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Splash Screen. Chapter 4. Lesson 4-2. A. B. C . 4 D. 6. (over Lesson 4-1). A B C D. Express the ratio in simplest form : 6 grape candies out of a package of 24. (over Lesson 4-1). Express the ratio is simplest form : 3 cups to 2 pints. A B C D. A. 4:3 B. 3:4

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splash screen
Splash Screen

Chapter 4

Lesson 4-2

slide2

A.

B.

C.4

D.6

(over Lesson 4-1)

  • A
  • B
  • C
  • D

Express the ratio in simplest form:

6 grape candies out of a package of 24

slide3

(over Lesson 4-1)

Express the ratio is simplest form: 3 cups to 2 pints

  • A
  • B
  • C
  • D

A. 4:3

B. 3:4

C. 3:2

D. 2:3

slide4

(over Lesson 4-1)

Express the rate as a unit rate: $27 for 6 pizzas

  • A
  • B
  • C
  • D

A. $27/pizza

B. $21/pizza

C. $6/pizza

D. $4.50/pizza

slide6

Preparation for Standard 7AF3.4Plot 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.

slide7

Identify Proportional Relationships

HOUSE CLEANING A house-cleaning service charges by the hour. For the 1st 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.

slide8

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.

90

75

45

1

75

2

No, the fee & hours worked is not proportional.

Method 1

slide9

Method 1

90

225

405

75

210

420

105

3

135

4

45

1

75

2

75

2

105

3

As I said, the fees & hours worked aren’t proportional.

slide10

Method 1

90

225

405

75

210

420

105

3

135

4

45

1

75

2

75

2

105

3

So why aren’t the fees proportional to the hours worked?

The fees aren’t proportional to the hours worked because………

slide11

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

slide12

Method 2

75

2

105

3

45

1

3 7 . 5

3 5

4 5

=

=

=

3

1

2

1 0 5

4 5

7 5

Once again I have proven the fees & hours worked aren’t proportional.

slide13

Method 2

75

2

105

3

45

1

3 7 . 5

3 5

4 5

=

=

=

2

3

1

1 0 5

4 5

7 5

So why aren’t the fees proportional to the hours worked?

The fees aren’t proportional to the hours worked because………

slide14

We used two methods to determine whether the fees were proportional to the hours worked.

3 7 . 5

4 5

2

1

7 5

4 5

Method 1

Method 2

75

2

90

75

45

1

=

45

1

75

2

=

In method 1 we created two ratios and crossed multiplied. The products weren’t equal, therefore the ratio’s weren’t PROPORTIONAL.

In method 2 we created two ratios then divided the ratios out. The quotients weren’t equal, therefore the ratio’s weren’tPROPORTIONAL.

slide15

How many like Method 1 “Cross Multiplying”?

So which method do you like? Let’s take a poll.

How many like Method 2 “Dividing Out”?

How many would use either one depending on the data you were working with?

slide16

Let’s Try One Out.

You Pick the Method You Want To Use.

slide17

PLUMBINGA 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?

  • A
  • B

Begin by creating a table to display your data in:

A. yes

B. no

slide18

PLUMBINGA 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?

  • A
  • B

Now use:

“Cross Multiplication”

OR

“Dividing Out”

A. yes

B. no

slide19

PLUMBINGA 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?

  • A
  • B

A. yes

B. no