Equivalent
Fractions
Worksheets





Introduction to equivalent
fractions
Equivalent fractions to
decimals
A third as a recurring
decimal
Converting common
fractions to decimals
Converting to decimals,
percentages and ratio
Trish Price & Peter Price
These worksheets are part of the Professor Pete’s Gadgets: Fractions eBooks.
Licensed for unlimited photocopying by original purchaser only.
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Equivalent Fractions
Equivalent fractions are often poorly understood by students. Too often fractions are taught as just
“do it this way” with no understanding behind what is happening and why the fractions are
equivalent.
Our Gadget series helps students to actually see what is happening and allows on screen
manipulation showing pinpoint accuracy in its animation.
Gadget Titles:





Counting in Fractions: count in fractions and mixed numbers
Equivalent Fractions: shows equivalence
Fraction Converter: converts between common, decimal, percentages and ratios
Adding and Subtracting Fractions: both horizontal and vertical algorithm
Number Facts: Interactive times tables and addition tables chart/grid
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These worksheets are part of the Professor Pete’s Gadgets: Fractions eBooks.
Licensed for unlimited photocopying by original purchaser only.
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Equivalent Fractions (set 1)
Name __________________
1
Common to Common - Multiplying
Cut each Fractional Piece into Two Pieces
Draw lines to cut each fractional piece in two pieces
to make new fractions.
Equivalent fractions
example:
2
3
=
4
6
Write the equivalent fraction that each shape now
shows.
1
2
=
3
4
=
1
3
=
1
4
=
5
8
=
3
5
=
2
6
=
4
9
=
Write the equivalent fraction of each of these if each fractional piece was cut in
two.
x2
x2
1)
6
8
=
4)
3
4
x2
2)
3)
2
5
=
7
8
=
=
7)
2
7
=
8)
1
12
=
5
6
=
x2
5
6)
3
9
=
6
10
=
9)
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Equivalent Fractions (set 2)
Name __________________
2
Simplifying Fractions - Dividing
Equivalent Fractions - Grouping 3 Fractional Pieces
Draw dark lines to group 3 fractional pieces
together to make new fractions. (to do this,
divide the numerator and denominator by 3)
Equivalent fractions
example:
÷3
3
9
=
÷3
15
18
1
3
Write the equivalent fraction that each shape now
shows.
Hint:
Blur your eyes see that 3 is the same as 1
9
3
9
12
=
3
6
=
=
÷3
9
15
6
9
=
2
6
=
=
÷3
Write the equivalent fraction of each of these if 3 of each fractional pieces are
grouped. ÷3
÷3
1)
15
21
=
4) 12
18
3)
9
18
6
24
=
=
7)
12
15
=
8)
18
24
=
3
18
=
÷3
÷3
2)
=
5)
6)
6
18
15
18
=
=
9)
These worksheets are part of the Professor Pete’s Gadgets: Fractions eBooks.
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Equivalent Fractions (set 3)
Name __________________
3
Using a Number Line
Locating Fractions on a Number Line
A half is always found at the midway point regardless of the number of other
finger slide or count the hops)
markers on the number line. (Use the
1
—
2
0
1
—
6
2
—
6
3
—
6
1
4
—
6
5
—
6
Find the half marker on these lines and label it above the line. Label the other
fractions underneath. (Remember to count the hops to find the fraction.)
1.
0
2.
1
0
3.
4.
1
1
0
1
0
5. For each number line above, loop the half and the fraction underneath. These
fractions are called equivalent fractions. Write all the equivalent fractions for a
half. (Don’t forget to include the example.)
1
—
2
=
__________________________________
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Licensed for unlimited photocopying by original purchaser only.
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Equivalent Fractions (set 4)
Name __________________
4
Common to Common - Multiplying
Cut each Fractional Piece into Tenths
Equivalent fractions example:
1
2
1
5
5
= 10
so
so
1
2
2
= 10
=
1
5
0.5
=
Shade the equivalent fractions on these shapes and then write the fraction and
decimal equivalents.
1)
4)
3
5
=
6
10
5
5
so
so
3
5
= 0.
2)
5
5
=
4
5
8
= 10
5)
1
2
5
= 10
so
so
1
2
3)
= 10
10
4
5
= 0.
=
Write the decimal equivalent of each of
these fractions.
2
5
4
= 10
2
5
=
1
5
=
1
2
=
=
3
5
=
4
5
=
5
5
=
so
2
5
These worksheets are part of the Professor Pete’s Gadgets: Fractions eBooks.
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Equivalent Fractions (set 4)
Name __________________
5
Common Fractions to Decimals
Investigating a Third as Hundredths and a Decimal
We can convert some common fractions into equivalent decimal fractions like
this:
3
4
3x25
4x25
=
75
100
=
0.75
=
For some fractions, this method does not work.
INVESTIGATION
Look at the two circles:
1
of the pieces are shaded.
3
You cannot multiply 3 by anything to get to 100 so it is
Colour the second circle so that roughly
100 ÷ 3 = 33
1
3
necessary to round the numerator.
Complete:
So
1
3
≈
33
100
2 x (100 ÷ 3) = 2 x 33
≈
1
3
1
3
is less than a half so rounds down.
0.
= 66 23
2 is more than a half so rounds up.
3
≈
N.B.
2
3
≈
means “approximately
equal to”
67
100
≈
0.
These worksheets are part of the Professor Pete’s Gadgets: Fractions eBooks.
Licensed for unlimited photocopying by original purchaser only.
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Equivalent Fractions (set 4)
Name __________________
6
Common Fractions to Decimals
Cut each Fractional Piece into Hundredths
Equivalent fractions example:
1
2
=
1
4
100
=
100
so
so
1
2
1
4
= 0.
= 0.
Shade the equivalent fractions on these shapes and then write the fraction and
decimal equivalents.
1)
3)
3
4
1
5
=
so
so
3
4
=
1
5
= 0.
2)
3
5
=
0.
=
so
3
5
=
0.
These worksheets are part of the Professor Pete’s Gadgets: Fractions eBooks.
Licensed for unlimited photocopying by original purchaser only.
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Equivalent Fractions (set 5)
Name __________________
7
Decimals, Percentage and Ratio
Write the missing common or decimal fraction and place it on the number line.
When drawing the fraction use the divisions as a guide.
1)
45
100
—–
%
1
0
2)
%
—–
1
0
3)
6%
—–
1
0
4)
0.14
—–
%
1
0
5)
%
95
100
—–
0
1
These worksheets are part of the Professor Pete’s Gadgets: Fractions eBooks.
Licensed for unlimited photocopying by original purchaser only.
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Equivalent Fractions (set 5)
Name __________________
8
Decimals, Percentage and Ratio
Writing ratio as a common fraction:
The first value (the shaded area) is the numerator.
The number of pieces altogether is the denominator.
1
2:1
Numerator
Common Fraction
2
——
3
Denominator
2
2+1=
3
Write the ratio of the shaded to unshaded areas.
Write the number of pieces altogether.
Then write the ratio as a common fraction.
1)
3:5
Common Fraction
5
=
3
——
2)
1:5
Common Fraction
——
=
3)
8:2
Common Fraction
=
——
4)
4:4
Common Fraction
=
——
These worksheets are part of the Professor Pete’s Gadgets: Fractions eBooks.
Licensed for unlimited photocopying by original purchaser only.
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Equivalent Fractions (set 1)
1
S
R
E
W
S
Name __________________
AN
Cut each Fractional Piece into Two Pieces
Draw lines to cut each fractional piece in two pieces
to make new fractions.
Equivalent fractions
example:
2
3
=
4
6
Write the equivalent fraction that each shape now
shows.
1
2
=
2
4
3
4
=
6
8
1
3
=
2
6
1
4
=
2
8
5
8
= 10
16
3
5
6
= 10
2
6
=
4
12
4
9
=
8
18
Write the equivalent fraction of each of these if each fractional piece was cut in
two.
x2
x2
1)
6
8
=
12
4)
16
3
4
x2
2)
3)
2
5
=
7
8
=
6
=
7)
8
2
7
=
1
12
=
5
6
=
4
14
x2
4
5)
10
14
16
6)
3
9
=
6
10
=
6
8)
18
12
20
9)
2
24
10
12
These worksheets are part of the Professor Pete’s Gadgets: Fractions eBooks.
Licensed for unlimited photocopying by original purchaser only.
http://www.professorpetesclassroom.com
Equivalent Fractions (set 2)
2
S
R
E
W
S
Name __________________
AN
Equivalent Fractions - Grouping 3 Fractional Pieces
Draw dark lines to group 3 fractional pieces
together to make new fractions. (to do this,
divide the numerator and denominator by 3)
Equivalent fractions
example:
÷3
3
9
=
÷3
15
18
=
1
3
Write the equivalent fraction that each shape now
shows.
Hint:
Blur your eyes see that 3 is the same as 1
9
3
9
12
5
6
=
3
6
3
4
=
1
2
÷3
9
15
=
3
5
6
9
=
2
6
2
3
=
1
3
÷3
Write the equivalent fraction of each of these if 3 of each fractional pieces are
grouped. ÷3
÷3
1)
15
21
=
5
7
4) 12
18
3)
9
18
6
24
=
=
7)
6
12
15
=
18
24
=
3
18
=
4
5
÷3
÷3
2)
=
4
3
5)
6
2
8
6)
6
18
15
18
=
=
2
8)
6
5
6
9)
6
8
1
6
These worksheets are part of the Professor Pete’s Gadgets: Fractions eBooks.
Licensed for unlimited photocopying by original purchaser only.
http://www.professorpetesclassroom.com
SFractions (set 3)
R
E
W
Equivalent
S
AN
3
Name __________________
Locating Fractions on a Number Line
A half is always found at the midway point regardless of the number of other
finger slide or count the hops)
markers on the number line. (Use the
1
—
2
0
2
—
6
1
—
6
3
—
6
1
4
—
6
5
—
6
Find the half marker on these lines and label it above the line. Label the other
fractions underneath. (Remember to count the hops to find the fraction.)
1
2
3
1.
—
—
—
0
2.
1
—
8
4
1
—
2
2
—
8
1
—
10
2
—
10
0
3.
4.
4
0
0
1
—
12
2
3
—
12
2
—
12
1
4
3
—
8
3
—
10
4
—
12
4
—
8
1
—
2
4
—
10
5
—
12
5
—
8
6
—
8
7
—
8
1
9
5
8
6
7
—
—
—
—
—
1
10
10
10
10
10
1
—
2
7
8
9
10
6
11
—
—
—
—
—
—
1
12
12
12
12
12
12
1
—
2
5. For each number line above, loop the half and the fraction underneath. These
fractions are called equivalent fractions. Write all the equivalent fractions for a
half. (Don’t forget to include the example.)
1
—
2
=
2
4
5
6
—
—
—
—
4
8
10
12
__________________________________
These worksheets are part of the Professor Pete’s Gadgets: Fractions eBooks.
Licensed for unlimited photocopying by original purchaser only.
http://www.professorpetesclassroom.com
Equivalent Fractions (set 4)
4
S
R
E
W
S
Name __________________
AN
Cut each Fractional Piece into Tenths
Equivalent fractions example:
1
2
1
5
5
= 10
so
so
1
2
2
= 10
=
1
5
0.5
=
0.2
Shade the equivalent fractions on these shapes and then write the fraction and
decimal equivalents.
1)
3
5
=
4)
6
10
5
5
so
so
3
5
=
0.6
2)
5
5
=
4
5
8
= 10
1.0
5)
1
2
5
= 10
so
so
1
2
3)
= 10
10
=
4
5
0.5
=
0.8
Write the decimal equivalent of each of
these fractions.
2
5
4
= 10
2
5
= 0.4
1
5
= 0.2
1
2
= 0.5
3
5
= 0.6
4
5
= 0.8
5
5
= 1.0
so
2
5
=
0.4
These worksheets are part of the Professor Pete’s Gadgets: Fractions eBooks.
Licensed for unlimited photocopying by original purchaser only.
http://www.professorpetesclassroom.com
Equivalent
RS Fractions (set 4)
ANSWE
5
Name __________________
Cut each Fractional Piece into Hundredths
Equivalent fractions example:
1
2
=
50
100
1
4
25
100
so
so
1
2
=
1
4
= 0.50
= 0.25
Shade the equivalent fractions on these shapes and then write the fraction and
decimal equivalents.
1)
3)
3
4
=
75
100
1
5
20
100
so
so
3
4
=
=
1
5
0.75
2)
3
5
=
=
0.20
60
100
so
3
5
= 0.60
These worksheets are part of the Professor Pete’s Gadgets: Fractions eBooks.
Licensed for unlimited photocopying by original purchaser only.
http://www.professorpetesclassroom.com
Equivalent Fractions (set 4)
S
R
E
W
S
Name __________________
AN
6
Investigating a Third as Hundredths and a Decimal
We can convert some common fractions into equivalent decimal fractions like
this:
3
4
3x25
4x25
=
75
100
=
0.75
=
For some fractions, this method does not work.
INVESTIGATION
Look at the two circles:
1
of the pieces are shaded.
3
You cannot multiply 3 by anything to get to 100 so it is
Colour the second circle so that roughly
100 ÷ 3 = 33
1
3
necessary to round the numerator.
Complete:
So
1
3
≈
33
100
2 x (100 ÷ 3) = 2 x 33
≈
1
3
1
3
is less than a half so rounds down.
0.33
= 66 23
2 is more than a half so rounds up.
3
≈
N.B.
2
3
≈
means “approximately
equal to”
67
100
≈
0.67
These worksheets are part of the Professor Pete’s Gadgets: Fractions eBooks.
Licensed for unlimited photocopying by original purchaser only.
http://www.professorpetesclassroom.com
Equivalent Fractions (set 5)
7
S
R
E
W
ANS
Name __________________
Write the missing common or decimal fraction and place it on the number line.
When drawing the fraction use the divisions as a guide.
1)
45
100
—–
2)
72
100
—–
3)
6
100
—–
0.45
0
45%
0.72
0
72%
0.06
0
6%
0.14
14%
4)
14
100
—–
5)
95
100
—–
1
1
1
1
0
0.95
0
95%
1
These worksheets are part of the Professor Pete’s Gadgets: Fractions eBooks.
Licensed for unlimited photocopying by original purchaser only.
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Equivalent Fractions (set 5)
8
S
R
E
W
ANS
Name __________________
Writing ratio as a common fraction:
The first value (the shaded area) is the numerator.
The number of pieces altogether is the denominator.
1
2:1
Numerator
Common Fraction
2
——
3
Denominator
2
2+1=
3
Write the ratio of the shaded to unshaded areas.
Write the number of pieces altogether.
Then write the ratio as a common fraction.
1)
3:5
5
3
Common Fraction
3
——
8
3+5 = 8
2)
1:5
1
1+5
5
3)
2
8
8:2
Common Fraction
=
1
——
6
6
Common Fraction
8
——
10
8 + 2 = 10
4)
4:4
4
4
Common Fraction
4+4 = 8
4
——
8
These worksheets are part of the Professor Pete’s Gadgets: Fractions eBooks.
Licensed for unlimited photocopying by original purchaser only.
http://www.professorpetesclassroom.com
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