Lesson 2

Meanings of Division

Let’s explore ways to think about division.

Problem 1

Twenty pounds of strawberries are being shared equally by a group of friends. The equation \(20 \div 5=4\) represents the division of strawberries.

  1. If the 5 represents the number of people, what does the 4 represent?
  2. If the 5 represents the pounds of strawberries per person, what does the 4 represent?

Problem 2

A sixth-grade science club needs $180 to pay for the tickets to a science museum. All tickets cost the same amount.

What could \(180 \div 15\) mean in this situation? Describe two different possible meanings of this expression. Then, find the quotient and explain what it means in each case.

Problem 3

Write a multiplication equation that corresponds to each division equation.

  1. \( 10 \div 5 = {?} \)
  2. \( 4.5 \div 3 = {?} \)
  3. \( \frac12 \div 4 = {?} \)

Problem 4

Write a division or multiplication equation that represents each situation. Use a “?” for the unknown quantity.

  1. 2.5 gallons of water are poured into 5 equally sized bottles. How much water is in each bottle?
  2. A large bucket of 200 golf balls is divided into 4 smaller buckets. How many golf balls are in each small bucket?

  3. Sixteen socks are put into pairs. How many pairs are there?

Problem 5

Find a value for \(a\) that makes each statement true.

  1. \(a\div6\) is greater than 1
  2. \(a\div6\) is equal to 1
  3. \(a\div6\) is less than 1
  4. \(a\div6\) is equal to a whole number
(From Unit 4, Lesson 1.)

Problem 6

Complete the table. Write each percentage as a percent of 1.

fraction decimal percentage
\(\frac14\) 0.25 25% of 1
0.1
75% of 1
\(\frac15\)
1.5
140% of 1
(From Unit 3, Lesson 14.)

Problem 7

Jada walks at a speed of 3 miles per hour. Elena walks at a speed of 2.8 miles per hour. If they both begin walking along a walking trail at the same time, how much farther will Jada walk after 3 hours? Explain your reasoning.

(From Unit 3, Lesson 8.)