Using an Algorithm to Divide Fractions: IM 6.4.11
[url=https://im.kendallhunt.com/MS/teachers/1/4/11/preparation.html]“Using an Algorithm to Divide Fractions”[/url] from IM Grade 6 by [url=https://www.geogebra.org/m/gus8ffvr]Open Up Resources[/url] and Illustrative Mathematics. Licensed under the [url=https://creativecommons.org/licenses/by/4.0/]Creative Commons Attribution 4.0 license[/url].
Table of Contents
- Lesson 6.4.11
- IM 6.4.11 Lesson: Using an Algorithm to Divide Fractions
- Practice 6.4.11
- IM 6.4.11 Practice: Using an Algorithm to Divide Fractions
IM 6.4.11 Lesson: Using an Algorithm to Divide Fractions
Evaluate each expression.
[math]\frac{2}{3}\cdot27[/math]
[math]\frac{1}{2}\cdot\frac{2}{3}[/math]
[math]\frac{2}{9}\cdot\frac{3}{5}[/math]
[math]\frac{27}{100}\cdot\frac{200}{9}[/math]
[math]\left(1\frac{3}{4}\right)\cdot\frac{5}{7}[/math]
Work with a partner.
One person works on the questions labeled “Partner A” and the other person works on those labeled “Partner B.”
Partner A: Find the value of this expression by completing the diagram.
How many [math]\frac{1}{8}[/math]s in [math]\frac{3}{4}[/math]?
Find the value of this expression by completing the diagram.
How many [math]\frac{3}{5}[/math]s in [math]\frac{9}{10}[/math]?
Use the applet to confirm your answers and explore your own examples.
Partner B:
Elena said: “If I want to divide 4 by [math]\frac{2}{5}[/math], I can multiply 4 by 5 and then divide it by 2 or multiply it by [math]\frac{1}{2}[/math].”[br][br]Find the value of each expression using the strategy Elena described.[br][br][math]\frac{3}{4}\div\frac{1}{8}[/math]
[math]\frac{9}{10}\div\frac{3}{5}[/math]
Both Partner A and B:
What do you notice about the diagrams and expressions? Discuss with your partner.
Complete this sentence based on what you noticed:[br][br]To divide a number [math]n[/math] by a fraction [math]\frac{a}{b}[/math], we can multiply [math]n[/math] by ________ and then divide the product by ________.
Select [b]all [/b]equations that represent the statement you completed.
Calculate each quotient. Show your thinking and be prepared to explain your reasoning.
[math]\frac{8}{9}\div4[/math]
[math]\frac{3}{4}\div\frac{1}{2}[/math]
[math]3\frac{1}{3}\div\frac{2}{9}[/math]
[math]\frac{9}{2}\div\frac{3}{8}[/math]
[math]6\frac{2}{5}\div3[/math]
After biking [math]5\frac{1}{2}[/math] miles, Jada has traveled [math]\frac{2}{3}[/math] of the length of her trip. How long (in miles) is the entire length of her trip? Write an equation to represent the situation, and then find the answer.
Suppose you have a pint of grape juice and a pint of milk. You pour 1 tablespoon of the grape juice into the milk and mix it up. Then you pour 1 tablespoon of this mixture back into the grape juice. Which liquid is more contaminated?
IM 6.4.11 Practice: Using an Algorithm to Divide Fractions
Select [b]all [/b]the statements that show correct reasoning for finding [math]\frac{14}{15}\div\frac{7}{5}[/math].
Clare said that [math]\frac{4}{3}\div\frac{5}{2}[/math] is [math]\frac{10}{3}[/math]. She reasoned: [math]\frac{4}{3}\cdot5=\frac{20}{3}[/math] and [math]\frac{20}{3}\div2=\frac{10}{3}[/math]. [br][br]Explain why Clare’s answer and reasoning are incorrect. Find the correct quotient.
Find the value of [math]\frac{15}{4}\div\frac{5}{8}[/math]. Show your reasoning. You can use the app below.
Consider the problem: Kiran has [math]2\frac{3}{4}[/math]pounds of flour. When he divides the flour into equal-sized bags, he fills [math]4\frac{1}{8}[/math]bags. How many pounds fit in each bag?[br][br]Write a multiplication equation and a division equation to represent the question. Then, find the answer and show your reasoning. You can use the applet below to show your reasoning.
[size=150]Divide [math]4\frac{1}{2}[/math] by each of these unit fractions. [br][/size][br][math]\frac{1}{8}[/math]
[math]\frac{1}{4}[/math]
[math]\frac{1}{6}[/math]
[size=150]Consider the problem: After charging for [math]\frac{1}{3}[/math]of an hour, a phone is at [math]\frac{2}{5}[/math]of its full power. How long will it take the phone to charge completely?[br][br]Decide whether each equation can represent the situation.[br][/size][br][math]\frac{1}{3}\cdot?=\frac{2}{5}[/math]
[math]\frac{1}{3}\div\frac{2}{5}=?[/math]
[math]\frac{2}{5}\div\frac{1}{3}=?[/math]
[math]\frac{2}{5}\cdot?=\frac{1}{3}[/math]
[size=150]Elena and Noah are each filling a bucket with water. Noah’s bucket is [math]\frac{2}{5}[/math] full and the water weighs [math]2\frac{1}{2}[/math] pounds. How much does Elena’s water weigh if her bucket is full and her bucket is identical to Noah’s?[/size][br][br]Write multiplication and division equations to represent the question.
Draw a diagram to show the relationship between the quantities.
Find the answer to the problem above.