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 Description  
 Common Denominator:  A whole number that is a common multiple of the denominators of two or more fractions.
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, etc. are candidates for a common denominator of our fractions. How do we convert the fractions to fractions with a common denominator? For example, let's make the common denominator equal to 20. Since 20 is the fourth multiple of 4, 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 the purple rectangles in relation to all of the rectangles below:



And 8/20 can be represented by the purple rectangles in relation to all the rectangles below:




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 are called like fractions, and it is much easier to add or subtract like fractions.

For example,
2 + 3
5   4
=
8 + 15
20   20
=
23
20

or graphically,
+ =


+ =




In the example above, any of the common multiples could have been used. The number 20 was used because it's the smallest multiple, or the least (smallest) common denominator.