Lesson 9

The Distributive Property, Part 1

Let's use the distributive property to make calculating easier.

Problem 1

Select all the expressions that represent the area of the large, outer rectangle.

Area diagram. A large rectangle partitioned into two smaller rectangles.
A:

\(5(2+4)\)

B:

\(5 \boldcdot 2 + 4\)

C:

\(5 \boldcdot 2 + 5 \boldcdot 4\)

D:

\(5 \boldcdot 2 \boldcdot 4\)

E:

\(5 + 2+ 4\)

F:

\(5 \boldcdot 6\)

Problem 2

Draw and label diagrams that show these two methods for calculating \(19 \boldcdot 50\).

  • First find \(10\boldcdot 50\) and then add \(9 \boldcdot 50\).

  • First find \(20 \boldcdot 50\) and then take away 50.

Problem 3

Complete each calculation using the distributive property.

\(\displaystyle 98 \boldcdot 24\) \(\displaystyle (100-2) \boldcdot 24\) \(\displaystyle \ldots\)

\(\displaystyle 21 \boldcdot 15\) \(\displaystyle (20 + 1) \boldcdot 15\) \(\displaystyle \ldots\)

\(\displaystyle 0.51 \boldcdot 40\) \(\displaystyle (0.5 + 0.01) \boldcdot 40\) \(\displaystyle \ldots\)

Problem 4

A group of 8 friends go to the movies. A bag of popcorn costs $2.99. How much will it cost to get one bag of popcorn for each friend? Explain how you can calculate this amount mentally.

Problem 5

  1. On graph paper, draw diagrams of \(a+a+a+a\) and \(4a\) when \(a\) is 1, 2, and 3. What do you notice?
  2. Do \(a+a+a+a\) and \(4a\) have the same value for any value of \(a\)? Explain how you know.
(From Unit 6, Lesson 8.)

Problem 6

120% of \(x\) is equal to 78.

  1. Write an equation that shows the relationship of 120%, \(x\), and 78.
  2. Use your equation to find \(x\). Show your reasoning.

(From Unit 6, Lesson 7.)

Problem 7

Kiran’s aunt is 17 years older than Kiran.

  1. How old will Kiran’s aunt be when Kiran is:

    15 years old?

    30 years old?

    \(x\) years old?

  2. How old will Kiran be when his aunt is 60 years old?
(From Unit 6, Lesson 6.)