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Tutor: Kat



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 100100". So, 35%35\%​ literally means "3535​ out of 100100​". Another way of writing this is 35100\frac{35}{100}​, or 0.350.35​.

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%35\% of 160160?

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

35%35\%of 160160 =35100×160= \frac{35}{100}\times160

Put this into a calculator:


35%35\% of 160160 is 56\underline{56}.

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

35%35\% of ​​160=35100×160 =35100×1601 =5600100=56160= \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 6060​ questions. If I answered 5454 questions correctly, what percentage of questions did I get correct?

First, find the relevant fraction:

I answered 5454 questions correct out of 6060​ questions in total. 

So, the relevant fraction is 5460\frac{54}{60}.

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


Now, convert the decimal to a percentage:


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

Note: In this example, you also could have simplified the fraction to 910\frac{9}{10}.  Using your common conversions, you should know that 910=90%\frac{9}{10}=90\%.

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FAQs - Frequently Asked Questions

How do you express one number as a percentage of another?

How do you find percentages of a number?

What does the percentage symbol mean?


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