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How do you simplify # 1/3+1/2+1/5#?

Answer 1

Eva Abramson

#=31/30#

#1/3+1/2+1/5# #=(10+15+6)/30# #=31/30#

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Answer 2

Genesis Allen

In order to add fractions, you need to get the bottom numbers to equal in order to have common denominators.

The least common multiple of #3#, #2#, and #5# is #30#, since #3xx2xx5 = 30#, and #3#, #2#, and #5# are all prime numbers.

Therefore, you just need to get #30# in the denominators by multiplying by unit fractions. i.e. #x/x = y/y = z/z = 1#.

#1/3*stackrel(= 1)overbrace(10/10) + 1/2*stackrel(= 1)overbrace(15/15) + 1/5*stackrel(= 1)overbrace(6/6)#

#= 10/30 + 15/30 + 6/30#

#= color(blue)(31/30)#

Or, if you're a decimal person...

#1/3 + 1/2 + 1/5#

#= 0.bar(33) + 0.5 + 0.2#

#= 1.0bar(33)#.

Since #0.0bar(33) = (0.bar(33))/10 = 1/3*1/10 = 1/30#,

#1.0bar(33) = 1/30 + 30/30 = color(blue)(31/30)#.

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Answer 3

Eli Assouline

[ \frac{31}{30} ]

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.