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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.

a.  The parts were joined together in ______.

=  

÷     

  =   


÷       

b.  The parts were joined together in ______.

=  

÷     

  =   


÷       



2. Write the simplifying process. You can write the arrows and the divisions to help you.

a. The slices were
    joined together
    in ___________.

=

÷ 3

3

6

  =  

 

 


÷ 3

b. The slices were
    joined together
    in ___________.

=

c. The slices were
    joined together
    in ___________.

=

d. The slices were
    joined together
    in ___________.

=

e. The slices were
    joined together
    in ___________.

=

 

 
 

f. The slices were
    joined together
    in ___________.

=

g. The slices were
    joined together
    in ___________.

=

h. The slices were
    joined together
    in ___________.

=

3. Draw a picture and simplify the fractions.

a. Join together each two parts.

 
 

2

6

=

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.

÷  4

28

40

  =   

7

10


÷  4  

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.

÷  1

6

17

  =   

6

17


÷  1  

4. Simplify the fractions to the lowest terms.

  ÷    
a. 

6

16

 =

 
÷    
  ÷    
b. 

15

25

 =

 
÷    
  ÷    
c. 

3

9

 =

 
÷    
  ÷    
d. 

4

8

 =

 
÷    
  ÷    
e. 

16

24

 =

 
÷    
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 warm-up, the practice, and the stretching. 

    What part of the total time is the warm-up time?

    What part of the total time is the actual practice time?

 

9. Color the parts of this 24-part 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.



Math Mammoth Fractions 2

A self-teaching 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.

=> Learn more and see the free samples!

See more topical Math Mammoth books



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