Percentage
CraigsMaths
Mathematics Teaching for Learning
Number, Stage 9, Standard 3
July 14th, 2008 by Craig Rose
Permalink: http://www.craigsmaths.com/number/percentage/
This lesson covers:
- Definition of percentage with reference to common fractions.
- Explanation of percentage notation.
- Exploring where percentages are used.
- Converting percentages to fractions and decimals.
- Converting fractions and decimals to percentages.
What are percentages?
50 percent
This diagram shows 100 squares. 
of the squares are shaded. We can also say that 
squares are shaded. Another way to say this is “50 percent of the squares are shaded”.
50 percent
This diagram also has of the squares shaded. squares are shaded, so therefore we can still say “50 percent of the squares are shaded”. It doesn’t matter which squares are shaded, just the size of the proportion of the whole.
50 percent
This diagram also has of the squares shaded. This time it’s 
are shaded. But it doesn’t matter how big the whole is. If we shade of the squares it is still “50 percent of the squares are shaded”.
Rule: A percentage is a portion of a quantity expressed as the number of parts if each part were 100th of the whole.
Excercise resources:
Set of simple fractions
Do the following with the simple fractions, thier decimal equivalents and their percentage equivalents :
- Identify the percentage, decimal equivalent and fraction of a numbered and shaded grid.
- Shade the correct portion of a numbered grid given a decimal, fraction or percentage.
- Identify the percentage, decimal equivalent and fraction of a unumbered and shaded grid.
- Shade the correct portion of a unnumbered grid given a decimal, fraction or percentage.
What is the symbol for percent?
This is the shorthand symbol we use to write percentages. It is called the “percent sign” and is simply used to replace the word “percent”. For example we can write “50 percent” as “50%”.
Hint: Look at the percent sign. You can see two small circles or “0″’s . There are two “0″’s in 100 as well. Use this as a reminder that you are looking for the number of parts in 100.
Hint: Per”cent”. There are 100 cents in 1 dollar. The “cent” is another reminder that we are looking for the number of parts in 100.
Where are percentages used?
Discuss the different places that percentages are used. This should extend the concept beyond the 100×100 grid to real life objects and quantities.
Exercise resources:
- Identify the percentage and fraction of a portion of shapes.
- Identify the percentage and fraction of a portion of a group of objects.
- Calculate the price given a discount.
- Calculate the GST given a price.
Rule: A percentage is used when we want to calculate the size of a portion of a quantity.
Converting between percentages, fractions and decimals
Fractions to percent:
Using a calculator
A fraction can be expressed as a division. To convert from fractions to percent we simply do the division and then multiply the answer by 100.
Step 1: Divide the denominator into the numerator.
Step 2: Multiply by 100.
Step 3: Write the answer with the % sign.
Exercise resources
- Calculate the percentages for the set of simple fractions using a calculator.
By hand
Remember that a percentage is the number of parts out of 100. A fraction is the number of parts out of the denominator. If the denominator were 100 then the numerator would be the percentage.
Step 1: Think: “What number must we multiply the denominator by to get 100?”
Step 2: Multiply the numerator by that number.
Step 3: Write the answer with the % sign.
Exercise resources
- Find the number that is needed to multiply each of the numerators in the set of simple fractions to get 100.
- Calculate the percentages for the set of simple fractions by hand. Check these against the calculator results.
Hint: Remember to write your answer with the % sign following it.
