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 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?
2 and 3
5   4

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,
2 + 3
5   4
=
8 and 15
20   20
=
23
20

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 non-example of equivalent fractions. 0.3333... and 0.3 are not equal, so 1/3 and 3/10 are not equivalent fractions.