# What is the total fraction of 1/2 plus 3/20? The question involves two fractions, 1/2 and 3/20, and we need to solve for their sum—that is,

1/2 + 3/20

To solve such a question, consider two fractions, a/b and c/d.

a/b + c/d

First, we need to find the Least Common Multiplier of the denominators (i.e., b and d).

If the LCM is bd, then we can solve the numerical as:

a/b + c/d = [(axd) + (cxb)] / (bxd) = (ad + bc)/bd

In case the LCM of b and d is a number m, then

a/b + c/d = [(a x m/b) + (c x m/d)]/m

For our scenario, a = 1, b = 2, c = 3 and d = 20

The LCM of the denominators, 2 and 20, is calculated as:

LCM (2,20) = (2 x 20)/ gcf(2,20)

where gcf is the greast common factor. Now the gcf of 2 and 20 is 2, since 2 is the greatest common factor for both the numbers.

Hence, LCM (2,20) = (2 x 20)/ 2 = 40/2 = 20 = m

Using the above example, 1/2 + 3/20 = [(1 x 20/2 + 3 x 20/20] / 20

= (1x10 + 3x1)/20 = 13/20

Similarly, by using the above given example, the sum of any fractions can be found. We can also extend the given analogy to the sum of more than two fractions as well.

Hope this helps.

Approved by eNotes Editorial Team