Question

How do you write `3 1/2` as a percent?

Answer 1

`3 1/2=350%`

Explanation:

`color(red)("Shortcut approach")`

1 is the same as 100%. So `1/2` is the same as 50% and 3 is the same as 300%

so `3+1/2 -= 300%+50% = 350%`

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`color(red)("First principle method - takes longer to explain than to do.")`

`color(blue)("First convert to an improper fraction")`

write as `3+1/2`

Multiply by 1 and you do not change the value but 1 comes in many forms. So you can change the way a number looks without changing what it is 'worth'.

write as `" "color(green)([3color(red)(xx1)]+1/2`

`" "color(green)([3color(red)(xx2/2)]+1/2`

`" "6/2" "+1/2" " =" " 7/2`

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`color(blue)("Converting to percentage")`

We need `" "("some number")/100`

`("some number")/100 -=7/2`

Change the 2 into 100. For multiply or divide what we do to the bottom we also do to the top.

Not that `-=` means 'equivalent to'

`("some number")/100 -=7/2 -=(7xx50)/(2xx50) =350/100`
.....................................................................................................

Note that % is a unit of measurement and is worth `1/100`
So we have:

`" "color(blue)(bar(ul(|color(white)((2^2)/(2^2))3 1/2 =350/100-= 350%" "|)))`