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

4 Answers
Jul 12, 2016

#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.

Jul 12, 2016

#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%

Jul 12, 2016

#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%#

Jul 12, 2016

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 %#