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

Jul 12, 2016

46 2/3%

#### Explanation:

$\frac{14}{30}$

Multiply the numerator and denominator by $3. \overline{3}$ so that the denominator is equal to $100$.

$\frac{14 \times 3. \overline{3}}{30 \times 3. \overline{3}}$

$\frac{46. \overline{6}}{100}$

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 $\frac{46.66666 \ldots}{100}$

From this we see that it is 46.6666 %

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

$\frac{1}{3} = 0.333333 \ldots . \mathmr{and} \frac{2}{3} = 0.666666 \ldots$

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.

$\textcolor{red}{\text{number of correct questions")/color(blue)("total number of questions}}$

$\Rightarrow \textcolor{red}{\text{14")/color(blue)("30}}$

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

$\Rightarrow \frac{14}{30} \times \frac{100}{1}$

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 $\frac{25}{100}$

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 $\to x$ out of 100

Write this as a ratio

$\frac{14}{30} = \frac{x}{100}$

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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 $\frac{14}{30}$ becomes 100

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

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Method 1}}$- Shortcut method

$\frac{14}{30} = \frac{x}{100} \text{ "->" } \frac{14}{30} \times 100 = x$

$x = \frac{140 \cancel{0}}{3 \cancel{0}} = 46.6 \overline{6} \to 46 \frac{2}{3}$
So $\frac{x}{100} \to \textcolor{m a \ge n t a}{\frac{46 \frac{2}{3}}{100}}$

To write $\textcolor{m a \ge n t a}{\underline{\text{just the denominator as a percentage}}}$ we write 46 2/3%

$\textcolor{red}{\text{The % means that this number of "46 2/3 " is the numerator of a}}$$\textcolor{red}{\text{fraction that has a denominator of 100}}$
,~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

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

$\frac{14}{30}$ To change 30 into 100 first divide by 30 then multiply by 100. In other words; multiply by $\frac{100}{30}$

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

$\frac{14 \times \frac{100}{30}}{30 \times \frac{100}{30}} = \textcolor{m a \ge n t a}{\frac{46 \frac{2}{3}}{100} \text{ "larr" The same as the shortcut}}$

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