Lesson 5 — Activity 1: Working with Fractions with Like Denominators


Getting Ready

Fractions are used in many daily activities and expressions. For example, you might say that it is half an hour until the bell rings, or that there are three quarters of a pizza left. These are both fractions.


This image shows you which is the numerator and which is the denominator.

You may remember from previous courses that there are three main types of fractions: proper, improper, and mixed.

A proper fraction is a fraction that expresses a number between 0 and 1. You can easily identify a proper fraction. In a proper fraction, the numerator is SMALLER than the denominator. 


The following are all examples of proper fractions:

                    Examples of proper fractions

Notice that all of the above fractions have numerators that are smaller than their denominators — their "tops" are smaller than their "bottoms"!

An improper fraction is a fraction that expresses a number that is 1 or larger than 1.

Again, it is fairly easy to identify an improper fraction since in an improper fraction, the numerator is THE SAME AS or LARGER than the denominator.


The following are all examples of improper fractions:

     Examples of improper fractions

All of the above fractions have numerators that are the same size or larger than their denominators — their "tops" are the same size or larger than their "bottoms".

A mixed number is made up of a whole number and a proper fraction.

Mixed numbers, like improper fractions, also express a number that is 1 or larger than 1.


The following are all examples of mixed numbers:

Examples of mixed fractions

It is important to remember that since improper fractions and mixed numbers express the same thing, they can be converted from one to the other.



Try This:

Click here to practise identifying fractions. You can identify both proper fractions and mixed numbers. Start with any level you'd like. Try to complete at least three levels.


There may be times when you want to add or subtract fractions.

Here's an example:

Fay made two pies for a picnic. 2/8 of her apple pie and 3/8 of her cherry pie were left. How much pie in total did she take home?


Pies are often cut into fractional pieces.

In order to add or subtract fractions, you must have a common denominator.


For example, if you wished to solved the pie problem, you would do this:

  • Check to see if you have a common denominator. In this case, the denominator is 8 in both fractions.
  • Because we have a common denominator, we can add the numerators together and put them over the common denominator. The denominator stays the same.

                    Equation #1

This drawing shows how you would show the equation in a picture format.

An equation shown in a picture format

Fay took home 5/8 pie in total. (You should always write a statement to complete a problem.)



Try This:


Here is a subtraction problem for you to solve.


Over the weekend, Jon drank 4/5 of a bottle of soda and Kris drank 1/5 of a bottle. How much more soda did Jon drink than Kris? (Don't forget your statement.)



4/5 – 1/5 = 3/5

Jon drank 3/5 more soda than Kris.




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Sometimes you have to work with mixed numbers in order to solve a problem.


For example, you want to double a recipe for chocolate chip cookies. The original recipe calls for 2  1/3 cups of flour.
                                                                                   

To double the recipe, you would add:

               Image 9

To add mixed numbers with the same denominator:


  • Add the whole numbers together.


  • Add the numerators.


  • The denominator stays the same.

        Image 10

To double the recipe, you would add 4  2/3 cups of flour.
                                                                                   


Solutions for fraction problems should be shown in their lowest form or smallest equivalent fraction.


You can reduce fractions to their lowest form by:


  • dividing


  • using greatest common factors


Here's an example:

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Les baked 48 cookies for the bake sale at school and sold 36 of them. In fraction form, how many cookies did Les sell?

Les sold 36/48 cookies.

  • Go to Tab 1 to see how to reduce this fraction using division.

  • Go to Tab 2 to see how to reduce this fraction using greatest common factor.

Find a number that can be divided into both the numerator and denominator. Divide, then repeat until the numerator and denominator cannot be divided further.


Reducing fractions

3/4 is the lowest form of 36/48. 


  • Identify factors and the greatest common factor (GCF) of the two numbers.


The set of factors for 36 is:

36: {1, 2, 3, 4, 6, 9, 12, 18, 36}

The set of factors for 48 is:

48: {1, 2, 3, 4, 6, 8, 12, 16, 24, 48}


The GCF of 36 and 48 is 12.


  • Divide

        Reducing fractions

Again, it is shown that 3/4 is the lowest form of 36/48.



Try This:


Here's another subtraction problem for you to solve, this time with mixed numbers.


A bannock recipe calls for 2 3/4 cups of flour. Robert added 1 1/4 cups and then ran out of flour. How much more flour needs to be added?

When you get your answer, see if the fraction can be reduced and show a method to do this.



Mixed Numbers Subtraction
Reduce 2/4 by dividing:
Image 15

1 1/2 cups of flour needs to be added.









Image 16
Images courtesy of www.imagesgoogle.com

Go to the next page to try a Self-check Activity on adding and subtracting fractions.