Lesson 11

Using an Algorithm to Divide Fractions

Let’s divide fractions using the rule we learned.

Problem 1

Select all the statements that show correct reasoning for finding \(\frac{14}{15}\div \frac{7}{5}\).


Multiplying \(\frac{14}{15}\) by 5 and then by \(\frac{1}{7}\).


Dividing \(\frac{14}{15}\) by 5, and then multiplying by \(\frac{1}{7}\).


Multiplying \(\frac{14}{15}\) by 7, and then multiplying by \(\frac{1}{5}\).


Multiplying \(\frac{14}{15}\) by 5 and then dividing by 7.


Multiplying \(\frac{15}{14}\) by 7 and then dividing by 5.

Problem 2

Clare said that \(\frac{4}{3}\div\frac52\) is \(\frac{10}{3}\). She reasoned: \(\frac{4}{3} \boldcdot 5=\frac{20}{3}\) and \(\frac{20}{3}\div 2=\frac{10}{3}\)

Explain why Clare’s answer and reasoning are incorrect. Find the correct quotient.


Problem 3

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

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

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

  1. \(\frac18\)
  2. \(\frac14\)
  3. \(\frac16\)
(From Unit 4, Lesson 10.)

Problem 6

Consider the problem: After charging for \(\frac13\) of an hour, a phone is at \(\frac25\) of its full power. How long will it take the phone to charge completely?

Decide whether each equation can represent the situation.

  1. \(\frac13\boldcdot {?}=\frac25\)
  2. \(\frac13\div \frac25={?}\)
  3. \(\frac25 \div \frac13 ={?}\)
  4. \(\frac25 \boldcdot {?}=\frac13\)
(From Unit 4, Lesson 9.)

Problem 7

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 4, Lesson 8.)