From Multiplying by Fractions to Dividing by Whole Numbers
1 Under each Circle of Evaluation, write the equivalent arithmetic expression.
(* 12 1/4) |
= |
(/ 12 4) |
× |
= |
÷ |
2 What will the first Circle evaluate to? The second Circle?
3 Under each Circle of Evaluation, write the equivalent arithmetic expression.
(* 35 1/5) |
= |
(/ 35 5) |
× |
= |
÷ |
4 What will the first Circle evaluate to? The second Circle?
5 What do you Notice? What do you Wonder?
Did you know that multiplying by 1/4 is the same as dividing by 4?
6 In the table below, fill in the blanks to demonstrate how multiplying by a fraction produces the same result as dividing by the fraction’s reciprocal. Then write the equivalent arithmetic expression for each of the Circles.
(* 30 1/5) |
= |
(/ ) |
× |
= |
÷ |
7 This time, we’ve completed the division Circle of Evaluation. You fill in the multiplication Circle of Evaluation.
(* ) |
= |
(/ 18 3) |
× |
= |
÷ |
Practice
Rewrite multiplication as division, and division as multiplication.
$$\displaystyle 20 \times \frac{1}{4} =$$ |
100 ÷ 25 = |
$$\displaystyle 27 \times \frac{1}{9} =$$ |
$$\displaystyle = 6 \times \frac{1}{18}$$ |
= 35 ÷ 7 |
$$\displaystyle = 5 \times \frac{1}{6}$$ |
These materials were developed partly through support of the National Science Foundation, (awards 1042210, 1535276, 1648684, 1738598, 2031479, and 1501927). 
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