Simplifying fractions
In this 5th grade lesson, I explain how to simplify a fraction using a visual model and an arrow notation. Simplifying fractions is like joining or merging pieces together, and it is the opposite of finding equivalent fractions and splitting the pieces further.
The video below explains many of the same ideas as the lesson below.
Do you remember how to convert fractions
into equivalent fractions? 

= 


×
2


3
4 
= 
6
8 
Each slice has been split two ways. 

× 2 


= 


×
3


1
3 
= 
3
9 
Each slice has been split three ways. 

× 3 

We can also reverse the process. Then it is
called SIMPLIFYING: 

= 


÷ 2


6
8 
= 
3
4 
The slices have been joined
together in twos. 

÷ 2 


= 


÷ 3


3
9 
= 
1
3 
The slices have been joined
together in threes. 

÷ 3 

Notice:
 Both the numerator and the denominator change into smaller numbers, but the value
of the
fraction does not. In other words, you get the SAME AMOUNT of pie either way.
 The fraction
is now written 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.
 Both the numerator and the denominator are
divided by
the same
number.
This number shows how many slices are joined together.

1. Write the simplification process, labeling
the arrows. Follow the examples above.
2. Write the simplifying process.
You can write the arrows and the divisions to help you.
3. Draw a picture and simplify the fractions.
a. Join together each two parts.

b. Join together each four parts.

c. Join together each three parts.

d. Join together each six parts.

e. Join together each seven parts.

f. Join together each four parts.

When you simplify, you divide the numerator and the denominator by the same
number, so you need a number that “goes” into both the numerator and the
denominator evenly.
The numerator and the denominator have to
be divisible by the same number. 
Simplify

28
40 
. 
Since both 28 and 40 are divisible
by 4, we can divide the
numerator
and denominator by
four. This
means that each four slices
are
joined together. 


Simplify

6
17 
. 
We cannot find any number that
would go into 6 and 17 (except 1,
of course). So 6/17 is already as
simplified as it can be. It is
already in its lowest terms. 


4. Simplify the fractions to the lowest terms.





f. 
12
20 
= 

g.

24
32 
= 

h.

3
15 
= 

i.

15
18 
= 

j.

16
20 
= 

5. Simplify the fractional parts
of these mixed numbers. The whole number does not change. Study
the example.
a. 1 
4
16 
= 1 
1
4 

b. 5 
3
27 
= 

c. 7 
5
20 
= 

d. 3 
14
49 
= 

6. You cannot simplify some of these fractions because they are already in
the lowest terms. Cross out
the fractions that are already in the lowest terms and simplify the rest.
a. 
2
3 

b. 
2
6 

c. 
6
13 

d. 2 
7
12 

e. 
11
22 

f. 5 
6
12 

g. 
5
11 

h. 
9
20 

i. 1 
4
7 

j. 3 
4
28 

k. 
5
29 

l. 
6
33 

7. Use a line to connect the fractions
and mixed numbers that are equivalent. 
2 
6
24 


28
12 


1 
3
4 


2 
4
12 








14
8 


2 
2
8 


2 
5
15 


21
12 








2 
1
3 


7
4 


9
4 


2 
1
4 


8. Tommy is on the track team. He spends 10 minutes warming up before
practice and 10 minutes stretching after practice. All together, he spends
a total of one hour for the
warmup, the practice, and the stretching.
What part of
the total time is the warmup time?
What part of the total
time is the actual practice time?
9. Color the parts of this 24part circle according to how you spend
your time during a typical day.
Include sleeping, eating, bathing, school, housework, TV, etc. Write the name of each
activity and
what fractional part
of your day it takes. Simplify the fractional part if you can.
This lesson is taken from Maria Miller's book Math Mammoth Fractions 2, and posted at www.HomeschoolMath.net with permission from the author. Copyright © Maria Miller.
A selfteaching worktext that teaches fractions using visual models, a sequel to Math Mammoth Fractions 1. The book covers simplifying fractions, multiplication and division of fractions and mixed numbers, converting fractions to decimals, and ratios.
Download ($5.75). Also available as a printed copy.
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