Understanding Percentages: Calculations and Changes

Study Notes

To express a number as a %, multiply by 100.
To express a % as a fraction or decimal, divide by 100.
A % of a number can be found using multiplication.
Example: 25% of $26 = 0.25 x $26 = $6.50
One quantity can be expressed as a % of another quantity by writing as a fraction using the same units and converting it to a %.
To find an original amount, use the unitary method or use division.
Example: 3% of an amount is $36.
Using the unitary method: 1% of the amount is $36 3 = $12
100% of the amount is $12 × 100 = $1200
Using division: 3% of the amount is $36
0.03 x amount = $36
amount = $36 ÷ 0.03 = $1200

To increase an amount by a given %, multiply by 100% plus the given %.
Example: to increase by 30%, multiply by 100% + 30% = 130% = 1.3
To decrease an amount by a given %, multiply by 100% minus the given %.
Example: to decrease by 25 %, multiply by 100% - 25% = 75% = 0.75
To find a % change or absolute % difference use Percentage change= change / original amount × 100%
Percentage error is calculated in the same way: %Error = difference between measured value / theoretical value× 100%

Profit is the amount of money made on a sale.
If the profit is negative the result is a loss.
Profit = selling price - cost price
Mark-up is the amount added to the cost price to produce the selling price.
Selling price = cost price + mark-up
The % of profit or loss can be found by dividing the profit or loss by the cost price and multiplying by 100. %Profit or loss = profit or loss / cost price × 100%
Discount is the amount by which an item is marked down.
New price = original price - discount
Discount = %discount × original price

To calculate simple interest: I = P x r /100 x t or I= Prt/100
I is the amount of simple interest (in $ )
P is the principal amount; the money invested, borrowed or loaned (in $ )
r % is the rate per unit time; usually per annum (p.a.), which means per year
t is the period of time, expressed in the stated units, usually years.
When using simple interest, the principal amount is constant and remains unchanged from one period to the next.
The total amount ($A) equals the principal plus interest: A = P + I