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what would be the common denominator in 9 and 12

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2 Answers

The simplest way to find a common denominator is to "skip count" (count by multiples) by each of the numbers in question. For example, 9, 18, 27, 36, 45, 54, 63, 72 . . . and 12, 24, 36, 48, 60, 72, 84, . . . . Any numbers on both lists are "common denominators" (36 and 72); the first such number on both lists is the Lowest Common Denominator (LCD). 

A more complicated way involves using the prime factorizations of the numbers in question. The p. f. for 9 = 3 x 3; the p. f. for 12 = 2 x 2 x 3. Next, line the two p.f.'s up like this, showing where any factors from the p.f.'s overlap:

2 x 2 x 3

           3 x 3

Now, write the factors out in one line, using all the factors from the 2 lines, but where they overlap, write only one of the 2 overlapping factors:

2 x 2 x 3 x 3 = 36 (the LCD)

A denominator is the number on the bottom in a fraction. In this case, 9 and 12 are both whole numbers. The common denominator would be 1 because both numbers would have a fraction of 9/1 and 12/1. However, if 9 and 12 are denominators to fractions (i.e. 1/9 and 1/12) that would be a different story. In this case you would find the smallest number that both numbers can be divided in to completely.

For example:

9 and 12 can both be divided into 36

36 / 9 = 4

36 / 12 = 3

Now you can just multiply each fraction by the respective number to get fractions over 36.

1 / 9     Multiply both the top and the bottom number by 4 giving you    4 / 36

1 / 12   Multiply both the top and the bottom number by 3 giving you    3 / 36

Your common denominator would be 36.

Another way to find this would be to multiply each fraction by the other fractions denominator.

I.E. 9 * 12 = 108

(1 / 9) * (12 / 12) = 12 / 108

(1 / 12) * (9 / 9) = 9 / 108

 

 

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