How do you add #(- \frac { 1} { 2} + ( - \frac { 1} { 4} ) ) + ( \frac { 1} { 2} + \frac { 1} { 4} )#?

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Answer 1 · 2016-12-21T06:48:56

They are additive inverses. The sum is #0#

There are 2 terms, each requires addition of fractions.

#(-1/2-1/4) + (1/2+1/4)#

You should notice immediately that the values in each term are the same, except the first term has negative signs and the second has positive signs.

These are known as additive inverses and their sum is always #0.#

For example: #" "+3-3 = 0" " -12+12 = 0#

So without any further working we can give the answer as #0#

To show the working would be:

#(-2-1)/4 + (2+1)/4#

#=-3/4 + 3/4#

#=0#