# What Does Percentage Mean?

Percentages are one of the most commonly used mathematical tools in our daily lives. Whenever you are out shopping and there is a sale, or you borrow money for a car or an apartment, you use percentages. Pay close attention, when you learn about percentages.

Rule

Percent means hundredth, such that

 $\text{%}=\frac{1}{100}$

When you write percentages, you can easily change the percentage symbol $\text{%}$ with the fraction $\frac{1}{100}$. This makes the mathematics much simpler when you don’t have a calculator.

You’ll calculate percentages to find out how large of a share you have of something. If you have a hundred dollar bill that you want to share with four people, it is easy to see that $\frac{100}{4}=25$ and each person gets \$$25$.

Rule

Percent means hundredths, such that

 $50\phantom{\rule{0.17em}{0ex}}\text{%}=\text{HALF}$

But what if you share $\text{}20\phantom{\rule{0.17em}{0ex}}000\phantom{\rule{0.17em}{0ex}}000$ with three people, and the money isn’t to be shared equally. Say Thomas receives $\frac{3}{10}$, Alex receives $\frac{6}{25}$, and Victoria receives $\frac{23}{50}$. It is much easier to use percentages. You can say that Thomas gets $30\phantom{\rule{0.17em}{0ex}}\text{%}$, Alex gets $24\phantom{\rule{0.17em}{0ex}}\text{%}$, and Victoria gets $46\phantom{\rule{0.17em}{0ex}}\text{%}$.

The calculation of percentages isn’t here to be an annoyance. But much like many other things in mathematics, it is here to make life easier. Throughout your life, you will find great joy in the fact that you know percentages, so make sure you spend enough time to truly understand it.

Rule

Percent means hundredth, such that

Here are a couple of important expressions:

• These are the relations between percentages and decimal numbers:

 $0=0\phantom{\rule{0.17em}{0ex}}\text{%},\phantom{\rule{1em}{0ex}}0.5=50\phantom{\rule{0.17em}{0ex}}\text{%},\phantom{\rule{1em}{0ex}}1=100\phantom{\rule{0.17em}{0ex}}\text{%}$

 $0=0\phantom{\rule{0.17em}{0ex}}\text{%}\phantom{\rule{2em}{0ex}}0.5=50\phantom{\rule{0.17em}{0ex}}\text{%}\phantom{\rule{2em}{0ex}}1=100\phantom{\rule{0.17em}{0ex}}\text{%}$

• $0$ % is none of it since

 $0\phantom{\rule{0.17em}{0ex}}\text{%}=0\cdot \frac{1}{100}=0$
• $50$ % is half of it since

$\begin{array}{llll}\hfill 50\phantom{\rule{0.17em}{0ex}}\text{%}& =50\cdot \frac{1}{100}=\frac{50}{100}=\frac{50:50}{100:50}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =\frac{1}{2}=0.5\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\end{array}$

 $50\phantom{\rule{0.17em}{0ex}}\text{%}=50\cdot \frac{1}{100}=\frac{50}{100}=\frac{50:50}{100:50}=\frac{1}{2}=0.5$

• $100$ % is all of it since

 $100\phantom{\rule{0.17em}{0ex}}\text{%}=100\cdot \frac{1}{100}=\frac{100}{100}=1$

Example 1

How much is $\text{}50\text{}\phantom{\rule{0.17em}{0ex}}\text{%}$ of 250?

$\begin{array}{llll}\hfill 250\cdot 50\phantom{\rule{0.17em}{0ex}}\text{%}& =250\cdot \frac{50}{100}=250\cdot \frac{1}{2}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =\frac{250}{2}=125\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\end{array}$

 $250\cdot 50\phantom{\rule{0.17em}{0ex}}\text{%}=250\cdot \frac{50}{100}=250\cdot \frac{1}{2}=\frac{250}{2}=125$

Remember that finding $50$ % of something is the same as dividing it by $2$.

Example 2

How much is $\text{}100\text{}\phantom{\rule{0.17em}{0ex}}\text{%}$ of 400?

 $400\cdot 100\phantom{\rule{0.17em}{0ex}}\text{%}=400\cdot 1=400$

Remember that finding $100$ % of something is the same as keeping the number unchanged.

Example 3

How much is $\text{}0\text{}\phantom{\rule{0.17em}{0ex}}\text{%}$ of 1250?

 $1250\cdot 0\phantom{\rule{0.17em}{0ex}}\text{%}=1250\cdot 0=0$

Remember that finding $0$ % of something is the same as finding $0$ of it.