How do you evaluate #\frac { 1} { 2} + \frac { 1} { 4} + \frac { 2} { 3} #?

1 Answer
Tony B
Dec 31, 2016

#17/12 -> 1 5/12#

Explanation:

#color(blue)("A preliminary comment 1")#

A fraction consists of #" "("count")/("size indicator")->("numerator")/("denominator")#

You can not #ul("directly")# add or subtract the counts unless the size indicators are the same.

Example: Note that these numbers are not normally written this way

#3+5=8 -> 3/1+5/1=8/1 larr" size indicators are all 1"#

#color(blue)("A preliminary comment 2")#

Multiply by 1 and you do not change the value. However, 1 comes in many forms. So you can change the way a fraction looks without changing its actual value.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Answering the question")#

#color(green)([1/2color(red)(xx1)]+[1/4color(red)(xx1)]+[2/3color(red)(xx1)]#

#color(green)([1/2color(red)(xx6/6)]+[1/4color(red)(xx3/3)]+[2/3color(red)(xx4/4)]#

#" "6/12" "+" "3/12" "+" "8/12#

#=17/12#

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