# Lesson 8 Equivalent Fractions on the Number Line

Let’s use number lines to reason about equivalent fractions.

## Warm-up Estimation Exploration: A Shaded Portion

If the entire diagram represents 1 whole, about what fraction is shaded?

Make an estimate that is:

too low | about right | too high |
---|---|---|

## Activity 1 Handy Number Lines

## Problem 1

Andre used number lines to find fractions that are equivalent to

Then, he drew three more lines and wrote a fraction for the point on each line:

How did Andre use the number lines to find fractions equivalent to

## Problem 2

How can number lines be used to show whether the following fractions are equivalent?

and and

## Problem 3

Find three fractions that are equivalent to

## Activity 2 Can It Be Done?

Priya wants to find fractions that are equivalent to

, other than . She wonders if she can find equivalent fractions with denominator 9, 10, and 12. Can it be done? Use number lines to show your reasoning.

Represent

on a number line. Then, find two fractions that are equivalent to . How would you use the number line to show that they are equivalent to ? Can you find an equivalent fraction for

with 100 for the denominator? Explain or show your reasoning.

## Practice Problem

## Problem 1

Which of these could be the fraction that the point represents? Explain your reasoning.