How do you evaluate #-\frac { 3} { 4} + \frac { 1} { 12}#?

1 Answer
smendyka
Oct 3, 2017

See a solution process below:

Explanation:

To add or subtract fractions they must have common denominators. We can multiply the fraction on the left by the appropriate form of #1# to give a denominator of #12# without changing the value of the fraction:

#(3/3 xx -3/4) + 1/12 =>#

#(3 xx -3)/(3 xx 4) + 1/12 =>#

#-9/12 + 1/12#

We can now add the numerators over the common denominator:

#(-9 + 1)/12 =>#

#-8/12#

We can now reduce this fraction by factoring the numerator and denominator and cancelling common factors:

#-8/12 =>#

#-(4 xx 2)/(4 xx 3) =>#

#-(color(red)(cancel(color(black)(4))) xx 2)/((color(red)(cancel(color(black)(4))) xx 3) =>#

#-2/3#

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