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

Answer 1

#-2#

#-2 1/2+1/2#

First, we convert the mixed fraction into an improper fraction by multiplying the whole number by the denominator, adding the product to the numerator and placing the result on the same denominator.

#2 1/1=>5/2#

Hence:

#-5/2+1/2#

Keeping the minus sign outside, place the two terms inside brackets. The plus sign will change to a minus sign because of this.

#-(5/2-1/2)#

Since the denominator is the same, we simply subtract the numerators.

#-((5-1)/2)#

#-(4/2)#

Since the numerator is completely divisible by the denominator, we reduce the fraction.

#-(2)#

Open the brackets keeping the minus sign.

#-2#

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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.