# Percentages (Mathematics Curriculum)

# What Is a Percentage?

A percentage is a part of a whole. It expresses a part of a whole number as parts out of 100.A percentage is written as a number followed by the percentage symbol % (said as "percent"):

This is 20% (said as "20 percent"). It means 20 parts out of 100.

A grid with 100 squares is a useful way of visualizing percentages.

In the grid below, 20 out of 100 squares are colored blue. 20% of the squares are blue.

#### Dictionary Definition

The Merriam-Webster dictionary defines a percentage as "a part of a whole expressed in hundredths."Understanding percentages ( interactive widget)

# Why Do We Use Percentages?

Percentages are useful because they express what proportion a part is out of the whole.Imagine two students who took two different mathematics exams. One student got 10 marks and the other got 20 marks. Who did better?

Our first reaction may be that the student who got 20 marks did better than the student who got 10 marks. But we can't really say because we don't know how many marks were available in each test.

The first student (who got 10) took a test with 50 marks. The second student (who got 20) took a test with 100 marks.

In this case, both students did equally well. They both got 20% of the marks.

20% means getting 20 out of every 100 marks.

- If there were 50 marks, you would have got 10 marks.
- If there were 100 marks, you would have got 20 marks.

# How to Find a Percentage

- A percentage expresses a proportion (or ratio) of one quantity out of another.

Imagine there are 25 students in a class. 15 of these students think mathematics is the best subject (which is the correct answer!).

60% of the class prefer mathematics.

15 ÷ 25 × 100% = 0.6 × 100% = 60%

This is example of expressing one number our of another as a percentage. The answer itself is a percentage. - Finding a percentage can also mean finding the number that is a certain percentage of another number.

Imagine you were told that 60% of a class of 25 students prefered mathematics.

15 students prefer mathematics.

60% ÷ 100% × 25 = 0.6 × 25 = 15

This is example of finding a percentage of a number. The answer itself is a number.

Read more about finding a percentage of a number

# Percentage Changes

A percentage change is a change from one value to another value, expressed as a percentage.An increase from 100 to 120 would be a 20% change:

This is because there is a change of 20 (120 - 100), which is 20% of the original number (100).

Percentage changes are useful because it shows how big a change is in proportion to the orginal number.

Read more about percentage changes

Read more about finding a percentage change

# Converting Percentages

Percentages represent parts of a whole. There are other ways to represent parts of a whole: decimals and fractions.A percentage can be converted to a decimal or a fraction.

Read more about converting percentages

Read more about converting a percentage to a decimal

Read more about converting a percentage to a fraction

##### Curriculum

# Percentages Lessons

Here is a handy list of our percentages lessons. The lessons and tests on these pages are designed to take a beginner through the basics of percentages.# Percentages Basics

Understanding percentagesUnderstanding percentages ( interactive widget)

# Finding Percentages

Expressing one number our of another as a percentageFinding a percentage of a number

# Percentage Changes

Understanding percentage changesFinding percentage changes

# Converting Percentages

Converting percentagesConverting a percentage to a decimal

Converting a percentage to a fraction