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Splash Screen Chapter 4 Lesson 4-2

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A.A B.B C.C D.D Express the ratio in simplest form: 6 grape candies out of a package of 24 (over Lesson 4-1) A. B. C. 4 D. 6

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1.A 2.B 3.C 4.D A.4:3 B.3:4 C.3:2 D.2:3 Express the ratio is simplest form: 3 cups to 2 pints (over Lesson 4-1)

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1.A 2.B 3.C 4.D A.$27/pizza B.$21/pizza C.$6/pizza D.$4.50/pizza Express the rate as a unit rate: $27 for 6 pizzas (over Lesson 4-1)

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proportional nonproportional Identify proportional and nonproportional relationships.

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Preparation for Standard 7AF3.4 Plot the values of quantities whose ratios are always the same (e.g., cost to the number of an item, feet to inches, circumference to diameter of a circle). Fit a line to the plot and understand that the slope of the line equals the quantities.

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Identify Proportional Relationships HOUSE CLEANING A house-cleaning service charges by the hour. For the 1 st hour they charge $45. Each hour after that costs $30 more. The service completes a cleaning in 4 hours. Is the fee proportional to the number of hours worked? Make a table of values to solve. Begin by making a table to display numbers and cost. Find the fee for 1, 2, 3, and 4 hours worked and place this data into the table.

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Identify Proportional Relationships Yesterday we worked with ratios. Today we will use our knowledge of ratios to help us determine whether the data in the table shows a proportional relationship or not. Watch & observe how I check to find whether the fee for services is “proportional” to the cost. *There will be two different ways or “Methods” to solve this type of problem. 45 1 75 2 Method 1 90 75 No, the fee & hours worked is not proportional.

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Method 1 45 1 75 2 90 75 As I said, the fees & hours worked aren’t proportional. 75 2 105 3 225 210 105 3 135 4 420 405

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45 1 75 2 90 75 2 105 3 225 210 105 3 135 4 420 405 So why aren’t the fees proportional to the hours worked? The fees aren’t proportional to the hours worked because……… Method 1

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Let’s use another method to determine whether the hours worked are proportional to the fees charged.

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45 1 = 4 51 75 2 = 7 52 3 7. 5 105 3 = 1 0 53 3 5 Once again I have proven the fees & hours worked aren’t proportional. Method 2

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So why aren’t the fees proportional to the hours worked? The fees aren’t proportional to the hours worked because……… 45 1 = 4 51 75 2 = 7 52 3 7. 5 105 3 = 1 0 53 3 5 Method 2

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We used two methods to determine whether the fees were proportional to the hours worked. Method 1 45 1 75 2 90 75 In method 1 we created two ratios and crossed multiplied. The products weren’t equal, therefore the ratio’s weren’t PROPORTIONAL. 45 1 = 4 51 75 2 = 7 52 3 7. 5 Method 2 In method 2 we created two ratios then divided the ratios out. The quotients weren’t equal, therefore the ratio’s weren’t PROPORTIONAL.

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So which method do you like? Let’s take a poll. How many like Method 1 “Cross Multiplying”? How many like Method 2 “Dividing Out”? How many would use either one depending on the data you were working with?

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Let’s Try One Out. You Pick the Method You Want To Use.

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1.A 2.B A.yes B.no PLUMBING A plumbing company charges $50 for the first hour and $40 for each additional hour. Suppose a service call is estimated to last 4 hours. Is the fee proportional to the number of hours worked?

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1.A 2.B A.yes B.no PLUMBING A plumbing company charges $50 for the first hour and $40 for each additional hour. Suppose a service call is estimated to last 4 hours. Is the fee proportional to the number of hours worked? Hours1234 Cost$50$90$130$170

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1.A 2.B A.yes B.no PLUMBING A plumbing company charges $50 for the first hour and $40 for each additional hour. Suppose a service call is estimated to last 4 hours. Is the fee proportional to the number of hours worked?

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Lesson 1 MI/Vocab ratio rate unit rate Express ratios as fractions in simplest form and determine unit rates.

Lesson 1 MI/Vocab ratio rate unit rate Express ratios as fractions in simplest form and determine unit rates.

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