Have you ever made your own game? Take a look at this dilemma.
Julie isn’t sure. She needs your help. To figure out the problem, Julie will need to divide fractions. You can help her. Pay attention in this Concept and you will learn all that you need to know about dividing fractions.
You have learned a couple of things about dividing fractions. The first is that to divide fractions we are actually use the inverse operation, multiplication. The second is that the second fraction is going to become its reciprocal or opposite. These are a few basic notes, but we haven’t applied them to actually dividing yet. Let’s begin.
How do we divide a fraction by a whole number?
To divide a fraction by a whole number we have to think about what we are actually being asked to do. We are being asked to take a part of something and split it up into more parts.
This problem is asking us to take one-half and divide into three parts. Here is a picture of what this would look like.
This is one half. If we were going to divide one-half into three parts, how much would be in each part?
Here we divided the one-half into three sections. But we couldn’t just do that with one part of the whole so we divided the other half into three sections too.
How can we do this without drawing a lot of pictures?
That is where multiplying by the reciprocal comes in handy.
Notice that the answer is the same as when we divided using the pictures!!
Practice solving these on your own. Remember to simplify the quotient (the answer) if you can.
Now let's help Julie figure out how to make her game.
Our first step is to change the operation to multiplication and to multiply 20 by the reciprocal of three-fourths.
Notice that we also made 20 into a fraction over one. Now we are ready to multiply and simplify.
Here are the vocabulary words in this Concept.
opposite operation. Multiplication is the inverse operation of division. Addition is the inverse operation of subtraction.
the inverse of a fraction. We flip a fraction’s numerator and denominator to write a reciprocal. The product of a fraction and its reciprocal is one.
Here is one for you to try on your own.
To begin, we have to rewrite this problem as a multiplication problem.
This is our answer.
Here are videos for review.
Khan Academy Dividing Fractions Example
James Sousa Dividing Fractions
James Sousa Example of Dividing Fractions
Directions: Divide each fraction and whole number.