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

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.

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 hour55 miles/1 hour  27 calories per 3 pieces27 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) = $

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.

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.

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

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

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.

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 $ 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.

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.

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.

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.

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

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

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

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

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

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.

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