Lesson 11: Practice Problems

Problem 1

For each expression, use the distributive property to write an equivalent expression.

$4 (x + 2)$
$(6 + 8) \cdot x$
$4 (2 x + 3)$
$6 (x + y + z)$

Problem 2

Priya rewrites the expression $8 y - 24$ as $8 (y - 3)$ . Han rewrites $8 y - 24$ as $2 (4 y - 12)$ . Are Priya’s and Han’s expressions each equivalent to $8 y - 24$ ? Explain your reasoning.

Problem 3

Select all the expressions that are equivalent to $16 x + 36$ .

$16 (x + 20)$
$x (16 + 36)$
$4 (4 x + 9)$
$2 (8 x + 18)$
$2 (8 x + 36)$

Problem 4

The area of a rectangle is $30 + 12 x$ . List at least 3 possibilities for the length and width of the rectangle.

Problem 5 From Unit 6 Lesson 8

Select all the expressions that are equivalent to $\frac{1}{2} z$ .

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

Problem 6 From Unit 6 Lesson 6

What is the perimeter of a square with side length:

$3$ cm

$7$ cm

$s$ cm
If the perimeter of a square is 360 cm, what is its side length?
What is the area of a square with side length:

$3$ cm

$7$ cm

$s$ cm
If the area of a square is 121 cm², what is its side length?

Problem 7 From Unit 6 Lesson 5

Solve each equation.

$10 = 4 a$
$5 b = 17.5$
$1.036 = 10 c$
$0.6 d = 1.8$
$15 = 0.1 e$