Making Equivalent Fractions
One half is equivalent to two fourths.
1
X
2
0
1
1
2
0
2
0
4
1
4
2
4
2
2
3
4
4
4
2
2
2 = 4
Or:
1
2
x2
=
x2
2
4
To create equivalent fractions, we must maintain
the same relationship (x 2 in this case) between
the two numerators and the two denominators.
Making Like Denominators to Add/Subtract Fractions
2
+
5
2
2
1
2
5
5
x
x
=
4
10
=
5
10



9
10
What is the least common multiple
for these two denominators? (10)
This will be our denominator for
our equivalents.
How can I make an equivalent for
my fifths using tenths? x 2
2
How can I make an equivalent for
my halves using tenths?
5
x
5
When we’re multiplying to form equivalent fractions, we’re
actually multiplying by a form of 1 whole (2/2, 5/5, etc.),
which is why, although the digits look different the portion the
fraction represents remains equal!
Adding and Subtracting Fractions
If we have like units (like denominators)...

we add or subtract the numerators and
maintain the same denominator.
4
10
+
5
10
9
10
Or:


9
10
-
5
10
4
10
4 tenths + 5 tenths = 9 tenths
9 tenths - 5 tenths = 4 tenths
If we have unlike units (unlike denominators)…

we need to create equivalent fractions using a
least common multiple as our denominator.

What is the least common denominator for
these two denominators? (10)

How can I make an equivalent for my fifths
using tenths?

How can I make an equivalent for my halves
using tenths?
2
5
x
2
2
=
4
10
1
+ 2
x
5
5
=
5
10
9
10
Improper Fractions and Mixed Numbers
Changing Improper Fractions to Mixed Numbers:

Add or subtract the numerators and
maintain the same denominator.
3 + 3+ 2
3
3
3
2
3 8
-6
2

Add or subtract the numerators and
maintain the same denominator.
2
8
3
Or:
Changing Mixed Numbers to Improper Fractions:
=
2
3
2
2
3
2
= (2 groups of 3 )+ 2
3
3
3
= (2 x 3 ) + 2
3
3
8
= 3
Interpreting Fractions As Division
1
1 ÷ 3 = 1/3 = 3
1
1
3
Fractions of a Set
2
6 ÷ 3 = 2 per unit
6
2
(2 groups of 2) = 4
(3 groups of 2) = 6
Or:
Or:
2
2
2 x 6 = 12 = 4
3 1 3
3 x 6 = 18 = 6
3 1 3
Multiplying Fractions by Fractions
When multiplying fractions, the
operation applies to both the numerators
and denominators.
Check out the model to understand why!
Multiplying and Relating Fractions and Decimals
When multiplying fractions using
either tenths or hundredths, the
fraction can easily be related to
decimals using tenths or
hundredths.
Dividing Whole Numbers
by Fractions
Dividing Fractions
by Whole Numbers
5
1 1
4 4
...
1
1
4
1
20
5 ÷ 4 = ___
When dividing by fractions…we
should think about the fraction that
represents one unit.
There are 4 fourths in 1 whole.
There are 20 fourths in 5 wholes.
1
2
1 =3
2 6
1 = 3
2 6
1 half ÷ 3 =
3 sixths ÷ 3=1 sixth
1
1 ÷ 3 = ___
6
2