# Percentages (%)

Percent - means?The Word"Percent" comes from the latin?Per Centum. The latin word?Centum?means 100, for example a Century is 100 years.So?50%?means 50 per 100(50% of this box is gray)And?25%?means 25 per 100(25% of this box is gray)Example 1 100% means?all. Calculate 100% of 80.Example 2 50% means?half. Calculate 50% of 80.Example 3 5% means?5/100ths. Calculate 5% of 80.What does 200 % mean?Example 4Calculate 200% of 80Example 5Calculating percent without a calculatorFind 10% of 67Find 10% of 9804Find 10% of 45.21Find 1% of 67Find 1% of 9804Find 1% of 67Find 3% of 2400Find 13% of 2400A?Percent?can also be expressed as a?Decimal?or a?FractionA Half?can be written...??As a percentage:As a decimal:As a fraction:Converting Between Percentage and DecimalTo?convert from percentage to decimal: divide by 100 (and remove the "%" sign).To?convert from decimal to percentage: multiply by 100 (and add a "%" sign).The easiest way to multiply (or divide) by 100 is to?move the decimal point 2 places. Example 6 Convert 0.125 to a percentExample 7 Convert 75% into a decimalExample 8 15% of 200 apples were bad. How many apples were bad??Example 9 if only 10 of the 200 apples were bad, what percent is that??Example 10 A Skateboard is reduced 25% in price in a sale. The old price was $120. Find the new price.Converting Between Fractions and DecimalsThe easiest way to?convert a fraction to a decimal?is to divide the top number by the bottom number (divide the numerator by the denominator in mathematical language)Example 11 Convert?2/5?to a decimalExample 12 Convert 0.75 to a fractionConverting Between Percentages and FractionsThe easiest way to?convert a fraction to a percentage?is to divide the top number by the bottom number, then multiply the result by 100 (and add the "%" sign)Example 13 Convert?3/8?to a percentageExample 14Keena’s brother told her that these things were true:If you buy something on sale at 10% off and then you get another 15% off, you could have taken 25% off the original price.If you buy something on sale at 10% off and then you pay 13% tax, you could have just added 3% to the original price.If the discount at a store is 35%, you can calculate the sale price by using 65% of the original price.If a smaller number is 80% of a larger one, then the larger one is 120% of smaller one.With which do you agree? Explain why.With which do you disagree? Explain why.Example 15 Which of these make sense? Why? Do not use a calculator!30% of 58 is about 1274% of 82 is about 60110% of 93 is about 100.Example 16 People often recommend giving a 15% tip for good service. If a meal costs $45.29, what tip would you leave if you wanted to leave about 15%? Explain how to estimate without using a calculator.Example 17 The Harmonized Sales Tax (HST) is 13%. Suppose an item costs $89 and you have to pay HST.How might you estimate the HST on the item before calculating it?What is the HST on that item?How much is the total cost including tax?Anita calculated the price for an item including HST by multiplying by __________. Why does that make sense?Example 18 Jayda bought a sweater on sale. The discount was 30%. Before the tax was added, the sale price of the sweater was $34.97. Figure out the original price and describe the strategy you used.Example 19 Ethan had $550 in the bank. He took out $50 to spend on a present.What percent of his money is still in the bank?How much could he have taken out if he wanted to make sure that 70% was still in the bank?Example 20 A new employee in a company earns only 63% the salary of a more experienced employee. If the experienced employee earns $57 000, what would be the salary of the new employee?Example 21 A town of 4827 people is expected to grow by 3.2% next year. What is the expected population for the next year?What percent of the old population is the new one?What percent of that new population is the old one?What is the expected population in 2 years?What is the expected population in 3 years?Example 22 What is the same and what is different about how you solve these two problems? A: I spent $40 and it was 24% of what I had. How much did I have?B: I spent 24% of the $40 I had. What did I spend?Challenge: The side length of one square is 112.5% of the side length of another. What percent of the area of the small square is the area of the larger one? Explain why your answer seems reasonable. ................

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