Math - Percentages
Discount
A discount results in a price reduction. New price = original price - discount. Eg. 20% off $70. $70 - (0.20 x 70) = 70 - 14 = $56
Markup
A markup results in a price increase. New price = original price + markup. Eg. $20 marked up by 70%. (100 + 70)% of 20= 170% of 20 = 1.7 x 20 = 34
Percentage increase
Add the percentage to 100, and then convert the percentage (>100%) to a decimal. Then multiply the decimal by the initial value. Eg. Increase 850 by 6.5%. (100 + 6.5)% of 850 = 106.5% x 850 = 1.065 x 850 = 905.25
Percentage Change
Calculate difference between initial and final values, then divide the difference by initial value and multiply by 100%. i.e. Percentage change = change/original value x 100%. Eg. Find the percentage increase in the value of a house valued at $200 000 in January 1996 and at $324 000 in January 2003. Increased value = $324 000 - $200 000 = $124 000. Percentage increase = 124 000/200 000 x 100% = 62% increase.
Fractional Percentage to Fractions
Convert to an improper fraction, and multiply fraction denominator by 100 to get denominator, then simplify. Eg. 6 1/4% = 25/4% = 25/4 divided by 100 = 25/4 x 1/100 = 25/400 = 1/16
Percentage decrease
Minus the percentage from 100, and then convert the percentage (<100%) to a decimal. Then multiply the decimal by the initial value. Eg. Decrease 750 by 9.5%. (100 - 9.5)% of 750 = 0.905 x 750 = 678.75
Discount and Markup
Most items that you buy have a retail price. If the price is reduced it is said to be discounted. If the price is increased it is said to be marked up. The amount of discount or markup is usually stated as a percentage.
Decimal to Percentage
Multiply decimal by 100 by moving the decimal point TWO places to the RIGHT. Eg. 0.36 x 100 = 36%
Fraction to Percentage
Multiply the fraction by 100/1, then simplify.
Percentage to Fractions
Put percentage value over 100, and simplify the fraction. Eg 25% = 25/100 = 1/4
Profit/Loss
Selling price - cost price
Expressing one quantity as a percentage of another
Set up as a fraction, and then multiply by 100/1. Then simplify. Eg. What percentage is a score of 22 out of 50? 22/50 x 100/2 = 2200/100 = 44/1
Cost Price
The price the business buys an item for.
Selling Price
The price the consumer buys an item for.
Percentage to Decimal
Write decimal as a fraction over 100, and then convert to a decimal by moving the decimal point TWO places to the LEFT. Eg. 45% = 45/100 (45 divided by 100) = 0.45
Finding a percentage of a quantity
Write percentage in decimal form, then multiply by the initial value. Eg. Find 40% of 250 mL. 0.40 x 250 = 100 mL