What is a percentage?

As the image suggests a percentage is just a fraction that is out of 100

For example: 25% is the same as 25/100

Percentages OF an amount

In Maths the word 'OF' means MULTIPLY

To calculate a percentage of an amount it is first best to convert the percentage back into a decimal (divide by 100) before multiplying the amount by the decimal.

Example:

Find 32% of 6400

32 ÷ 100 = 0.32

0.32 × 6400 = 2048

Percentage Increases and Decreases

Increasing or decreasing by a percentage can be done in two steps

Find that percentage of the original amount
Add the answer onto the original amount if increasing, subtracting from the original amount if decreasing

Percentage Decrease Example

Decrease 72 by 36%

Step 1 (Find 36% of 72):

0.36 × 72 = 25.92

Step 2 (Add the 12% onto the original amount):

72 - 25.92 = 46.08

Percentage Increase Example

Increase 80 by 12%

Step 1 (Find 12% of 80):

0.12 × 80 = 9.6

Step 2 (Add the 12% onto the original amount):

80 + 9.6 = 89.6

One-Step (Calculator) Method

This calculation can be completed in one step.

To increase by a percentage you are adding the percentage onto the original amount (100%). Therefore if we were to increase by 25% the percentage would be 125% of the original (1.25 as a decimal)

To decrease by a percentage you are subtracting the percentage from the original amount (100%). Therefore if we were to decrease by 25% the percentage would be 100%-25% = 75% remaining (0.75 as a decimal)

Percentage Increase Example

Increase 80 by 12%

To increase by 12% we need to add it onto the original amount (100%). Therefore we need to find 112% of 80

1.12 × 80 = 89.6

Percentage Decrease Example

Decrease 72 by 36%

To decrease by 36% we need to subtract it from he original amount (100%).

100% - 36% = 64%

Therefore we need to find 64% of 72

0.64× 72 =46.08

GST

GST stand for Goods and Services Tax and is a tax that is added onto many products in New Zealand.

Some times prices are GST inclusive (has GST added on)

Other times prices are GST exclusive (GST has not yet been added)

NZ's GST is 15%

To add GST multiply by 1.15

To remove GST divide by 1.15

Percentage Change

To find the percentage change the change from the original amount needs to be found. This amount is then put as a fraction of the original amount to find the change.

Example 1 (Increase):

The weekly rent for a house went from $400 per week to $460 per week. What is the percentage change?

The percentage change is a 15% Increase

Example 2 (Decrease):

The number of people that went to a fair on Saturday was 1450 people, but on Sunday it was raining and only 850 people attended. What is the percentage change?

Reverse Percentages

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