Lesson 11

The Distributive Property, Part 3

Let's practice writing equivalent expressions by using the distributive property.

Problem 1

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

  1. \(4(x+2)\)
  2. \((6+8)\boldcdot x\)
  3. \(4(2x+3)\)
  4. \(6(x+y+z)\)

Problem 2

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

Problem 3

Select all the expressions that are equivalent to \(16x + 36\).

A:

\(16(x+20)\)

B:

\(x(16+36)\)

C:

\(4(4x+9)\)

D:

\(2(8x+18)\)

E:

\(2(8x+36)\)

Problem 4

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

Problem 5

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

A:

\(z + z\)

B:

\(z \div 2\)

C:

\(z \boldcdot z\)

D:

\(\frac{1}{4}z + \frac{1}{4} z\)

E:

\(2z\)

(From Unit 6, Lesson 8.)

Problem 6

  1. What is the perimeter of a square with side length:

    3 cm?

    7 cm?

    \(s\) cm?

  2. If the perimeter of a square is 360 cm, what is its side length?

  3. What is the area of a square with side length:

    3 cm?

    7 cm?

    \(s\) cm?

  4. If the area of a square is 121 cm2, what is its side length?
(From Unit 6, Lesson 6.)

Problem 7

Solve each equation.

\(10=4a\)

\(5b=17.5\)

\(1.036=10c\)

\(0.6d=1.8\)

\(15=0.1e\)

(From Unit 6, Lesson 5.)