# working out percentages on paper

• Sep 17th 2010, 09:23 AM
mike2000
working out percentages on paper
Hello i apoligise if this is in the wrong forum but, i was wondering could anyone be kind enough to explain how i would work out the following problem on paper

if i had 70 calls and 24 of those were loan applications, what % of my calls were loan applications?

I think using a calculator i would 24/70=0.34 x100 =34% for my answer.

However how would i do this without a calculator? im not sure how i would work this division out on paper.

• Sep 17th 2010, 09:28 AM
e^(i*pi)
Cancel out factors: $\displaystyle \dfrac{24}{70} = \dfrac{12}{35}$. Since 35ths aren't common then division will be necessary to get the necessary numbers of decimal places.
• Sep 17th 2010, 09:28 AM
Quote:

Originally Posted by mike2000
Hello i apoligise if this is in the wrong forum but, i was wondering could anyone be kind enough to explain how i would work out the following problem on paper

if i had 70 calls and 24 of those were loan applications, what % of my calls were loan applications?

I think using a calculator i would 24/70=0.34 x100 =34% for my answer.

However how would i do this without a calculator? im not sure how i would work this division out on paper.

$\displaystyle \displaystyle\frac{24}{70}=\frac{x}{100}$

where x is the percentage.
Multiply both sides by 100

$\displaystyle \displaystyle\frac{2400}{70}=x=\frac{240}{7}$

Just divide through by 7.
• Sep 17th 2010, 09:31 AM
RHandford
• Sep 17th 2010, 10:13 AM
mike2000
Hiya thanks for the help, could you show how you get those numbers? im sorry im a bit lost as to were you have gotten 2400/70 and 240/7 from

Thank you
• Sep 17th 2010, 11:14 AM
Quote:

Originally Posted by mike2000
Hiya thanks for the help, could you show how you get those numbers? im sorry im a bit lost as to were you have gotten 2400/70 and 240/7 from

Thank you

Sure..

24 out of 70 calls were loan applications, so your fraction is $\displaystyle \frac{loan\ apps}{total\ calls}=\frac{24}{70}$

You want to write this fraction as a percentage.
Percent means "per century" or "per hundred".

For instance, exam results are typically given as a percentage,
which is a fraction.

$\displaystyle 80\%$ means "80 out of 100", so written as a fraction it's $\displaystyle \frac{80}{100}$

We want to express your fraction as "something" out of 100, so we write

$\displaystyle \frac{24}{70}=\frac{x}{100}$

We want x by itself. We can obtain that by multiplying both sides by 100

$\displaystyle 100\frac{24}{70}=100\frac{x}{100}$

$\displaystyle \frac{24(100)}{70}=\frac{100x}{100}$

$\displaystyle \frac{2400}{70}=x$ which can be simplified by writing this as $\displaystyle \frac{10}{10}\ \frac{240}{7}=\frac{240}{7}$