Unit Rates and Proportional Reasoning

1. Unit Rates and Proportional Reasoning LESSON 5-2 Problem of the Day Solve using distributive property 1) 8y -(2y -3) = 9 2) 6(x + 4) -2x = -8 1) y = 1 2) X = -8 5-2

2. Unit Rates and Proportional Reasoning LESSON 5-2 Recall (For help, go to Lesson 5-1.) What is a ratio? - Compares two quantities measured in the same unit - It can be written as a fraction - It has no units 5-2

3. Unit Rates and Proportional Reasoning LESSON 5-2 What are you going to learn? (For help, go to Lesson 5-1.) • 3 main concepts – • Finding unit rate • Finding total cost using unit cost • Using unit cost to compare and find out better buy 5-2

4. Unit Rates and Proportional Reasoning LESSON 5-2 RATE? Rate compares two quantities measured in different units It is a form of ratio in which the two terms are in different units Unit Rate – Rate for one unit of a given quantity. Simply put, rate which has denominator of 1. Examples? mi/hr, $/kg, m/s To find the unit rate, simply divide the first quantity by the second. Unit Cost – A unit rate that gives cost per unit. 5-2

5. dollars 33 Divide the first quantity by the second quantity. = 8.25 hours 4 $8.25 1 hour The unit rate is , or $8.25 per hour. Unit Rates and Proportional Reasoning LESSON 5-2 Additional Examples Find the unit rate: earn $33 for 4 hours of work. Quick Check 5-2

6. = $2.73 unit price • number of units = total price Unit Rates and Proportional Reasoning LESSON 5-2 Additional Examples Use the unit price to find the total price: 7 yd of ribbon at $.39 per yard. $.39 • 7 The total price of 7 yd of ribbon is $2.73. Quick Check 5-2

7. price number of lb $.89 3 $.30/lb price number of lb $1.59 5 $.32/lb Unit Rates and Proportional Reasoning LESSON 5-2 Additional Examples Find each unit price. Then determine the better buy. 3 lb of potatoes for $.89 5 lb of potatoes for $1.59 Remember: Better buy has the smallest price / unit Divide to find the unit price of each size. Since $.30 < $.32, 3 lb of potatoes for $.89 is the better buy. Quick Check 5-2

8. Unit Rates and Proportional Reasoning LESSON 5-2 Using conversion factors • We are going to use ratios to convert a measurement from one system to another. • Conversion factor is a rate that equals 1. • Note: This method of canceling units is quite useful especially in Science. This technique is called ‘unit analysis’ or ‘dimensional analysis’ – I’ve introduced this to you as “multiplying by a fraction equal to 1” • Main principle – multiplying / dividing something by 1 doesn’t change the value. 5-2

9. 4.35 mi/h $1.08/lb; $1.10/lb; 20 lb for $21.50. Unit Rates and Proportional Reasoning LESSON 5-2 Lesson Quiz 1. It took Anthony 5 h 45 min to complete a 25-mi walkathon. What was his average speed in miles per hour? Round your answer to the nearest hundredth. 2. A 20-lb bag of dog food costs $21.50. A 30-lb bag of the same dog food costs $32.90. Find each unit price. Then determine the better buy. 5-2

10. Unit Rates and Proportional Reasoning LESSON 5-2 Lesson Quiz • 1. If a car travels 45 miles in 30 min, what is the rate at which the car is travelling? • If John bought 2.5 kg of rice for $7.5, what is the unit price of rice? • It takes 30 min for a tap to fill one bucket, how much time (in hrs) would it take to fill 6 buckets? • You can buy 28 fl oz of fruit juice for $1.69 or 64 fl oz for $3.19. Which size is a better buy? 90 mi/hr or 1.5 mi/min $3/kg Total 3 hrs 64 fl oz for $3.19 5-2

11. HOMEWORK • Homework: • Lesson 5-2: p. 234-236: 1, 6 – 28 e, 29 • p. 236: # 1-9 all – This should be review. Show all work.