Lesson 10 Fractional Side Lengths Less Than 1

- Let’s find the area of rectangles with a fractional side length.

Warm-up Estimation Exploration: What is the Area?

What is the area of the shaded region?

Area diagram, Length, 7. Width, more than 1 half and less than 1.

Record an estimate that is:

too low	about right	too high

Activity 1 Rectangle With a Fractional Side Length

Write a multiplication expression to represent the area of each shaded region. Then find the area.

Activity 2 What Are the Side Lengths?

Problem 1

Write a multiplication expression to represent the area of the shaded region. What is the area?

Problem 2

Here are two diagrams. Consider each expression and decide whether it represents the shaded region in one of the diagrams. Be prepared to share your thinking.

Area diagram. Length, 3. Width, 4 fifths. — X

Area diagram. Length, 5. Width, 3 fourths. — Y

$\frac{3}{4} \times 5$
$3 \times \frac{3}{5}$
$3 \times 4 \times \frac{1}{5}$
$4 \times \frac{3}{4}$
$3 \times 3 \times \frac{1}{4}$
What is the area of the shaded region in figure Y?
What is the area of the shaded region in figure X?

Practice Problem

Problem 1

What is the area of this rectangle? Explain or show your reasoning.
What is the area of the shaded region? Explain or show your reasoning.
How are these two area calculations the same? How are they different?