What is 16 2/3% as a fraction?

##1/6##

##color(blue)("I have given an 'over the top' explanation so that")## ##color(blue)("you see where everything comes from. Also")## ##color(blue)("introducing you to some useful methods.")##

Percentage is parts of 100. An example: 2% is ##2/100##

So we need to convert your ##16 2/3% " "##into parts of 100 Write ##16 2/3## as ##16 + 2/3##

Change into fractions of 100 parts

##16/100 +(2/3)/100##

But ##(2/3)/100 = 2/3 times 1/100##

Now we have ##16/100 + (2 times 1)/(3 times 100)##

##16/100 + 2/300##

Before we can add these directly we need to make the bottom numbers the same (denominators)

Need to change the 100 in ##16/100## into 300.

Multiply by 1 but in the form of ##3/3##

##(16 times 3)/(100 times 3 ) + 2/300##

##=48/300 + 2/300 = 50 /300##

Simplifying gives:

##=(50 divide 10)/(300 divide 10) =5/30##

##=(5 divide 5)/(30 divide 5) = 1/6 ##