Lesson 11 Subtract Fractions Flexibly

- Let’s find all kinds of differences.

Warm-up Which One Doesn’t Belong: Fractional Values

Which one doesn’t belong?

$2 - \frac{3}{5}$
$\frac{10}{5} - \frac{3}{5}$
$1 \frac{3}{5} - \frac{1}{5}$
$\frac{10}{5} - 1$

Activity 1 Friendship Bracelets

Clare, Elena, and Andre are making macramé friendship bracelets. They’d like their bracelets to be $9 \frac{4}{8}$ inches long. For each question, explain or show your reasoning.

Clare started her bracelet first and has only $\frac{7}{8}$ inch left until she finishes it. How long is her bracelet so far?
So far, Elena’s bracelet is $5 \frac{1}{8}$ inches long and Andre’s is $3 \frac{5}{8}$ inches long. How many more inches do they each need to reach $9 \frac{4}{8}$ inches?
How much longer is Elena’s bracelet than Andre’s at the moment?

Activity 2 Multiple Ways to Subtract

Problem 1

Here are four expressions that you may have written about the friendship bracelets.

$9 \frac{4}{8} - \frac{7}{8}$

$9 \frac{4}{8} - 5 \frac{1}{8}$

$9 \frac{4}{8} - 3 \frac{5}{8}$

$5 \frac{1}{8} - 3 \frac{5}{8}$

Here is one way to find the value of the first expression. Analyze the calculation. Talk to your partner about why $9 \frac{4}{8}$ is written as different sums.

Subtract. 9 and 4 eighths minus 7 eighths.

Problem 2

Here are some unfinished calculations. Complete them to find the value of each difference.

Practice Problem

Problem 1

Elena is making friendship necklaces and wants the chain and clasp to be a total of $18 \frac{1}{4}$ inches long. She is going to use a clasp that is $2 \frac{3}{4}$ inches long. How long does her chain need to be? Explain or show your reasoning.