How do you simplify #1/4 + 1/5#?

2 Answers
May 6, 2018

Answer:

#:. 9/20#

Explanation:

To simplify #1/4 + 1/5#, we need to make both of the fractions as the same base.

#=> (1)/4 + 1/5#

#=> 5/20 + 4/20#

#:. 9/20#

May 6, 2018

Answer:

Rewrite each fraction so they have the same denominator.

Explanation:

Least Common Multiple (LCM) Route:

Multiples of 4 are 4, 8, 12, 16, 20, 24, 28
Multiples of 5 are 5, 10 ,15, 20, 25, 30
The Smallest Multiple that 4 and 5 have in common is 20.

Change #1/4# to a denominator of 20 by multiplying top and bottom by 5: #1/4 * 5/5 = 5/20#.

Change #1/5# to a denominator of 20 by multiplying top and bottom by 4: #1/5 * 4/4 = 4/20#.

Now Add the 2 new fractions together and simplify if possible:
#5/20 + 4/20 = 9/20#

Cross Multiply Route:
#a/c + b/d = (ad + bc)/(cd)#

#1/4 + 1/5 = (1*5 + 1*4)/(4*5) = (5 + 4)/20 = 9/20#

Remember to always Simplify if possible.