Lesson 11

Using an Algorithm to Divide Fractions

Problem 1

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

A:

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

B:

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

C:

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

D:

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

E:

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

Solution

Teachers with a valid work email address can click here to register or sign in for free access to Formatted Solution.

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.

 

Solution

Teachers with a valid work email address can click here to register or sign in for free access to Formatted Solution.

Problem 3

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

Solution

Teachers with a valid work email address can click here to register or sign in for free access to Formatted Solution.

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.

Solution

Teachers with a valid work email address can click here to register or sign in for free access to Formatted Solution.

Problem 5

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

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

Solution

Teachers with a valid work email address can click here to register or sign in for free access to Formatted Solution.

(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. \(\frac25 \boldcdot {?}=\frac13\)

Solution

Teachers with a valid work email address can click here to register or sign in for free access to Formatted Solution.

(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.

Solution

Teachers with a valid work email address can click here to register or sign in for free access to Formatted Solution.

(From Unit 4, Lesson 8.)