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# Rate of Change

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Use this PowerPoint to review Rate of Change in preparation to your Unit 3 Test.

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### Rate of Change

1. 1. Rate Problems
2. 2. Unit Rates A rate compares two quantities with different units. A unit rate is a rate in which the second number is 1. 48 miles in 8 hours 6 gallons per minute \$0.60 for 1 apple \$12.50 for 1 T-shirt 42 miles per gallon \$70 for 5 DVDs \$3.60 for 12 oranges Which rates are unit rates?
3. 3. Find Unit Rates Divide the first term in the rate by the second term. When the second term is 1 unit, it becomes the unit rate . Find the unit rate or unit price. Emma hiked 9 miles in 4 hours . What is her rate of speed? 9 ÷ 4 = 2.25 The unit rate (rate of speed) is 2.25 miles per hour. A store charges \$5.70 for 15 ounces of oregano. What is the unit price? 5.70 ÷ 15 = 0.38 The unit price is \$0.38 per ounce. 810 miles in 15 hours \$504 for 32 cases of juice drinks
4. 4. Find Unit Rates Divide the first term in the rate by the second term. When the second term is 1 unit, it becomes the unit rate . Find the unit rate or unit price. Emma hiked 9 miles in 4 hours . What is her rate of speed? 9 ÷ 4 = 2.25 The unit rate (rate of speed) is 2.25 miles per hour. A store charges \$5.70 for 15 ounces of oregano. What is the unit price? 5.70 ÷ 15 = 0.38 The unit price is \$0.38 per ounce. 810 miles in 15 hours 54 miles per hour \$504 for 32 cases of juice drinks \$15.75 per case
5. 5. Rate Problems Involving Distance, Rate, and Time Use this formula to solve rate problems involving distance, rate, and time: Maya rode 18 miles on her bicycle at an average rate of 5 miles per hour . How long did it take Maya to ride 18 miles? d = rt d = distance r = rate t = time Hayden drove 468 miles to Flagstaff in 9 hours. What was his average rate of speed? Kelley averaged 3.5 miles per hour on a mountain hike. She hiked for 8 hours. How many miles did she hike? Solve the rate problems. d = r t 18 = 5 t It took Maya 3.6 hours to ride 18 miles. 3.6 = t 18 5 t 5 5 =
6. 6. Rate Problems Involving Distance, Rate, and Time Use this formula to solve rate problems involving distance, rate, and time: Maya rode 18 miles on her bicycle at an average rate of 5 miles per hour . How long did it take Maya to ride 18 miles? d = rt d = distance r = rate t = time Hayden drove 468 miles to Flagstaff in 9 hours. What was his average rate of speed? 52 miles per hour Kelley averaged 3.5 miles per hour on a mountain hike. She hiked for 8 hours. How many miles did she hike? 28 miles Solve the rate problems. d = r t 18 = 5 t It took Maya 3.6 hours to ride 18 miles. 3.6 = t 18 5 t 5 5 =
7. 7. Rate Problems Involving Simple Interest Use this formula to solve problems involving simple interest: I = prt I = Interest (amount of money earned) p = Principal (initial amount of money) r = Rate (usually given as a percent; convert to decimal form) t = Time (if less than a year, convert to decimal form) Conrad deposited \$1,250 in a bank account that earns 4% simple interest. How much will be in his account after 6 months? I = p r t I = 1,250 × 0.04 × 0.5 4% = 0.04; 6 months = 0.5 year I = 25 \$1,250 + \$25 = \$1275 Conrad will have \$1275 in his account after 6 months. Solve the simple interest problem. Kayla paid \$3,360 in interest on a car loan. She paid 8% interest for 3 years. What was the price of the car?
8. 8. Rate Problems Involving Simple Interest Use this formula to solve problems involving simple interest: I = prt I = Interest (amount of money earned) p = Principal (initial amount of money) r = Rate (usually given as a percent; convert to decimal form) t = Time (if less than a year, convert to decimal form) Conrad deposited \$1,250 in a bank account that earns 4% simple interest. How much will be in his account after 6 months? I = p r t I = 1,250 × 0.04 × 0.5 4% = 0.04; 6 months = 0.5 year I = 25 \$1,250 + \$25 = \$1275 Conrad will have \$1275 in his account after 6 months. Solve the simple interest problem. Kayla paid \$3,360 in interest on a car loan. She paid 8% interest for 3 years. What was the price of the car? \$14,000