Calculating Percentages

Students in House Colours
Image Source:

In this lesson we are Calculating One Amount of Another, as a Percentage.

In the above picture, we have a number of student leaders dressed in their House Colours.

What percentage of the students are in Green House ?

Checking the photo, six out of the 16 students are wearing Green.

The Fraction of students wearing Green is therefore 6 out of 16 or 6/16.

We then Multiply this fraction by 100/1 to convert it into a percentage.

Eg. 6/16 x 100/1 = 600 / 16 (Divide by 4)

= 150 / 4 = (Divide by 2) = 75 / 2 = 37.5 %

So 37.5% of the students in the photo belong to Green House.

Note that we could have first simplified 6/16 by dividing by 2 to make 3 /8 .

3/8 is then a simpler fraction to do the mathematics with.

Eg. 3/8 x 100/1 = 300 / 8 (Divide by 2)

= 150 / 4 = (Divide by 2) = 75 / 2 = 37.5 %


In Red House there are also six student leaders.

Students in Red House
Image Source:

What is the percentage of boys compared to girls in Red House ?

In the Red House photo, there are 2 boys compared to 4 girls.

The Ratio or Fraction of boys compared to girls is therefore 2/4 which simplifies to 1/2.

We can now Multiply this fraction by 100/1 to convert it into a Percentage:

1/2 x 100/1 = 1/2 of 100 = 50% .

Eg. 2 / 4 x 100/1 = 200 / 4 = 50 %

There is 50%, or half as many, boys as girls in Red House.


Comparing Items in Different Units

When we compare items and calculate percents, it is important that the items are both in the same units.

For example let’s compare how far the 800m running race in the Olympics is compared to the Marathon.

Steve Monagetti Marathon on Sydney Bridge
Image Source:

The Marathon is a long-distance running event with an official distance of 42.195 kilometres (26 miles and 385 yards), that is usually run as a road race.

The event was instituted in commemoration of the fabled run of the Greek soldier Pheidippides, a messenger who ran from the Battle of Marathon to Athens.

So we have:

800m Running Race compared to

42.195 km Marathon.

Some people will immediately do the calculation as follows:

800 / 42.195 X 100/1 = 1896 %

This Percentage answer is way too big and makes it appear that an 800m race is much bigger than a 42 km Marathon!

We need to convert units before working out the Percentage.

Calculating Percentages
Image Copyright 2012 by Passy’s World

For 800m and 42.195km the smaller unit is meters “m”, because a meter is much shorter than a whole km.

Each km = 1000m, and so we multiply the km by 1000

Eg. 42.195 x 1000 = 42 195 m.

So we work out our Percentage as follows:

% = 800 / 42195 X 100/1

% = 1.8959592

% = 2 %

Since 2% = 2/100 = one fiftieth, this means we would need to do fifty 800m runs to reach the distance of the Marathon.

The Marathon is a LONG race !


How to Calculate Percentage

In this lesson we are Calculating One Amount of Another, as a Percentage.

This is a three step process.

Calculating Percentage
Image Copyright 2012 by Passy’s World


Calculating Percentages Examples

The following examples show how we can calculate percentages of one amount expressed as part of another amount.

Calculating Percentages Examples
Image Copyright 2012 by Passy’s World


Videos About Percentage Calculations

This quick intoductory video which shows how to do a basic two numbers into a Percent question.


Here is Part 1 of a two part video all about calculating percentage values of two nukmbers.


Here is Part 2 of the previous video which deals with Improper Fractions creating Percentage answers that are bigger than 100.


This next video shows an alternative way of working out the Percentage, by using Proportion and Cross Multiplying.


Related Items

Introduction to Percentages
Converting Percentages to Fractions
Converting Percentages to Decimals
Converting Fractions to Percentages
Converting Decimals to Percentages
Converting Percentages (All Types)
Interesting Percentages
Percentages and Weight Training
Decimals and Percentages Games


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  1. Pingback: Percentage Discounts | Passy's World of Mathematics

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