What is #3/8 + 5/12 + 1/15#?

Question

1598 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-05-05T06:19:22

#3/8 + 5/12 + 1/15 =103/120#

To add fractions, you need to first make sure they have the same denominator.

In our example, the least common multiple (LCM) of #8#, #12# and #15# makes a good common denominator allowing us to add all three in one go.

First let's express each of #8#, #12# and #15# as products of prime factors:

#8 = 2 xx 2 xx 2#

#12 = 2 xx 2 xx 3#

#15 = 3 xx 5#

So the LCM, which is the simplest number containing all these factors in at least these multiplicities is:

#2 xx 2 xx 2 xx 3 xx 5 = 120#

So now we can write:

#3/8 + 5/12 + 1/15#

#=(3 xx 15)/(8 xx 15) + (5 xx 10)/(12 xx 10) + (1 xx 8)/(15 xx 8)#

#=45/120+50/120+8/120#

#=(45+50+8)/120#

#=103/120#

The numbers #103# and #120# have no common factor, so this cannot be simplified. In fact #103# is prime.