Lesson 9 Use Equivalent Expressions

- Let’s use equivalent expressions to add and subtract fractions with unlike denominators.

Warm-up True or False: Fraction Addition and Subtraction

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

$\frac{1}{4} + \frac{2}{4} = \frac{3}{4}$
$\frac{1}{2} + \frac{1}{4} = \frac{2}{4}$
$\frac{3}{4} - \frac{1}{2} = \frac{2}{4}$

Activity 1 Equal Sums

Problem 1

Explain or show why each expression is equivalent to $\frac{2}{3} + \frac{10}{12}$ .

$\frac{8}{12} + \frac{10}{12}$
$\frac{4}{6} + \frac{5}{6}$

Problem 2

Find the value of the expression $\frac{2}{3} + \frac{10}{12}$ . Explain or show your reasoning.

Activity 2 Find the Value of the Difference

Find the value of the expression $\frac{16}{12} - \frac{3}{6}$ . Explain or show your reasoning.
Compare your strategy with your partner’s strategy. What is the same? What is different?

Activity 3 Grow Plants

Jada and Andre compare the growth of their plants. Jada’s plant grew $1 \frac{3}{4}$ inches since last week. Andre’s plant grew $\frac{7}{8}$ inches. How much more did Jada’s plant grow? Explain or show your reasoning.

Practice Problem

Problem 1

Explain why the expressions $\frac{2}{3} - \frac{7}{12}$ and $\frac{8}{12} - \frac{7}{12}$ are equivalent.
How is the expression $\frac{8}{12} - \frac{7}{12}$ helpful to find the value of $\frac{2}{3} - \frac{7}{12}$ ?