Question

Lisa got 14 out of 30 questions correct on her quiz. What is this as a percent?

Answer 1

`46 2/3%`

Explanation:

`14/30`

Multiply the numerator and denominator by `3.bar3` so that the denominator is equal to `100`.

`(14times3.bar3)/(30times3.bar3)`

`(46.bar6)/100`

`46 2/3%`

Or just use a calculator to divide.

Answer 2

`46.666666 = 46 2/3%`
But as this is a test results, it would probably be given as 47% by rounding to the nearest whole number.

Explanation:

Fractions, decimals and percentages are all different way of expressing the same relationship between two numbers. They are interchangeable.

Just dividing will give 0.466666666...

But the first 2 decimal places represent hundredths which indicate percent.

So this value could also be written as `(46.66666...)/100`

From this we see that it is 46.6666 %

However, recurring decimals in percentages (especially thirds and sixths) are better written in fraction form.

`1/3 = 0.333333.... and 2/3 = 0.666666...`

So the best way of giving an exact answer without rounding off is as `46 2/3%`

Or multiply by 100% (100% = 1,) so we are not changing the value.

`14/30 xx 100%`

= `46.666666 = 46 2/3%`
However as this is for a test, a whole number answer would probably be given as 47%

Answer 3

`46 2 /3%`

Explanation:

To construct a percentage we require to form a fraction and multiply it by 100.

The required fraction is found as follows.

`color(red)("number of correct questions")/color(blue)("total number of questions")`

`rArrcolor(red)("14")/color(blue)("30")`

To obtain this fraction as a percentage, multiply by 100.%

`rArr14/30xx100/1`

which may be simplified by 'cancelling' the 30 and 100 (dividing both by 10)

Thus `(14)/(cancel(30)^3) xxcancel(100)^(10)/1 %=(14xx10)/(3xx1)=140/3 %`

and `140/3%=46 2/ 3%=46.66...=46.6bar6%`

Answer 4

There are two ways of writing percentage. Suppose we are talking about 25 percent.

The most common way of seeing this is in the format of `25%`

For the purpose of calculations it is convenient to write `25/100`

The word percent can be split into 2 parts

Part 1: 'per' means for each of.

Part 2: 'cent' means 100. Think of centenary,
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Using the principle of the fraction format.

Let the unknown count be `x`

14 out of 30 `-> x` out of 100

Write this as a ratio

`14/30 = x/100`

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
From here we have two options of approach.

Method 1: ( shortcut approach) Multiply both sides by 100 so that you find the value of `x`

Method 2: Treat as a ratio and proportion up so that the denominator of `14/30` becomes 100

The shortcut method really is the same as method 2 but it cuts out some steps

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Method 1")`- Shortcut method

`14/30=x/100" "->" "14/30xx100=x`

`x=(140cancel(0))/(3cancel(0)) =46.6bar6 -> 46 2/3`
So `x/100 -> color(magenta)((46 2/3)/(100))`

To write `color(magenta)(ul("just the denominator as a percentage"))` we write `46 2/3%`

`color(red)("The % means that this number of "46 2/3 " is the numerator of a")` `color(red)("fraction that has a denominator of 100")`
,~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

`color(blue)("Method 2") larr " solve as a ratio"`

`14/30` To change 30 into 100 first divide by 30 then multiply by 100. In other words; multiply by `100/30`

For multiply or divide, what we do to the bottom we do to the top!

`(14xx100/30)/(30xx100/30) =color(magenta)( (46 2/3)/100" "larr" The same as the shortcut")`

As a percentage we write it as `46 2/3 %`