# What percent of 15,000 is 18,000?

Oct 11, 2017

120%

#### Explanation:

x%" of "15000=18000

$\implies \frac{x}{1 \cancel{00}} \times 150 \cancel{00} = 18000$

$\implies 150 x = 18000$

Dividing both sides by 150,

=>(cancel(150)x)/color(red)((cancel(150)))=18000/color(red)(150

$\implies x = \frac{1800}{15} = 120$

Therefore, 120% of $15000$ is $18000$.

Oct 14, 2017

Quick solution plus some teaching.

120%

#### Explanation:

Percentage is basically just a fraction. It is however a special fraction in that the denominator is always fixed at 100.

Thing is; there is a convention to use the symbol %.
This may be considered a ul("bit"color(red)(" like")) units of measurement but one that is worth $\frac{1}{100}$

This is similar ( just using 3 as it happened to come to mind)

$3 \text{ centimetres}$

centi is $\frac{1}{100} {\textcolor{w h i t e}{}}^{\text{th}}$ so 3 cm $\to 3 \times \frac{1}{100} \times 1 \text{ metre}$

$\textcolor{w h i t e}{\text{dddddddddd}}$Thus 3% $\to 3 \times \frac{1}{100} \times \text{Something}$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

$\textcolor{w h i t e}{\text{dddddddddddd")color(blue)(ul(bar(|color(white)(2/2)"Quick solution } |}$

The wording 'percent of' make the 15000 the basis for comparison. So if we express this as a fraction we have:

$\frac{18000}{15000}$

(18cancel(000))/(15cancel(000)

$\textcolor{b r o w n}{\text{Shortcut method}}$

$\textcolor{w h i t e}{\text{d}} \frac{18}{15} \times 100$ and stick a % on the end ->120%

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

$\textcolor{b r o w n}{\text{ Why do we stick a % on the end?}}$

Taking a step back we have: $\frac{18}{15}$

Fraction wise we need to change this to $\frac{\textcolor{w h i t e}{\text{d")("something}}}{100}$

Look at the denominator of 15 from $\frac{18}{15}$. If we do this to it $\text{ } 15 \times \frac{100}{15}$ we get 100. What we do to the bottom for multiply or divide we also do to the top.

Now look at the numerator of 18. We do this: $\textcolor{g r e e n}{\text{ } 18 \times \frac{100}{15}}$ that is the shortcut bit.

However, all of this is over the $\textcolor{b l u e}{\text{final denominator of 100}}$. So lets include this giving:

$\textcolor{g r e e n}{18 \times \frac{100}{15}} \textcolor{b l u e}{\times \frac{1}{100}}$

but another way of writing $\frac{1}{100}$ is % so we end up with 18/15xx100xx%

But the same way in algebra we do not write (example) $3 \times x$ but $3 x$ then in the same way we do not write the cross for multiply in front of the %

THUS WE HAVE

(18/15xx100)%-> 120%

which is another way of saying $120 \times \frac{1}{100}$