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Equivalent fractions
a free lesson with a video

This is a free lesson for fifth grade math, teaching the concept of equivalent fractions. We get an equivalent fraction by splitting the existing pieces further into a certain number of new pieces.

The video below shows you how to get an equivalent fraction by splitting the existing pieces further into a certain number of new pieces (such as into four new pieces). This can be shown using an arrow notation, signifying that both the numerator and the denominator get multiplied by 4. Now there are four times as many colored pieces and four times as many pieces in total.

Besides the video, please also see this free sample worksheet: Equivalent Fractions worksheet. The worksheet shows the same notation and the same idea as the video and the lesson below.




Equivalent Fractions 1

 =         These two fractions are equivalent fractions because they
picture the same amount. You could say that you get to “eat” 
the same amount of “pie” either way. 

In the second picture, each slice has just been split into
two pieces
. The arrows show into how many new pieces
each piece was split.

× 2

3

4

   =   

6

8


× 2

 
 =         Each slice has been split into four.

BEFORE: 1 colored piece, 3 total.
AFTER: 4 colored pieces, 12 total.

Notice: we get FOUR times as many colored pieces and FOUR times as many total pieces. Both the numerator and the denominator get multiplied by 4.

× 4

1

3

=

4

12


× 4

 
When all of the pieces are split the same way, both the number of colored pieces (the numerator)
and the total number of pieces (the denominator) get multiplied by the same number.

1. Connect the pictures that show equivalent fractions. Write the name of each fraction beside its picture.

1

2

 

 

 

 

                  

                         

2. Make a chain of equivalent fractions.

= = =

1

2

= =

=

 

 

 = 

5

 

 = 

6

 

 =       =     


3. Split the pieces by drawing the new pieces in the right-hand picture. Write the equivalent
    fractions.

a.  Split each piece in two.

=

× 2

2

5

=

 

 


× 2

b.  Split each piece into three.

=

× 3

1

2

=

 

 


× 3

c.  Split each piece in two.

=

× 2

2

3

=

 

 


× 2

d.  Split each piece in two.

=

 
=

 

 

e.  Split each piece into three.

=

 

 

 
=

f.  Split each piece in two.

=

 

 

 
=

g.  Split each piece in two.

=

h.  Split each piece in two.

=

i.  Split each piece into five.

=

4. Write the equivalent fraction. Imagine or draw the helping arrows.

a. Split each
piece into four.

3

4

 =  

b. Split each
piece in two.

5

8

 =  

 

c. Split each
piece into six.

1

2

 =  

d. Split each
piece into four.

2

7

 =  

e. Split each
piece into five.

1

4

 =  

f. Split each
piece into three.

2

7

 =  

g. Split each
piece into ten.

5

8

 =  

h. Split each
piece into eight.

1

2

 =  

i. Split each
piece into seven.

3

5

 =  

j. Split each
piece into eight.

3

7

 =  

 



5. Figure out how many ways the pieces were split and write the missing numerator or denominator.

a. Pieces were
    split into three.

× 3

4

7

=

 

21


× 3

b. Pieces were
    split into ____ .

×    

4

5

=

 

20


×    

c. Pieces were
    split into ____ .

×    

1

6

=

 

18


×    

d. Pieces were
    split into ____ .

×    

6

7

=

 

14


×    

e. Pieces were
    split into ____ .

×    

2

3

=

8

 


×    

f.

7

10

=

14

 

g.

5

9

=

15

 

h.

1

8

=

6

 

i.

4

9

=

 

54

j.

8

11

=

 

44

k.

3

10

=

9

 

l.

2

11

=

6

 

m.

4

7

=

 

56

n.

1

6

=

 

54

o.

7

8

=

 

64

6. Mark the equivalent fractions on the number lines.

    a.   

2

3

 = 

     

12

 = 

     

24

 

    b.   

5

6

 = 

     

12

 = 

     

24

 

    c. Find and mark two fractions on the 12th parts number line that do not
        have an equivalent fraction on the 3rd parts number line. Write them here →

    d. Find and mark two fractions on the 24th parts number line that do not
        have an equivalent fraction on the 12th parts number line. Write them here →

 

7. A family of four baked two pizzas. Dad ate 1/2 of
one pizza, Mom and Cindy ate 1/3 of a pizza each,
and Derek ate the rest.

a. Write equivalent fractions for the fractions
    mentioned in the problem, using 1/12 parts.

b. Figure out which fraction of a pizza Derek ate.

  Fraction Equivalent fraction
Dad 1/2  
Mom    
Cindy    
Derek    



This lesson is taken from Maria Miller's book Math Mammoth Fractions 1, and posted at www.HomeschoolMath.net with permission from the author. Copyright © Taina Maria Miller.



Math Mammoth Fractions 1

A self-teaching worktext for 5th grade that teaches fractions and their operations with visual models. The book covers fractions, mixed numbers, adding and subtracting like fractions, adding and subtracting mixed numbers, adding and subtracting unlike fractions, and comparing fractions.

Download ($3.50). Also available as a printed copy.

Learn more and see the free samples!

See more topical Math Mammoth books



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