Dividing by Unit & Non-Unit Fractions: IM 6.4.10
[url=https://im.kendallhunt.com/MS/teachers/1/4/10/preparation.html]“Dividing by Unit & Non-Unit 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 6.4.10
- IM 6.4.10 Lesson: Dividing by Unit and Non-Unit Fractions
- Practice 6.4.10
- IM 6.4.10 Practice: Dividing by Unit and Non-Unit Fractions
IM 6.4.10 Lesson: Dividing by Unit and Non-Unit Fractions
Work with a partner. One person solves the problems labeled “Partner A” and the other person solves those labeled “Partner B.” Write an equation for each question. If you get stuck, consider drawing a diagram.
Partner B
What do you notice about the diagrams and equations? Discuss with your partner.
Complete this sentence based on what you noticed:[br]Dividing by a whole number a produces the same result as multiplying by ________.
To find the value of [math]6\div\frac{1}{2}[/math], Elena thought, “How many [math]\frac{1}{2}[/math]s are in 6?” and then she drew this tape diagram. It shows 6 ones, with each one partitioned into 2 equal pieces.[br][math]6\div\frac{1}{2}[/math] 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[/img][br][br]
For each division expression below, complete the diagram using the same method as Elena. Then, find the value of the expression.
For each division expression below, complete the diagram using the same method as Elena. Then, find the value of the expression.
Examine the expressions and answers more closely. Look for a pattern. How could you find how many halves, thirds, fourths, or sixths were in 6 without counting all of them? Explain your reasoning.
Use the pattern you noticed to find the values of the expressions. If you get stuck, consider dawing a diagram.
[math]6\div\frac{1}{8}[/math]
[math]6\div\frac{1}{10}[/math]
[math]6\div\frac{1}{25}[/math]
[math]6\div\frac{1}{b}[/math]
Find the value of each expression.
[list][*][math]8\div\frac{1}{4}[/math][br][/*][*][math]12\div\frac{1}{5}[/math][br][/*][*][math]a\div\frac{1}{2}[/math][br][/*][*][math]a\div\frac{1}{b}[/math][/*][/list]
To find the value of 6 divided by 2/3, Elena started by drawing a diagram the same way she did for 6 divided by 1/3.
For each division expression, complete the diagram using the same method as Elena. Then, find the value of the expression. Think about how you could find that value without counting all the pieces in your diagram.
Elena says, “To find [math]6\div\frac{2}{3}[/math], I can just take the value of [math]6\div\frac{1}{3}[/math] and then either multiply it by [math]\frac{1}{2}[/math] or divide it by 2.” Do you agree with her? Explain your reasoning.
Elena examined her diagrams and noticed that she always took the same two steps to show division by a fraction on a tape diagram. She said:[br][br]“My first step was to divide each 1 whole into as many parts as the number in the denominator. So if the expression is [math]6:\frac{3}{4}[/math], I would break each 1 whole into 4 parts. Now I have 4 times as many parts.[br][br]My second step was to put a certain number of those parts into one group, and that number is the numerator of the divisor. So if the fraction is [math]\frac{3}{4}[/math], I would put 3 of the [math]\frac{1}{4}[/math]s into one group. Then I could tell how many [math]\frac{3}{4}[/math]s are in 6.”[br][br]Which expression represents how many [math]\frac{3}{4}[/math]s Elena would have after these two steps? Be prepared to explain your reasoning.
Use the pattern Elena noticed to find the values of these expressions. If you get stuck, consider drawing a diagram.
[list][*][math]6\div\frac{2}{7}[/math][br][/*][*][math]6\div\frac{3}{10}[/math][br][/*][*][math]6\div\frac{6}{25}[/math][br][/*][/list]
Find the missing value.
IM 6.4.10 Practice: Dividing by Unit and Non-Unit Fractions
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, [math]24\div4=6[/math] means that if each person gets 4 apples, then 6 people can have apples. Here are some other calculations:[br][br][math]24\div4=6[/math] [math]24\div2=12[/math] [math]24\div1=24[/math] [math]24\div\frac{1}{2}=?[/math][br][br]Priya thinks the “?” represents a number less than 24. Do you agree? Explain or show your reasoning.[br]
In the case of [math]24\div\frac{1}{2}=?[/math], how many people can have apples?
Here is a centimeter ruler.
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[/img][br][br]Use the ruler to find [math]1\div\frac{1}{10}[/math] and [math]4\div10[/math].
What calculation did you do each time?
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[/img][br][br]Use this pattern to find [math]18\div\frac{1}{10}[/math].
Explain how you could find [math]4\div\frac{2}{10}[/math] and [math]4\div\frac{8}{10}[/math].
Find each quotient.
[math]5\div\frac{1}{10}[/math]
[math]5\div\frac{3}{10}[/math]
[math]5\div\frac{9}{10}[/math]
Use the fact that [math]2\frac{1}{2}\div\frac{1}{8}=20[/math] to find [math]2\frac{1}{2}\div\frac{5}{8}[/math]. Explain or show your reasoning.
Consider the problem: It takes one week for a crew of workers to pave kilometer of a road. At that rate, how long will it take to pave 1 kilometer?[br][br]Write a multiplication equation and a division equation to represent the question. Then find the answer and show your reasoning.
A box contains [math]1\frac{3}{4}[/math] pounds of pancake mix. Jada used [math]\frac{7}{8}[/math] pound for a recipe. What fraction of the pancake mix in the box did she use? Explain your reasoning. Draw a diagram, if needed.
Calculate each percentage mentally.
25% of 400
50% of 90
75% of 200[br]
10% of 8,000[br]
5% of 20[br]