equation: 1/2 + 8/9 - 2/3
To add these fractions, find the lowest common denominator for the three numbers, in this case it is 18. Change the fractions so the denominator equals 18, so you can add them after.
Okay so i know how to do it after i find the Least Common Denominator but i dont understand how to find the least common denominator? Please explain.
There are several ways you can add fractions (which really amount to the same thing in the end). The basic method is to find a common denominator (not necessarily the least common denominator). The way to do this is to multiply all the denominators together. In this case the denominators are 2, 3, and 9 and a common denominator is 2 * 3 * 9 which is 54. However, we note the we don't need the 3 by itself and also the 9 by itself since if a number is divisible by 9 it is divisible by 3, so we can get by with 2 * 9 = 2 * 3 * 3 = 18. Now there are no more numbers in the list which can be divided by another so we have our least common denominator.
To put it more formally, write each denominator as a factor of primes to a power
2 = 2
1
9 = 3
2
3 = 3
1
Now go through the list and, for each prime, choose just the one to the highest power, i.e. the highest power for 2 is 2
1 = 2, the highest power for 3 is 3
2 = 9 and that exhausts the list of primes we have. So the least common denominator is 2 * 9 = 18.
Doing just a common denominator will also work and, sometimes if you have a hard time finding the primes you need, you might use that. For the problem you would get
\(\displaystyle \frac{27}{27}\frac{1}{2} + \frac{6}{6}\frac{8}{9} - \frac{18}{18}\frac{2}{3}\)
\(\displaystyle = \frac{27 + 6 * 8 - 18 * 2}{54} = \frac{39}{54}\)
Now notice that we can factor out that extra 3 to get 13/18 as we would if we had used the least common denominator.
