Everything to learn better...

Tutor: Kat

# Percentages

## In a nutshell

Percentages are used very often in the real world as they are very easy to interpret and understand. It is important to know how to find one quantity as a percentage of another as well as how to find percentages of a quantity.

### Interpreting percentages

The percent symbol ($\%$​) means "out of $100$". So, $35\%$​ literally means "$35$​ out of $100$​". Another way of writing this is $\frac{35}{100}$​, or $0.35$​.

## Finding percentages of a number

A common problem is to find percentages of a number. To approach these questions, use the fraction interpretation of the percentage symbol. It is also helpful to read the word "of" as "times".

##### Example 1

What is $35\%$ of $160$?

Write the percentage symbol as $\frac{}{100}$ and the "of" as the multiplication symbol:

$35\%$of $160$ $= \frac{35}{100}\times160$

Put this into a calculator:

$\frac{35}{100}\times160=56$​​

$35\%$ of $160$ is $\underline{56}$.

However, if you don't have a calculator you can follow this method:

$35\%$ of ​​$160= \dfrac{35}{100}\times160\\ \ \\= \dfrac{35}{100}\times\dfrac{160}{1}\\ \ \\=\dfrac{5600}{100}=56$​​

## Expressing one number as a percentage of another

You may be asked to compare one number as a percentage of another number. To do this, first write what you want to find as a fraction. Then, convert it to a decimal, and then convert it to a percentage.

##### Example 2

A quiz has $60$​ questions. If I answered $54$ questions correctly, what percentage of questions did I get correct?

First, find the relevant fraction:

I answered $54$ questions correct out of $60$​ questions in total.

So, the relevant fraction is $\frac{54}{60}$.

To convert this to a percentage, first convert it to a decimal:

$\frac{54}{60}=54\div60=0.9$

Now, convert the decimal to a percentage:

$0.9=(0.9\times100)\%=90\%$

I answered $\underline{90\%}$ of questions correctly.

Note: In this example, you also could have simplified the fraction to $\frac{9}{10}$.  Using your common conversions, you should know that $\frac{9}{10}=90\%$.

## FAQs - Frequently Asked Questions

### What does the percentage symbol mean?

Beta

I'm Vulpy, your AI study buddy! Let's study together.