Unit 4, Lesson 11
Using an Algorithm to Divide Fractions
Grade 6
Practice
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-size 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.
Divide \(4\frac12\) by each of these unit fractions.
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\(\frac18\)
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\(\frac14\)
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\(\frac16\)
Problem 6
A phone’s battery is out of power. After charging for \(\frac{1}{3}\) of an hour, the battery is at \(\frac{2}{5}\) of its full power. How long (in total) will it take the battery to charge completely?
Decide whether each equation can represent the situation.
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\(\frac13\boldcdot {?}=\frac25\)
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\(\frac13\div \frac25={?}\)
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\(\frac25 \div \frac13 ={?}\)
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\(\frac25 \boldcdot {?}=\frac13\)
Problem 7
Elena is filling a bucket with water. When her bucket is \(\frac{2}{5}\) full, the water weighs \(2\frac{1}{2}\) pounds. How much would the water weigh if her bucket is full?
- Write multiplication and division equations to represent the question.
- Draw a diagram to show the relationship between the quantities and to find the answer.