Embed Size (px)
Citation preview
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
Sometimes fractions with different numerators and denominators can be equal to one another.
2
1 Numerator
Denominator
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 = 3/12 of a pizza
THESE FRACTIONS ARE ALL EQUAL
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:
36
27
Simplifying Fractions
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
=
36
27
36
2712
93
3
Simplifying Fractions
So now we have , but is this number in the simplest form yet?
Are there any numbers that go into both 9 and 12? How about 3?
Divide 9 by 3 and get 3 = Divide 12 by 3 and get 4
Thus, we have:
= = OR =
12
9
12
9
4
3
36
2712
9
4
336
27
4
3
¾ is the simplest form of this fraction!
3
3
3
3
3
3
)33(
)33(
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:
= = =
= = = =
72
4598
95
8
5
64
4888
68
222222
23222
4
3
33222
335
2424
2324
Challenge Problem!
Simplify this fraction:
108
72
Challenge Problem!
108
72
108
72
54
36
9
63
2
108
72254
98
2)96(
)33()24(
23323
33222
3
2
2
2
6
6
3
3
Great Job!
Keep practicing!
