Lesson 9 Differences of Fractions

- Let’s explore differences of fractions on a number line.

Warm-up True or False: Sums of Tenths

Decide if each statement is true or false. Be prepared to explain your reasoning.

$\frac{1}{10} + \frac{2}{10} + \frac{3}{10} = 1$
$1 + \frac{7}{10} = \frac{3}{10} + \frac{4}{10} + \frac{10}{10}$
$\frac{5}{10} + 1 = \frac{6}{10}$
$\frac{2}{10} + \frac{10}{10} = 1 + \frac{1}{5}$

Activity 1 Jump to Subtract

Problem 1

To subtract different fractions from $\frac{11}{6}$ , Noah draws “jumps” on number lines.

Number line. 13 evenly spaced tick marks.

Number line. 13 evenly spaced tick marks.

Number line. 13 evenly spaced tick marks.

The first diagram shows how he finds $\frac{11}{6} - \frac{7}{6}$ . What is the value of $\frac{11}{6} - \frac{7}{6}$ ?
Write an equation to show the difference represented by each of Noah’s diagrams.

Problem 2

Here is another diagram Noah draws:

Number line. 13 evenly spaced tick marks.

Which equations could the diagram represent? Explain your reasoning.

$\frac{11}{6} - \frac{6}{6} = \frac{5}{6}$

$\frac{11}{6} - 1 = \frac{5}{6}$

$1 \frac{5}{6} - 1 = \frac{5}{6}$

Problem 3

Use a number line to represent each difference and to find its value.

$\frac{8}{3} - \frac{2}{3}$
$\frac{8}{3} - \frac{4}{3}$
$\frac{8}{3} - 1$

Activity 2 What’s the Difference?

Use a number line to represent each difference and to find its value.

$\frac{13}{8} - \frac{2}{8}$
$\frac{13}{8} - \frac{6}{8}$
$\frac{13}{8} - 1$
$1 \frac{5}{8} - \frac{7}{8}$
$1 \frac{5}{8} - 1$
$1 \frac{5}{8} - 1 \frac{4}{8}$

Activity 3 Make a Jump, Subtraction Edition

Here are four number lines, each with a point on it. Label each point with a fraction it represents.

The point you labeled is your target.

Pick a card from the set given to you. Locate and label the fraction on the number line.
From that point, draw one or more jumps to reach the target. What do you need to subtract? Label each jump you draw.
Write an equation to represent the difference of your two fractions.

Practice Problem

Problem 1

- Explain how the diagram represents $\frac{13}{5} - \frac{4}{5}$ .
- Use the diagram to find the value of $\frac{13}{5} - \frac{4}{5}$ .
Use a number line to represent and find the difference $\frac{9}{4} - \frac{3}{4}$ .