Chapter 5 : Ratios, Rates & Proportions Section 2

1. Chapter 5: Ratios, Rates & Proportions Section 2 Unit Rates and Proportional Reasoning

2. California Standards • Algebra and Functions 2.1: Convert one unit of measurement to another. • Algebra and Functions 2.2: Demonstrate an understanding that RATE is a measure of ne quantity per unit value of another quantity.

3. Key Vocabulary • RATE: Is a RATIO that COMPARES two quantities measured in different units. • Examples: • 16 ounces for 2 servings 16 ounces/2 servings • 55 miles per 1 hour 55 miles/1 hour • 27 calories per 3 pieces 27 calorie/3 pieces • UNIT RATE: A rate given for one unit of a given quantity. • Examples: • 16 ounces for 2 servings is 8 ounces for 1 serving. • 27 calories per 3 slices is 9 calories per 1 slice. • UNIT COST: A unit rate that gives the COST per unit. • Example: $0.15 per ounce. If you have 8 ounces, (8.0)($0.15) = $

4. What is a RATE? • A RATE is a comparison of two quantities measured in different units. • Example: $3.00 for 12 cookies $25.00 for 2 boxes • RATE applies to everyday life applications like shopping, manufacturing and driving. • You have seen examples of RATE, UNIT RATE and UNIT COST at stores, books, and more.

5. Finding a UNIT RATE • Once again, UNIT RATE relies on previously covered skills. • Since RATE can be expressed in FRACTIONAL form, you can use DIVISION to simplify the FRACTION into a Unit Rate. • To solve, you simply start with the FRACTIONAL form of the RATE. • Then DIVIDE the Numerator by the Denominator. • The result will be the UNIT RATE. • EXAMPLE: A package of crackers has 160 crackers that can serve 20 people. Find the unit rate of crackers per serving. • Here, word form is written as a RATE, 160 crackers/20 servings. • Then 160 crackers is DIVIDED by 20 servings. Result is 8 crackers/1 serving. • The UNIT RATE is 8 crackers per 1 serving.

6. UNIT Cost to Determine TOTAL Cost • A UNIT RATE that gives the cost per unit is a UNIT COST. • This is most commonly used in production, budgeting and shopping. • Once you have a UNIT COST, you can determine the TOTAL COST. • To determine TOTAL COST, you need to MULTIPLY the UNIT COST by the number of units themselves. • Remember, UNIT COST refers to ONE unit only. • Example: The UNIT COST of shampoo is $0.25 per ounce. You plan on buying a 24 ounce bottle of shampoo. (Unit cost)(Number of Units) = TOTAL COST ($0.25)(24) = $6.00 TOTAL COST for a 24 ounce bottle of shampoo is $6.00

7. UNIT Cost to Determine TOTAL Cost • Example #2: • A candy store sells their treats by the piece. Each piece of candy cost $0.15. A customer buys 140 pieces of candy to share at a party. • What is the TOTAL Cost for all of the candy? • (Unit Cost)(Number) = Total Cost • ($0.15)(140) = $21.00 • The TOTAL COST is $21.00 • Example #3 • A fabric store sells Hello Kitty fabric for $4.50 a yard. My mother plans on buying 7.5 yards to make a dress for a party. • What is the TOTAL Cost for all of the yardage? • (Unit Cost)(Number) = Total Cost • ($4.50)(7.5) = $33.75 • The TOTAL COST is $33.75

8. Comparing UNIT Cost • Unit Cost is a good core skill to have. This skill can be used when shopping. Here, you NEVER want to be charged more for goods. • By reading UNIT Cost and understanding the VALUE of items, you will be saving yourself lots of money and becoming a shrewd consumer. • To compare UNIT COST, you need to take the earlier learned skill of determining Unit Rate to find the UNIT COSTand apply it to the items being compared. • Once you determine a UNIT COST for EACH separate unit, you compare the values side by side and see which is the better value.

9. Comparing UNIT Cost • Example #1: • Miss Graham is shopping at Target, she sees her favorite designer shampoo in two different sizes. A 24 ounce bottle is selling for $7.20 and a 50 ounce bottle is selling for $13.50. Which is the better buy? • Bottle #1: $7.20 for 24 ounces $7.20/24 ounces • Bottle #1 costs $0.24 an ounce • Bottle #2: $13.50 for 50 ounces $13.50/50 ounces • Bottle #2 costs $0.27 an ounce. • Comparing the UNIT COST of Bottle #1 against Bottle #2 means $0.30 vs $0.27 • Bottle #2 is the BETTER buy.

10. Comparing UNIT Cost • Example #2: • Mr. Lee is shopping at Kohl’s, he sees two bottles of the highly coveted “The MAN: Mr. Shuler” cologne. A 4.2 ounce bottle is selling for $59.00 and a 2.7 ounce bottle is selling for $40.o0. Which is the better buy? • Bottle #1: $59.00 for 4.2 ounces $59.00/4.2 ounces • Bottle #1 costs roughly $14.05 an ounce • Bottle #2: $40.00 for 2.7 ounces $40.00/2.7 ounces • Bottle #2 costs roughly $14.81 an ounce. • Comparing the UNIT COST of Bottle #1 against Bottle #2 means: • Bottle #1, $14.05 vs. Bottle #2, $14.81 • Bottle #1 is the BETTER buy.

11. Quick Review • The Basics of RATE: • RATE is a RATIO of two quantities measured in different units. • Examples: Calories per serving. Miles per hour. Cost per weight. • Finding a UNIT RATE • To determine a UNIT RATE, the goal is to find the rate for ONE unit. • To solve, your RATE should be written in FRA CTIONAL form. • Divide the Numerator by the Denominator and you are done. • Using UNIT COST to find TOTAL COST • Once a Unit Rate or Cost is determined, you can use that to find the TOTAL COST • Simply MULTIPLY the Unit Cost by the Number of Units to get the TOTAL COST. • Using UNIT COST to COMPARE • To COMPARE Unit Cost of differing items, you need to determine the Unit Cost of each item being looked at and then COMPARE then against one another.

12. Check for Understanding • Please determine the BEST answer for the following expression. • Carry out ALL work and calculations in your NOTES for later reference • Please write your answer on your wipe boards and wait for the teacher’s signal. • On the count of 3, hold up your wipe boards.

13. C4U Question #1 • Question #1: • Read the following: • A 70 ounce bag of chocolate cookies can yield 14 servings . • What is the UNIT RATE for the above? Select the BEST answer: A. 14 ounces per serving B. 84 ounces per serving C. 5 ounces per serving D. 56 ounces per serving

14. C4U Question #2 • Question #2: • Read the following: • A large can of 42 ounce luncheon meat can serve 7 people. • What is the UNIT RATE for the above? Select the BEST answer: A. 7 ounces per serving B. 4.9 ounces per serving. C. 3.5 ounces per serving D. 6 ounces per serving

15. C4U Question #3 • Question #3: • Read the following: • Cereal cost $0.38 an ounce. You plan on buying 24 ounces of cereal. • What is the TOTAL COST for the cereal? Select the BEST answer: A. $8.12 B. $7.88 C. $9.12 D. $9.54

16. C4U Question #4 • Question #4: • Read the following: • A candy store sells candy for $1.50 for each quarter pound. You plan on buying 2 pounds. • What is the TOTAL COST for the candy? Select the BEST answer: A. $3.00 B. $6.00 C. $12.00 D. $9.00

17. C4U Question #5 • Question #5: • There are 4 bottles of shampoo on the shelf at Target. • Bottle #1 cost $6.00 for 20 ounces. • Bottle #2 cost $15.00 for 60 ounces. • Bottle #3 cost $17.00 for 80 ounces • Bottle #4 cost $20.00 for 90 ounces • Which is the BETTER Buy? Select the BEST answer: A. Bottle #1 B. Bottle #2 C. Bottle #3 D. Bottle #4

18. Guided Practice • Students will work on a worksheet/book work, focusing only on the problems assigned by the teacher. • Work carefully, show your problem solving process, and double check all calculations. • Use scratch paper to carry out your work. • Once you have completed the assigned problems, please raise your pencil. • The teacher will then check your work and release you to complete the independent practice.

19. Independent Practice • Once you have been signed off and released to complete Independent Practice, please complete the following assignment: