Lesson 10 All Sorts of Denominators

- Let’s find common denominators.

Warm-up How Many Do You See: Fraction Sum

How many do you see? How do you see them?

Two diagrams, both squares with length and width, 1. Each partitioned into 3 rows of 4 of the same size rectangles. On left, 8 rectangles shaded. On right, 3 rectangles shaded.

Activity 1 Different Denominators

Find the value of each expression. Explain or show your thinking.

$\frac{3}{4} + \frac{7}{8}$
$\frac{3}{4} + \frac{4}{6}$
$\frac{3}{4} - \frac{2}{5}$

Activity 2 Multiply Denominators

Problem 1

Here is Lin’s strategy for finding the value of $\frac{2}{5} + \frac{4}{9}$ : “I know $5 \times 9$ is a common denominator so I’ll use that.” Does Lin’s strategy for finding a common denominator work? Explain or show your thinking and then find the value of $\frac{2}{5} + \frac{4}{9}$ .

Problem 2

Find the value of each expression using a method that makes sense to you.

$\frac{3}{8} + \frac{1}{5}$
$\frac{7}{10} - \frac{2}{3}$
$\frac{7}{20} + \frac{41}{50}$
$\frac{2}{9} - \frac{1}{6}$

Practice Problem

Problem 1

Find the value of each expression. Explain or show your reasoning.

$\frac{1}{4} + \frac{1}{5}$
$\frac{10}{9} - \frac{3}{4}$