Unit 5: Percent, Ratio, and Rate MATH 8 Unit 5: Percent, Ratio, and Rate

Relating Fractions, Decimals, and percent Unit 5.1 Relating Fractions, Decimals, and percent

Percent to Fraction Percent to fraction Step 1: Divide the number by 100 Step 2: Take out the percentage sign Step 3: Eliminate the decimals in the fraction Step 4: Reduce to lowest term 1) 19% 4) 92.5% 2) 36% 5) 47.25% 3) 85%

Percent to Fraction to Decimal Step 1: Get the denominator in a power of 10. Step 2: Divide the numbers. 1) 19% 4) 92.5% = 0.19 = 0.925 2) 36% = 0.36 5) 47.25% = 0.4725 3) 85% = 0.85

Fraction to Decimal If fraction has a denominator that is difficult to get to base 10, use calculator to divide 1) = 0.75 2) = 0.625

Fraction to Decimal to Percentage Put it back to fraction with base 10- denominator Get denominator to be 100. Take the numerator as the percentage. 1) = 0.75 = 75% 2) = 0.625 = 62.5%

More Questions Try to get the following fractions to decimal and then to percentage form 3) =0.6 = 60% 4) =0.4725 = = 47.25%

Unit 5.2 Calculating Percent

Steps… Calculating Percent of a number Step 1: Get percent in decimal form. Step 2: Multiply decimal to the number (i.e. 200).

Calculating Percent of a Number Question 1 What is 180% of 200? 200 ?? 0% 100% 180%

Calculating Percent of a Number Question 1 What is 180% of 200? 200 ?? 0% 100% 180% 180% = 1.8 1.8 * 200 = 360

Question 2 Question 2 What is 37.55% of 95? ?? 95 0% 37.55% 100% = 0.3755 0.3755 * 95 = 35.6725

Problem Question 3 Of the people who watched the Lego Movie, 30% of the viewers were adults. If there were 300 people watching over the weekend. How many of them were adults? 30% = 0.3 0.3 * 300 = 90

Terms Cost price is the price that the store has to pay to get the merchandise Selling price is the price that the store sells the merchandise

Question 4 Question 4 The cost price of a Wal-Mart T-shirt is $5.00. The selling price is 300% of the cost price. What is the selling price of the T-shirt? Illustrate the answer in a number line. 300% = 3 5* 3 = $15.00

Solving Percent Problems Unit 5.3 Solving Percent Problems

Question 1 a) Spiderman’s height was 165cm last year. After drinking some special juice, his height increased by 25%. What is his height now? Solution A 25% = 0.25 165×0.25 =41.25 cm 165+ 41.25 = 206.25 cm Solution B 100% + 25% = 125% (+) if increase, (-) if decrease 125% = 1.25 165 × 1.25 = 206.25 cm

Question 1 b) Solution A 30% = 0.30 Solution B The effect of this juice is weight loss. In the past, Spiderman kept a constant weight of 140 lbs. But after taking the juice, his weight decreased by 30%. What is his new weight. Solution A 30% = 0.30 140×0.3 =42 lbs 140 - 42 = 98 lbs Solution B 100% - 30% = 70% 70% = 0.7 140 × 0.7= 98 lbs

Question 2 a) Step 1: Get the percent in decimal form. 70% of a number is 63. What is the number? 63 ?? 0% 70% 100% Step 1: Get the percent in decimal form. Step 2: Divide the number by the decimal Solution: 70% = 0.7 63 ÷ 0.7 = 90

Question 2 b) Solution: 200% = 2 200% of a number is 96 ?? 96 0% 100% 96÷ 2 = 38

Percent Increase/Decrease The price of a T-shirt in Wal-Mart increased from $20 to $25. To find the percent increase/decrease Step 1: Divide final value to initial value Step 2: Subtract 100% to/from it Solution: 25 ÷ 20 = 1.25 1.25 = 125% 125% - 100% = 25%

More Percent Increase/Decrease A purse went on sale in Michael Kors. The bag’s original price was $500. After a marked down deduction, the price became $420. What was the percent decrease of the bag? Solution: 420÷500 = 0.84 0.84= 84% 100% - 84% = 16%

Unit 5.4 Sales Tax and discount

GST, PST, and HST GST – Goods and Services Tax Federal tax 5% PST – Provincial Sales Tax Provincial tax Depends on the province HST- Harmonized Sales Tax PST + GST combined Depends on the Province

Tax in our provinces The following link sends you to a website showing the current taxes in each provinces http://www.retailcouncil.org/quickfacts/taxrates

Tax questions A pair of jeans in American Eagle cost $55. How much is the final price of this jeans in… a) BC –(GST= 5% and PST = 7%) b) Quebec (GST=5% and PST= 9.975%) Solution a) tax = 5% + 7% = 12% 12%= 0.12 55 × 0.12 = 6.60 55 + 6.6 = $61.60

Tax questions A pair of jeans in American Eagle cost $55. How much is the final price of this jeans in… a) BC –(GST= 5% and PST = 7%) b) Quebec (GST=5% and PST= 9.975%) Solution b) tax = 5% + 9.975% = 14.975% 14.975%= 0.14975 55 × 0.14975 = 8.24 55 + 8.24 = $63.24

Discount and Taxes A dress shirt in Banana Republic is priced at $80. For the weekend, there is an additional 20% off. How much do I have to pay considering there is a tax of 12% in BC. Solution 1: 0.2 × 80 = $16 80-16 = $64 64 × 0.12 = $7.60 64 + 7.60 = $71.60

Double Discounts James work at Sport Chek as a cashier. He gets an employee discount of 10% on everything he buys. He wants to buy a new pair of Nike running shoes that is regularly priced at $79.99. The shoe is currently on sale for 30% off. How much is the shoe after the discounts. Discount #1 10% = 0.1 79.99 × 0.1 = 7.999 79.99 – 7.999 = 71.991 Discount #2 30% = 0.3 71.991 × 0.3 = 21.5973 71.991 – 21.5973 = $50.3937