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.
Close

Information: IM 6.4.10 Lesson: Dividing by Unit and Non-Unit Fractions