


Description 



Denominator: The number below the line in a fraction. The denominator indicates what kind or size of parts the numerator counts. 
Numerator & Denominator
A "fraction" is used to indicate the number of parts of a
whole. The denominator of the fraction indicates the number of equivalent pieces
the whole is divided into. The numerator indicates the number of these pieces to
be considered (i.e., the part).
3/4: How many units of size 4 can I break 3 into?
4/2: How many units of size 2 can I break 4 into?
5/2.5: How many units of size 2.5 can I break 5
into?
Denominators
What is the common denominator for the fractions
below?
First, find common multiples of the denominators, 5 and 4.
denominator 
multiples 
5 
5 
10 
15 
20 
25 
30 
35 
40 
4 
4 
8 
12 
16 
20 
24 
28 
32  The common multiples of 4 and 5 are 20, 40, 60, . . . So, 20, 40, 60, . . .
are candidates for a common denominator of our fractions. How do we convert the
fractions to fractions with common denominators? For example, let's make the
common denominator equal to 20. Since 20 is the fourth multiple of 5, we need to
multiply 2/5 by 4/4 to get 8/20. Since 20 is the fifth multiple of 5, we need to
multiply 3/4 by 5/5 to get 15/20.
Why do we multiply by 2/5 by 4/4? To ensure that 2/5
and 8/20 measure the same amount  that is, that they are equivalent fractions.
2/5 can be represented by
and 8/20 can be represented by
Also, note that 2/5 = 0.4 and 8/20 = 0.4; since
2/5 and 8/20 have the same decimal form, they are equivalent.
Why do we care about common denominators? Because fractions with common denominators (called like
fractions) can easily be added and subtracted.
For example,
or graphically,

+ 

= 

+ 

= 
In the example above, any of the common multiples
could have been used. 20 was used because it's the smallest multiple, or the
least (smallest) common denominator.
A nonexample of equivalent fractions. 0.3333...
and 0.3 are not equal, so 1/3 and 3/10 are not equivalent fractions.


