Section A Section A Checkpoint

Problem 1

Write a multiplication expression that represents the area of the shaded region. Explain or show your reasoning.

Diagram. Square, length and width, 1. Partitioned into 3 rows of 8 of the same size rectangles. 1 rectangle shaded.

Show Solution

Solution

\frac{1}{3} \times \frac{1}{8}

\frac{1}{8} \times \frac{1}{3}

. Sample response:

\frac{1}{3}

\frac{1}{8}

of the square is shaded. So, that's

\frac{1}{3} \times \frac{1}{8}

Show Sample Response

Sample Response

\frac{1}{3} \times \frac{1}{8}

\frac{1}{8} \times \frac{1}{3}

. Sample response:

\frac{1}{3}

\frac{1}{8}

of the square is shaded. So, that's

\frac{1}{3} \times \frac{1}{8}

Problem 2

Find the value of each expression. Draw a diagram if needed.

$\frac{1}{4} \times \frac{1}{5}$
$\frac{2}{3} \times \frac{3}{4}$
$\frac{5}{4} \times \frac{5}{6}$

Show Solution

Solution

$\frac{1}{20}$
$\frac{6}{12}$ or $\frac{1}{2}$
$\frac{25}{24}$ or $1\frac{1}{24}$

Show Sample Response

Sample Response

$\frac{1}{20}$
$\frac{6}{12}$ or $\frac{1}{2}$
$\frac{25}{24}$ or $1\frac{1}{24}$

Problem 3

A rectangular garden is $2\frac{1}{2}$ meters wide and $4\frac{1}{2}$ meters long. What is the area of the garden? Explain or show your reasoning.

Show Solution

Solution

$11\frac{1}{4}$ square meters (or equivalent). Sample response: $2 \times 2\frac{1}{2}$ is 5 so $4 \times 2\frac{1}{2} = 10$ . Then $\frac{1}{2} \times 2 = 1$ and $\frac{1}{2} \times \frac{1}{2} = \frac{1}{4}$ . So, that’s $10 + 1 + \frac{1}{4}$ or $11\frac{1}{4}$ square meters.

Show Sample Response

Sample Response