Lesson 5 — Activity 2: Working with Fractions with Unlike Denominators


Getting Ready

In the last activity, you practised adding and subtracting fractions and mixed numbers with the same denominator.


Now you will look at fractions where the denominators are not the same. It is necessary to make them the same before you can add or subtract a fraction.


Let's look at an example:

This problem will deal with an allowance for books.

You have allowed yourself half of your allowance to spend on books.

Of that half, you spent one third of your total allowance on one book.

What fraction of the money you allowed yourself for books do you have left?


You could write an equation like this:      

             Unlike fractions

You'll notice the denominators are not the same.





You can get a common denominator by finding the equivalent fractions with the lowest common denominator (LCD).


This is how to do this:

1. First, find the lowest common multiple of the denominators. (This will be called the lowest common denominator [LCD].)

The multiples are:

3: {3, 6, 9, 12}

2: {2, 4, 6, 8, 10}

The LCD of 3 and 2 is 6.


2. Multiply each fraction by the number of times the denominator goes into 6. Remember to multiply both the top and the bottom.
Common denominators

Now you have two fractions with a common denominator. You can now find out what fraction of your money you have left to spend on books.
       Common denominators   
You have one sixth of your money left to spend on books.

Let's say you have a blueberry pie. Your friend Sari eats 1/2 of the pie and you eat 1/8 of the pie. How much is left over?


Start with two circles. Each circle will represent a pie.
Draw a line down the middle of the first circle and colour it. This will represent half a pie.

         This image represents one half of the pie.
Divide the second circle into eight equal parts. Colour one part of the circle. This represents 1/8 of the pie.
        
          This image represents one eighth of the pie.
The drawings are not common so we cannot add the two fractions yet. However, you can divide the first picture into eight equal pieces by drawing three more lines. This now cuts the pie into eighths as well. Now it is possible to subtract the fractions.

Now you know how much of the pie was eaten. How much is left? Simple! Count the uncoloured portions of the final picture.

             This image shows how much of the pie is left.

There is 3/8 of the pie left.

Try This:


Here is a problem for you to solve.


A punch recipe calls for 3/4 cups of pop and 2/3 cups of juice.

How much punch will there be in total?

                                                                                 

1. Find the lowest common multiple of the denominators. This will be the lowest common denominator (LCD).

2. Multiply each fraction by the number of times the denominator goes into the LCD. Remember to multiply both the top and the bottom.

3. Make an equation with your new fractions and solve. You will have an improper fraction as your answer!

4: {4, 8, 12, 16}
3: {3, 6, 9, 12}
The LCD of 4 and 3 is 12.

3 x 3 =  9
4    3    12

2 x 4 =  8
3    4     12

 9   +  8  =   17
12      12       12



Your answer for the above problem was an improper fraction.

Before you are done with the problem, you must reduce this improper fraction by dividing the denominator into the numerator.

                     Image 8

There will be 1  5/12 cups of punch in total.


Let's now try the punch problem using mixed numbers.


The punch recipe calls for 2 1/4 cups of pop and 2/3 cup of cranberry juice. How much punch will there be in total?

Lowest Common Denominator

Then do the following:

Image 11

There will be 2 11/12 cups of punch in total.


Images courtesy of www.imagesgoogle.com and K&E Studio