The ideas in this fraction lesson are taken from the Fractions 2 ebook sold on this website. Only a few examples of each problem type are shown; you should make more problems of each kind for the student.

Simplifying fractions
Free fraction lesson plan from HomeschoolMath.net

Remember?  You know how to convert fractions to other equivalent fractions. =     ÷2 3 4    =    6 8 ÷2 Each slice has been split two ways.      =   ÷3    1 3    =    3 9 ÷3 Each slice has been split three ways. We can also reverse the process.  Then it is called SIMPLIFYING: =   ÷2    6 8    =    3 4 ÷2 Each two slices have been   joined together.      =   ÷3    3 9    =    1 3 ÷3 Each three slices have been   joined together. Notice that both numerator and the denominator change, but the value of the fraction  does not.  In other words, you get the SAME AMOUNT of pie either way, only  the fraction is written down in a simpler form.  We also say that the fraction is written  in lower terms, because the new numerator and denominator are smaller numbers  than the originals.

Example problem types

1.  Look at the pictures, and write down the simplifaction process.  Also mark how many slices were joined or merged together and show the arrows and the division process like in the example.

=    ÷2 6 10   =        ÷ 2 Each _______ parts were merged together.

Each _______ slices  were merged together. = ÷3 3 6  =      ÷3

Each _______ slices  were merged together. =

Each _______ slices  were merged together. =

Each _______ slices  were merged together. =

2.  Simplify the fractions.  Draw pie pictures of the process.

= 2 8 =

= 4 10 =

= 3 9 =

Since you need to divide both the numerator and the denominator by the same number,  they both need to be divisible by that number.   In other words, they both need to be in the same multiplication table.   ÷5 25 40   =   5 8 ÷5            ÷9 81 90   =   9 10 ÷9            ÷6 ÷2 36 48   =   6 8   =   3 4 ÷6 ÷2 25 and 40 are divisible by 5. 81 and 90 are divisible by 9.  Here the simplifying takes two steps, which is OK. You could also simplify by 12 in one step.

3.  Some of the following fractions are such that you CANNOT simplify them.  Cross them out.  Why is that?  
Discuss with your teacher.  Simplify the ones you can simplify.

4.  Simplify the following fractions.

6.  a)  Tommy practices running, and he is told to use 10 minutes for a warm-up before the practice, and 10 minutes for stretching after the practice.  All in all he uses one hour for the warm-up, practice, and stretching.  
What part of the total time is the warm-up time?  What part of the total time is the actual running practice time?  (Remember to simplify the result.)

b)    Computer screen is 800 pixels wide.  A horizontal line is 600 pixels wide.  What part of the screen width does it take?    (Remember to simplify the result.)
How wide should the line be if you want it to take up exactly 1/2 of the total width of the screen?  

Next lesson: Multiplying fractions by a whole number

The ideas in this fraction lesson are taken from the Fractions 2 ebook sold on this website. Only a few examples of each problem type are shown; you should make more problems of each kind for the student.

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