Section C: Practice Problems Area and Fractional Side Lengths

Section Summary

Details

In this section, we learned how to find the area of a rectangle with a fractional side length. The shaded region has an area of $4 \times \frac{2}{3}$ because there are 4 groups of $\frac{2}{3}$ of a square unit shaded. The area is $\frac{8}{3}$ or $2 \frac{2}{3}$ because there are 8 shaded parts and each one is $\frac{1}{3}$ of a square unit.

Area diagram. Length, 4. Width, 2 thirds.

We also learned to multiply a mixed number by a whole number. We used area diagrams and expressions to see why our strategies work. For example, to solve $3 \frac{3}{4} \times 2$ , we can use the expression $(3 \times 2) + (\frac{3}{4} \times 2)$ . We can see both of these expressions in the diagram.

Area Diagram. Length, 3 and 3 fourths. Width, 2.

Problem 1 (Lesson 9)

Area diagram. Length, 4. Width, 1 third.

How are the diagrams the same? How are they different?
How is finding the area of the shaded region the same? How is it different?

Problem 2 (Lesson 10)

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?

Problem 3 (Lesson 11)

The shaded part of this diagram shows the top of a stove. What is the area of the stove top? Explain or show your reasoning.

Area diagram. Length, 3 and 1 half feet. Width, 2 feet.

Problem 4 (Lesson 12)

Find the area of the shaded region. Explain or show your reasoning.

Area diagram. Length, 3 feet. Width, 4 and 1 fourth feet.

Problem 5 (Lesson 13)

Area diagram. Length, 5 and 3 fourths feet. Width, 3 feet.

Select all of the expressions that represent the shaded area in square feet.
1. $3 + 5 \frac{3}{4}$
2. $3 \times 5 \frac{3}{4}$
3. $3 \times (5 + \frac{3}{4})$
4. $(3 \times 5) + \frac{3}{4}$
5. $3 \times 6 - (3 \times \frac{1}{4})$
Write one more expression that represents the shaded area.

Problem 6 (Lesson 14)

A banner at a sporting event is 8 feet long and $2 \frac{1}{3}$ feet wide.

Sketch and label a diagram of the banner.
Find the area of the banner.

Problem 7 (Lesson 15)

Evaluate each expression. Explain or show your reasoning.

$3 \frac{2}{5} \times 10$
$8 \times \frac{14}{3}$
$3 \frac{41}{100} \times 5$

Problem 8 (Lesson 16)

Tyler says that $9 \frac{11}{12} \times 5$ is a little less than 50.

Do you agree with Tyler? Explain or show your reasoning.
What is the value of $9 \frac{11}{12} \times 5$ ?

Problem 9 (Exploration)

A regular sheet of paper is $8 \frac{1}{2}$ inches wide and 11 inches long. How many times would you need to fold the sheet of paper in half before the area is less than 1 square inch? Explain or show your reasoning.
A piece of chart paper is 23 inches wide by 33 inches long. How many times would you need to fold it in half before its area is less than 1 square inch?

Problem 10 (Exploration)

Part of the rectangle is shaded.

Area diagram. Length, 6. Width, 3 and 2 fifths.

Write a multiplication expression that represents the shaded area.
Write a division expression that represents the shaded area.
Write any other expressions that represent the shaded area.

Problem 11 (Exploration)

This is a picture of the Empire State Building:

The base of the Empire State Building is a rectangle. What do you think the area of the rectangle is in square meters?

Make an estimate that is too small.
Make an estimate that is too large.
The length of the rectangle is $129 \frac{1}{5}$ meters. The width is 57 meters. What is the area of the base of the Empire State Building?