# What does 1/20 + 2/5 equal?

The solution to the problem is 9/20. To add the two fractions, you first need to find the greatest common factor of 5 and 20, which will put them in like terms and make adding them easier. The question involves the addition of two fractions, 1/20 and 2/5, i.e.,

1/20 + 2/5

For two fractions with the same denominator, addition is easy. For example,

a/b + c/b

is reduced to only the sum of the numerators divided by the common denominator.

That is, a/b + c/b = (a+c)/b

In this case, the denominators 20 and 5 are different numbers, so we have to calculate their least common multiplier (LCM).

One way to do that is: LCM (20,5) = (20 x 5)/ gcf(20,5)

Where GCF(20,5) is the greatest common factor between 20 and 5. Now, we can also write 20 as the product of 5, 2 and 2.

That is, 20 = 5 x 2 x 2, and 5 can be written as 5 = 5 x 1

Comparing the factors of 20 and 5, the gcf is 5.

Thus, LCM(20,5) = 20x5 / 5 = 20

Now for adding the fraction, a/b and c/d, with an LCM of m, we have

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

Here, a = 1, b = 20, c = 2 and d = 5 and LCM (b,d)= LCM (20, 5) = 20

Thus, 1/20 + 2/5 = [(1 x 20/20) + (2x 20/5)]/20 = (1 + 8)/20

= 9/20

since, 9 and 20 do not have any common factor, this is the answer in fractions.

Approved by eNotes Editorial Team