From Dividing by Fractions to Multiplying by Whole Numbers
(/ 12 1/4) |
= |
(* 12 4) |
12 ÷ 1/4 |
= |
12 × 4 |
1 What will the first Circle evaluate to? 80 The second Circle? 80
2 How is this equation similar to the equations on the page you just completed? How is it different?
Did you know that dividing by 1/4 is the same as multiplying by 4?
3 In the table below, fill in the blanks to demonstrate how dividing by a fraction produces the same result as multiplying by the fraction’s reciprocal. Then write the equivalent arithmetic expression for each of the Circles.
(/ 10 1/5) |
= |
(* ) |
÷ |
= |
× |
4 This time, we’ve completed the multiplication Circle of Evaluation. You fill in the division Circle of Evaluation.
(/ ) |
= |
(* 18 3) |
÷ |
= |
× |
5 Provide another example that demonstrates how dividing by a fraction produces the same result as multiplying by the fraction’s reciprocal.
(/ ) |
= |
(* ) |
× |
= |
÷ |
Practice
Rewrite multiplication as division, and division as multiplication.
20 × 4 = |
$$\displaystyle 21 \div \frac{1}{3} =$$ |
12 × 4 = |
= 6 × 3 |
$$\displaystyle = 14 \div \frac{1}{7}$$ |
= 15 × 2 |
These materials were developed partly through support of the National Science Foundation, (awards 1042210, 1535276, 1648684, 1738598, 2031479, and 1501927). 
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