Question

What is `16 2/3%` as a fraction?

Answer 1

`1/6`

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`color(blue)("introducing you to some useful methods.")`

Explanation:

Percentage is parts of 100.

Note that the % sign is like units of measurement. Its value to be considered as: `1/100`

An example: 2% is the same as `2xx1/100 = 2/100`

So the `16 2/3% " "`is the same as `" "16 2/3xx1/100`

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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`

Answer 2

Alternative presentation of same idea

`1/6`

Explanation:

Note that `16 2/3` is the same as `color(white)("dd")16color(white)("d.d")+color(white)("dd")2/3`

Also: `3xx16 2/3` is the same as `[3xx16]+[3xx2/3] = 48+2=50`

Multiply by 1 and you do not change the value. However, 1 comes in many ways.

`color(green)(16 2/3% =color(white)("d")[16/100]color(white)("dd")+color(white)("dd")[(2/3)/100]`

`color(white)("ddddd")color(green)(->[16/100color(red)(xx1)]+[(2/3)/100color(red)(xx1)]`

`color(white)("ddddd")color(green)(->[16/100color(red)(xx3/3)]+[(2/3)/100color(red)(xx3/3)]`

`color(white)("ddddd")color(green)(->color(white)("dd")[48/300]color(white)("dd")+color(white)("dd")[2/300])`

`color(white)("dddddddddd")color(green)(->color(white)("d")(50-:50)/(300-:50)=1/6)`

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Answer 3

`1/6`

Explanation:

`%` means 'out of 100'

So `29%` means `29/100`

Sometimes the fraction can be simplified:

`35% =35/100 = 7/20`

In this case we have a mixed number as a percent.

Change it into an improper fraction:

`16 2/3% = 50/3%`

Write it in the same way as before: `(50/3)/100`

This actually means: `50/3 div 100/1`

`= 50/3 xx1/100" "larr` multiply by the reciprocal

Simplify: `cancel50/3 xx 1/cancel100^2`

`=1/6`

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You can also use the short cut rule:

`(a/b)/(c/d) = (axxd)/(bxxc) = (ad)/(bc)`

`(50/3)/100 = (50/3)/(100/1)`

`=(50xx1)/(100xx3)`

`=1/2 xx 1/3`

`= 1/6`