Expert: Josh - 1/17/2008

Question
How do you add 2/5   1/6   1/4? I do not know the steps to finding a common denominator?  Thanks!

Answer
Ramonia,

To add fractions, we need to express each one in terms of a common denominator. Otherwise, we cannot add the numbers in the numerator (what is written above the fraction bar) directly. The steps are as follows:

Method: Given 2/5, 1/6 and 1/4, we focus on the denominators "5", "6" and "4" and ask what is the least common multiple. In other words, what is the smallest number that can be divided BY all three numbers 5, 6 and 4. This is not too difficult to find because the numbers are small, in general there is a procedure for finding this based on "prime number factorization". I can tell you more if you are interested. But for now, we observe that we don't actually need the "smallest" common multiple, any number that can be divided by all three numbers will do.

Obviously, the number 120 (the product of 5,6 and 4) can be divided by all three numbers 5,6 and 4.

Consider the first fraction 2/5. Dividing 120 by the denominator, we get 120/5=24. We can multiply 2/5 by 24/24 without changing the ratio. This is important. But we can write this as (2*24)/(5*24) which equals 48/120.

Consider the second fraction 1/6. Dividing 120 by the denominator, we get 120/6=20. We can multiply 1/6 by 20/20 without changing the ratio. We end up with 20/120.

Finally, to rewrite 1/4 as .../120, we multiply top and bottom by 30. i.e., 1/4 is equivalent to 30/120.

So, the task of adding 2/5, 1/6 and 1/4 is the same as adding 48/120, 20/120 and 30/120. Since they have the same denominator, the individual fractions can be combined into one. We can now add the numerator terms directly. Putting everything together,

(2/5)+(1/6)+(1/4)
=(48/120) + (20/120) + (30/120)
=(48+20+30)/120
=98/120
we can simplify this further dividing top and bottom by 2 to get 49/60.

Good luck