Find #1/6+2/3#?

3 Answers
Sep 7, 2016

#1/6+2/3=5/6#

Explanation:

Least Common Denominator of the two denominators #6# and #3# is #6#

Hence #1/6+2/3#

= #1/6+(2xx2)/(2xx3)#

= #1/6+4/6#

= #5/6#

Very detailed explanation

#5/6#

Explanation:

#color(blue)("Important fact demonstrated by example")#

#color(green)("A fraction consists of:"#

#color(green)(("count")/("size indicator of what you are counting")#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#color(brown)("Consider the example of "2+3=5)#

This may sound obvious but you are adding the counts of 2 and 3.
What is not so obvious is that they are both of the same unit size.

#color(green)("You can not directly add or subtract values unless the unit size is the same")#

Think again about #2+3=5# The unit size is how many of what you are counting it takes to make a whole of something. In this case it takes 1. So if we chose we could write #2+3=5# as #2/1+3/1=5/1# which is not normally done.

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(brown)("Consider the example of "2/4+3/4=5/4)#

The unit size is such that it takes 4 of what you are counting to make a whole. They are all the same unit size so you can directly add the counts of #2+3#.

#color(green)("Adding the counts does not change the unit size.")#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

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

#1/6" and "2/3# are not of the same unit size. So we #color(red)(ul("can not say"))# the count is 1+2=3

So we need to make both unit sizes the same

Multiply by 1 and you do not change the inherent value. However 1 comes in many forms.

multiply #2/3# by 1 but in the form of #1=2/2# giving:

#1/6+(2/3xx1)" "->" "1/6+(2/3xx2/2)#

#1/6+4/6#

We can now directly add the counts: #1+4 = 5#

So we have: #(1+4)/6= 5/6#

Jun 20, 2018

If you cannot spot the lowest common multiple, one method that works every time is to cross multiply

#1/6 + 2/3#

Multiply the first fraction (top and bottom) by 3

Multiply the second fraction (top and bottom) by 6

#[3xx1]/[3xx6] +[6xx2]/[6xx3]#

#3/18 +12/18#

we now have the fractions over the same denominator so simply add the numerators

#15/18#

cancel down by dividing by 3

#5/6#

Sometimes it is longer to do it this way but it works every time and you do not waste time looking for the LCM.