(1/2) + (1/6) + (3/4)
To start, anything that is even will be divisible by 2, so you need to find the lowest even number that is divisible by both 6 and 4 to find what is called the lowest common denominator, in order to be able to add these numbers together.
Step 1 in finding the lowest common denominator is to list the multiples of the first denominator, up to the multiple of the first denominator times the second denominator.
4 * 1 = 4 : 4 * 2 = 8 : 4 * 3 = 12 : 4 * 4 = 16 : 4 * 5 = 20 : 4 * 6 = 24
Step 2: list the multiples of the 2nd denominator up to the 2nd denominator times the first denominator:
6 * 1 = 6 : 6 * 2 = 12 : 6 * 3 = 18 : 6 * 4 = 24
Step 3: Find the lowest common result:
4 * 3 = 12 and 6 * 2 =12
12 is the lowest common denominator of the 3 fractions.
Step 4: When changing a fraction to the lowest common denominator, you must change the numerator too, you just have to figure out, how much to change the numerator.
When figuring out how to change a fraction into something you can use for the problem, you take the lowest common denominator you found and divide by the denominator of the fraction:
12/2 = 6
6 is the number you multiply the top and bottom numbers of the first fraction by to get to the lowest common denominator:
(1/2) * (6/6)(which is just multiplying by 1) = 6/12
12/6 = 2
2 is the number you multiply the top and bottom numbers of the second fraction by to get to the lowest common denominator:
(1/6) * (2/2)(which is just 1) = 2/12
12/4 = 3
3 is the number you multiply the top and bottom numbers of the third fraction by to get to the lowest common denominator:
(3/4) * (3/3)(again just 1) = 9/12
Now that you have all 3 fractions with the same denominator, you just add the numerators together and keep the same denominator:
(6/12) + (2/12) + (9/12) = (6 + 2 + 9)/12 = 17/12 or 1 5/12
Vincent M.
01/12/15