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# Percentage

Mathematics

Study Guide

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Percentages
Percent means parts per 100, so it tells you a rao "out of 100". The symbol is %.
Ex: 30% means 30 per 100
You can express a percent as a decimal or as a fracon:
Example: 30% = 30/100 = 0.3
Types of percentage problems
amount = rate * base
1) Finding the amount
Ex: What is 20% of 600?
Rate = 20% = 20/100 = 0.2
Base = 600
Amount = 0.2*600 = 120
Notes:
If the rate is less than 100%, the amount will be less than the base.
If the rate is greater than 100%, the amount will be greater than the base.
If the rate is equal to 50%, the amount will be half of the base.
If the rate is equal to 25%, the amount will be the base divided by 4.
2) Finding the rate
Ex: 120 is what percent of 600?
Base = 600
Amount = 120
Rate = amount/base = 120/600 = 0.2 * 100= 20%
3) Finding the base
Ex: 120 is 20% of what number?
Rate = 20 % = 20/100 = 0.2
Amount = 120
Base = amount/rate = 120/0.2=600

Real world problems involving percentage
1. Calculang Tips
Calculate 15% p on a bill of \$50.00
Rate: 15% = 15/100 = 0.15
Base = \$50.00
Amount = 0.15 * \$50.00 = \$7.50 p
Total payment: \$50.00 + \$7.50 = \$57.50
2. Calculang sales tax
Total amount = item cost + tax
If you buy a car that costs \$ 20,000.00 and the tax is 10 %, what is the total amount of the car?
Item cost = \$ 20,000.00
Tax = 10% of 20,000.00 = 0.10 * 20,000.00 = \$2,000.00
Total amount = \$20,000.00 + \$ 2,000.00 = \$ 22,000.00
3. Discounts and sale prices
In a video store, a DVD that sells for \$15 is marked "10% o;." What is the discount? What is the sale
price of the DVD?
To <nd the discount, mulply the rate by the original price.
Rate: 10% = 10/100 = 0.1
Discount = 0.1 * \$15.00 = \$1.50
To <nd the sale price, subtract the discount from original price.
Sale price = \$15.00 - \$ 1.50 = \$ 13.50

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PercentagesPercent means parts per 100, so it tells you a ratio "out of 100". The symbol is %.Ex: 30% means 30 per 100You can express a percent as a decimal or as a fraction:Example: 30% = 30/100 = 0.3Types of percentage problemsamount = rate * base1) Finding the amountEx: What is 20% of 600?Rate = 20% = 20/100 = 0.2Base = 600Amount = 0.2*600 = 120Notes:If the rate is less than 100%, the amount will be less than the base.If the rate is greater than 100%, the amount will be greater than the base.If the rate is equal to 50%, the amount will be half of the base.If the rate is equa ...
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