Lesson 7 Generalize Fraction Multiplication

- Let’s use what we’ve learned to multiply any fractions.

Warm-up Notice and Wonder: Two Diagrams

What do you notice? What do you wonder?

Square, length and width, 1. Partitioned into 4 rows of 5 of the same size rectangles. 8 rectangles shaded.

Rectangle. Length, 4 fifths unit. Width, 1 half unit.

Activity 1 Equations and Area

Problem 1

Find the value of each product. Draw an area diagram if it is helpful.

$\frac{2}{5} \times \frac{3}{4}$
$\frac{3}{7} \times \frac{4}{5}$
$\frac{9}{11} \times \frac{5}{8}$

Problem 2

How did you decide whether or not to draw a diagram? How did the the diagrams influence how you found the products?
Diego drew this diagram for the product $\frac{9}{11} \times \frac{5}{8}$ . How can the diagram help Diego find the value of $\frac{9}{11} \times \frac{5}{8}$ ?

Activity 2 Multiply Fractions

Find the value that makes each equation true. Draw a diagram, if it is helpful.

$\frac{3}{8} \times \frac{2}{5} =$
$\frac{3}{4} \times \frac{9}{5} =$
$\frac{10}{5} \times \frac{6}{5} =$
$\frac{8}{9} \times$ $= \frac{56}{36}$
$5 \times$ $= \frac{15}{8}$

Practice Problem

Problem 1

Find the value that makes each equation true.

$\frac{7}{10} \times \frac{3}{5} =$
$\frac{2}{5} \times$ $= \frac{8}{45}$
$\times \frac{4}{9} = \frac{28}{45}$