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denominator
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denominator
The denominator is the number written below the line
of a fraction. E.g. in
3

7
the denominator is seven;
in
2

11
the denominator is eleven.
common denominator
Denominator that is a common multiple of, and hence exactly
divisible by, all the denominators of a set of fractions, and
which therefore enables their sums or differences to be found.
For example, 2/3 and 3/4 can both be converted to equivalent
fractions of denominator 12, 2/3 being equal to 8/12 and 3/4 to
9/12. Hence their sum is 17/12 and their difference is 1/12.
The lowest common denominator is the smallest common multiple
of the denominators of a given set of fractions.
Least Common Denominator
The Least Common Denominator (LCD) is the Least Common
Multiple of two or more denominators.
How to find the Least Common Denominator:
Find the Greatest Common Factor of the denominators.
Multiply the denominators together.
Divide the product of the denominators by the Greatest Common
Factor. Example:
Find the LCD of 2/9 and 3/12
Determine the Greatest Common Factor of 9 and 12 which is 3
Either multiply the denominators and divide by the GCF
(9*12=108, 108/3=36)
OR  Divide one of the denominators by the GCF and multiply
the quotient times the other denominator (9/3=3, 3*12=36)
How to rename fractions and use the Least Common Denominator:
Divide the LCD by one denominator.
Multiply the numerator times this quotient.
Repeat the process for the other fraction(s)
Example:
Add 2/9 + 3/12
LCD is 36
First fraction (2/9): 36/9 = 4, 4*2 = 8, first fraction is
renamed as 8/36
Second fraction (3/12): 36/12 = 3, 3*3 = 9, second fraction
is renamed as 9/36
It is possible to add or subtract fractions that have the
same denominator
8/36 + 9/36 = 17/36
