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Dividing Fractions

Part One

This game is intended to help you visualize what is going on with fraction division . If you get lost at
any point in the program, you can scroll down the window for instructions.

You will be shown a point of the number line for which you must enter the corresponding fraction. You must enter
the fraction in the form shown in the pictures below. The picture on the left shows how you would enter and
the other picture shows 5. (Why is this 5?)

The number you have entered re presents the dividend of your division problem. Next, you will see a second
number line showing a new fraction- the divisor. You must now enter this number. Finally, you must decide on
the answer (the quotient) and enter it. Click OK. Click DRAW to get a new problem.

Play the game for at least 5 complete division problems. Think about what it is that you are doing when you divide.

Write down your solution process for two of the problems you solved. Include number line drawings like the ones
on the computer. Explain why the solution to each problem makes sense.

Part Two

Pretend that you were given these problems on the computer:

Create drawings for each problem to imitate what the computer screen
would show. Explain in a sentence why the answer makes sense.

For example, the picture at right illustrates This
makes sense because six one-fourths fit into .

Part Three

Most of you remember the “flip and multiply” algorithm for dividing fractions:

Why does this method work ? The purpose of this part of the lab is to develop an understanding of why “flip and
multiply” works.

Example:
Wanda the Witch had 3 pounds of candy corn to give away at her Haunted House. She decided to make 1/4 pound
bags to give away. How many bags of candy corn could she make?

(a) Let’s represent this story with a picture and use the picture to de termine the
answer
.

Each rectangle represents 1 pound of candy corn. I divided each pound into 4 equal regions to represent
1/4 pound bags. Now I can solve the problem by counting the number of 1/4ths in the 3 pounds.
There are 12 1/4-pound bags in the 3 pounds of candy corn.

(b) Let’s write a division statement for this problem and connect each number to the
problem.
Division statement: 3 ÷ 1/4. The 3 represents the whole: 3 pounds. The 1/4 represents the size of the
part that I am repeatedly taking away: 1/4 pound bags. So 3 pounds ÷ 1/4 pounds per bag = 12 bags.

(c) Let’s write a multiplication statement for this problem and connect each number to
the problem.
Multiplication statement: 3 x 4. The 3 represents how many pounds of candy corn Wanda has. The 4
represents the number of 1/4 pound bags that are in each pound of candy corn.
So 3 pounds x 4 bags per pound = 12 bags.

Explore the fraction division problems be low by completing steps (a)-(c) as illustrated in the
example above.

(1) A turtle undertakes a journey of 2 miles. Each day, the turtle travels 1/5 of a mile. How many
days will it take the turtle to finish the journey?

(2) The Habitat for Humanity team can build 2/3 of a house in one day . They plan to build 4
houses. How long will it take to finish all 4 houses?

(3) The vet has a new bottle containing 4 ounces of special medicine. She will be administering
several doses of this medicine to her cats and dogs. Each dose is ounces. How many doses
are in the bottle?

Look back at your solutions to the problems above. Write an explanation for why it makes
sense to “flip and multiply” when you do fraction division.
 

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