How do you evaluate #\frac { 1} { 2} + \frac { 2} { 5} + \frac { 2} { 25}#?

1 Answer
Dan Kemp
Jun 10, 2017

#49/50#

Explanation:

#1/2 + 2/5 + 2/25#

to add or subtract fractions, we need to first get a common denominator.

We find the common denominator by finding the least common multiple of each of the denominators, and then do the same to the numerators (click the link to find out how to do this).

The least common multiple of #2, 5 " and " 25 " is " color(lime)(50)#

#2 xx 25 = 50#
#5 xx 10 = 50#
#25 xx 2 = 50#

Now we can do the same to the numerators.

#1/2 = x/50#

#2/5 = y/50#

#2/25 = z/50#

#(1 xx a = x)/(2 xx a = 50)#

#(2 xx b = y)/(5 xx b = 50)#

#(2 xx c = z)/(25 xx c = 50)#

#(1 xx 25 = x)/(2 xx 25 = 50)#

#(2 xx 10 = y)/(5 xx 10 = 50)#

#(2 xx 2 = z)/(25 xx 2 = 50)#

#1 xx 25 = 25#

#2 xx 10 = 20#

#2 xx 2 = 4#

#1/2 = 25/50#

#2/5 = 20/50#

#2/25 = 4/50#

Now we can do the equation

#1/2 + 2/5 + 2/25#

#25/50 + 20/50 + 4/50#

#45/50 + 4/50#

#color(blue)(49/50#

Because we can not simplify the fraction any further, this is our final answer.

Hope this helps :)

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