SIMPLIFYING FRACTIONS
Fraction Simplification and Equality
Some Fractions are Created Equal


Fractions represent a part of a whole number
They are made of numerators and denominators
1
2

Numerator
Denominator
Sometimes fractions with different numerators and
denominators can be equal to one another.
Equal Fractions



These two rectangles are the same size, but they are divided
into a different number of pieces
If we shade one piece on the first rectangle, it is the same as
shading two pieces on the second rectangle. Thus, the fractions
1/4 and 2/8 are EQUAL!
1/4
2/8
Equal Fractions


You can see examples of this in real life every day!
Check out these pizzas! They are all the same size but are
divided into different numbers of equally sized pieces
1/4 of a pizza
=
2/8 of a pizza
=
THESE FRACTIONS ARE ALL EQUAL
3/12 of a pizza
Simplify or Reduce? . . .
That is the question.



We have seen that 1/4 = 2/8 = 3/12
When we are given a fraction containing larger
numbers (3/12) and we are asked to simplify or
‘reduce’, which is the correct terminology? . . .
We already said that 3/12 = 1/4, did we reduce
or simplify this number? . . .
Simplify or Reduce? . . .
That is the question.
(ctd.)


We SIMPLIFIED it! Although the numbers in the
numerator and denominator are smaller than they
were before, these numbers alone don’t make up
the overall number.
The RATIO between the two stayed the same and
therefore the number cannot be ‘reduced’. It is
SIMPLIFIED.
Simplifying Fractions


Usually, fractions are easiest to understand in their
simplest form.
To get to the simplest form you must SIMPLIFY them,
if necessary.
 Example:
What is the simplified form of:
27
36
Simplifying Fractions



27
36
To simplify a fraction you must be able to divide both
the numerator and the denominator by the SAME
number.
Can you think of a number by which both 36 and 27
are divisible?
How about 3?
Divide 27 by 3 and get 9
 Divide 36 by 3 and get 12

27
36
3
=
3
9
12
Simplifying Fractions
So now we have 9 , but is this number in the
simplest form yet? 12



Are there any numbers that go into both 9 and 12?
How about 3?
9 3 3




Divide 9 by 3 and get 3
Divide 12 by 3 and get 4
Thus, we have:
27  3 = 9
 3 12
36
3
=
3
12
3
4
3
=
¾ is the
simplest form
of this
fraction!
4
OR
27
36
 (3  3)
 (3  3) =
3
4
Prime Factorization



Another way to think about simplifying fractions is through Prime Factorization:
In prime factorization, you reduce the numerator and the denominator into their
lowest factors. Then you can cancel out pairs of numbers appearing in both the
numerator AND the denominator.
Check out these fractions that we have simplified using Prime Factorization:
45 5  9
5
5 3 3
=
=
=
72 8  9 2  2  2  3  3 8
48
64
8 6
=
=
88
2  2  2  3 2
4  2  3 2
=
=
4 2 4 2 2 2 2 2 2 2
3
4
Challenge Problem!

Simplify this fraction:
72
108
Challenge Problem!

Simplify this fraction: 72
108
72
108
2
2
36
=
54
6
6
6
=
9
3
3
2
=
3
OR
72
8 9
2
(4  2)  (3  3) 2  2  2  3  3
=
=
=
=
3 2  3 3 2 3
(6  9)  2
108 54  2
Great Job!
Keep practicing!