Lesson 10: Practice Problems

Problem 1

Here is a rectangle.

A rectangle divided into 3 sections. The height is a and the widths are 2, 3, and 4.

Explain why the area of the large rectangle is $2 a + 3 a + 4 a$ .
Explain why the area of the large rectangle is $(2 + 3 + 4) a$ .

Problem 2

Is the area of the shaded rectangle $6 (2 - m)$ or $6 (m - 2)$ ?

Explain how you know.

A rectangle with a shaded blue part. The entire width is m and the white segment is 2. The height is 6.

Problem 3

Choose the expressions that do not represent the total area of the rectangle. Select all that apply.

A rectangle partitioned by a vertical line segment into two smaller rectangles. the vertical side is labeled t and the top horizontal side lengths are labeled 5 and 4.

$5 t + 4 t$
$t + 5 + 4$
$9 t$
$4 \cdot 5 \cdot t$
$t (5 + 4)$

Problem 4 From Unit 6 Lesson 9

Evaluate each expression mentally.

$35 \cdot 91 - 35 \cdot 89$
$22 \cdot 87 + 22 \cdot 13$
$\frac{9}{11} \cdot \frac{7}{10} - \frac{9}{11} \cdot \frac{3}{10}$

Problem 5 From Unit 6 Lesson 8

Select all the expressions that are equivalent to $4 b$ .

$b + b + b + b$
$b + 4$
$2 b + 2 b$
$b \cdot b \cdot b \cdot b$
$b \div \frac{1}{4}$

Problem 6 From Unit 6 Lesson 4

Solve each equation. Show your reasoning.

$111 = 14 g$
$13.65 = h + 4.88$
$k + \frac{1}{3} = 5 \frac{1}{8}$
$\frac{2}{5} m = \frac{17}{4}$
$5.16 = 4 n$

Problem 7 From Unit 6 Lesson 2

Andre ran $5 \frac{1}{2}$ laps of a track in 8 minutes at a constant speed. It took Andre $x$ minutes to run each lap. Select all the equations that represent this situation.

$(5 \frac{1}{2}) x = 8$
$5 \frac{1}{2} + x = 8$
$5 \frac{1}{2} - x = 8$
$5 \frac{1}{2} \div x = 8$
$x = 8 \div (5 \frac{1}{2})$
$x = (5 \frac{1}{2}) \div 8$