Lesson 14 How Do You Compare Fractions?

- Let’s represent and compare fractions.

Warm-up Number Talk: Which Whole Numbers?

Find the whole number that each fraction is equivalent to.

$\frac{16}{1}$
$\frac{16}{2}$
$\frac{16}{4}$
$\frac{20}{4}$

Activity 1 Equivalent or Not?

Are these fractions equivalent? Show your thinking using diagrams, symbols, or other representations.

$\frac{1}{2}$ and $\frac{1}{3}$
$\frac{4}{6}$ and $\frac{5}{6}$
$\frac{3}{4}$ and $\frac{6}{8}$

Activity 2 Same Fractions, Different Result?

Han says $\frac{4}{6}$ is less than $\frac{5}{6}$ . His work is shown.

Number lines.

Lin says $\frac{4}{6}$ is greater than $\frac{5}{6}$ . Her work is shown.

Two number lines. Top, 0 to 1 by sixths. Only 0 and 1 labeled. Point plotted at 4 sixths. Bottom, 0 to 1 by sixths, 0 and 1 labeled, point plotted at 5 sixths.

Why might Han and Lin make different comparison statements for the same fractions?

Practice Problem

Problem 1

Are $\frac{2}{3}$ and $\frac{4}{6}$ equivalent? Show your thinking using diagrams, symbols, or other representations.
Are $\frac{6}{8}$ and $\frac{7}{8}$ equivalent? Show your thinking using diagrams, symbols, or other representations.