Lesson 7

Finding an Algorithm for Dividing Fractions

Let’s look for patterns when we divide by a fraction.

Problem 1

Priya is sharing 24 apples equally with some friends. She uses division to determine how many people can have a share if each person gets a particular number of apples. For example, \(24 \div 4 = 6\) means that if each person gets 4 apples, then 6 people can have apples. Here are some other calculations:

\(24 \div 4 = 6\)

\(24 \div 2 = 12\)

\(24 \div 1 = 24\)

\(24 \div \frac12 = {?}\)

  1. Priya thinks the “?” represents a number less than 24. Do you agree? Explain or show your reasoning.

  2. In the case of \(24 \div \frac12 = {?}\), how many people can have apples?

Problem 2

Find the value of \(\frac{15}{4}\div \frac{5}{8}\). Show your reasoning.

Problem 3

Divide \(4\frac12\) by each of these unit fractions.

  1. \(\frac18\)
  2. \(\frac14\)
  3. \(\frac16\)

Problem 4

Consider the problem: Kiran has \(2\frac34\) pounds of flour. When he divides the flour into equal-sized bags, he fills \(4\frac18\) bags. How many pounds fit in each bag?

Write a multiplication equation and a division equation to represent the question. Then, find the answer and show your reasoning.

Problem 5

Elena and Noah are each filling a bucket with water. Noah’s bucket is \(\frac25\) full and the water weighs \(2\frac12\) pounds. How much does Elena’s water weigh if her bucket is full and her bucket is identical to Noah’s?

  1. Write multiplication and division equations to represent the question.
  2. Draw a diagram to show the relationship between the quantities and to find the answer.
(From Unit 3, Lesson 5.)

Problem 6

Calculate each percentage mentally.

  1. 25% of 400
  2. 50% of 90
  1. 75% of 200
  2. 10% of 8,000
  1. 5% of 20
(From Unit 2, Lesson 23.)