ $\frac{4}{7}$
$(1 - \frac{3}{8}) \times \frac{4}{7}$ $\frac{4}{7}$
$(1 + \frac{1}{8}) \times \frac{4}{7}$ $\frac{4}{7}$

Problem 3

Describe the value of the product when $\frac{4}{7}$ is multiplied by a fraction greater than 1. Explain your reasoning.
Describe the value of the product when $\frac{4}{7}$ is multiplied by a fraction less than 1. Explain your reasoning.

Practice Problem

Problem 1

Use the equation $\frac{5}{7} = (1 - \frac{2}{7})$ to explain why $\frac{5}{7} \times \frac{11}{3} < \frac{11}{3}$ .