adding and subtracting fractions with unlike denominators
2 answers
http://www.coolmath4kids.com/fractions/fractions-12-adding-subtracting-different-denominators-01.html
Simply start writing all the multiples of both denominators, beginning with the numbers themselves. For example: Multiples of 4 are 4, 8, 12, 16, and so on (because 1 × 4=4, 2 × 4=8, 3 × 4=12, 4 × 4=16, etc.). The multiples of 6 are 6, 12, …-- wait, stop! That's the number we're looking for, 12, because it's the first one that appears in both lists of multiples. It's the least common multiple, which we'll use as our least common denominator.
Now that we have our least common denominator, we can make equal like fractions by multiplying the numerator and denominator of each fraction by the factor needed. We multiply 3/4 by 3/3, since 3 times 4 is 12, and we multiply 1/6 by 2/2, since 2 times 6 is 12. This gives the equal like fractions 9/12 and 2/12. Now we can add the numerators, 9 + 2, to find the answer, 11/12. 11/12 is its simplest form, because we cannot divide it by 2 evenly and 11 is a prime number.
Now that we have our least common denominator, we can make equal like fractions by multiplying the numerator and denominator of each fraction by the factor needed. We multiply 3/4 by 3/3, since 3 times 4 is 12, and we multiply 1/6 by 2/2, since 2 times 6 is 12. This gives the equal like fractions 9/12 and 2/12. Now we can add the numerators, 9 + 2, to find the answer, 11/12. 11/12 is its simplest form, because we cannot divide it by 2 evenly and 11 is a prime number.