Chapter 4Chapter 4

Rates, Ratio, and Proportions.Rates, Ratio, and Proportions.

Ratio-Ratio-

• Is the comparison of two quantities that have Is the comparison of two quantities that have the same units, often written in fraction form.the same units, often written in fraction form.

• The first quantity mentioned is the numerator and the second quantity is the denominator.

• Always reduce the fraction to lowest terms. Leaving improper fractions as improper.

Examples of a RatioExamples of a Ratio

The ratio of 15 hours to 20 hours.The ratio of 15 hours to 20 hours.

15 hours15 hours

20 hours20 hours

= 3 hours

4 hours

Penny’s Kennel has 57 golden retriever puppies. Thirty- eight are females. What is the ratio of female puppies to male puppies?

Female puppies

Male puppies

= 38

19

RatesRates

• is the comparison of two is the comparison of two quantities with quantities with differentdifferent units units..

Unit Rate- is the rate whose denominator value equals one. (Divide)

Examples of Unit RatesExamples of Unit Rates

A car traveled 301 miles in 7 hours. Find the unit rate.

301 / 7 = 43 miles per hour

Example 2- Unit RateExample 2- Unit Rate

You spend $4.00 for 15 tablets. Find the unit rate.

4.00 / 15

= $ 0 .27 per tablet

= .2666 repeats

Example 3- Unit RateExample 3- Unit Rate

You spend $6150 on 150 shares. Find the unit rate.

6150 / 150 = $41 per share

ProportionsProportions

• states that two rates or two ratios are equal. • Important- When you write a proportion, order is important. Be sure you match up the rates

•To find out if it is true proportion cross multiply, and make sure they equal.

Example 1Example 1

Determine if the two ratios form a proportion

7 = 35

2 10

2 x 35 = 70

7 x 10 = 70YES

Example 2Example 2

3 ½ = 5 ¼

8 123 ½ x 12 = 42

5 ¼ x 8 = 42 YES

Example 3Example 3

2.5 = 4.3

3 52.5 x 5 = 12.5

4.3 x 3 = 12.9NO

Validation is not required

Solving ProportionsSolving Proportions

You cross multiply and divide.

Validate- by cross multiplying to make sure they are equal.

36 = 9

16 n

9 x 16 =

144 / 36 =

144

4

Example 2Example 2

5 = N

12 144144 x 5 = 720720 / 12 = 60

Example 3Example 3

6.5 = n

10 4.3

6.5 x 4.3 = 27.9527.95 / 10 = 2.795

Application ProblemsApplication Problems

Example 1

In the manufacturing process, it has been found that for every 192 items assembled, 3 are defective. At this rate, if 6400 items are assembled, how many will be defective?

192

3=

6400

N

6400 x 3 = 19200

19200 / 192= 100

Example 2Example 2

If 2 ½ inches on a map represent 48 miles, what distance does 6 inches represent?

2 ½

48=

6

N

6 x 48 = 288

288 / 2 ½ = 115.2

Example 3Example 3

During a sunset, a pole barn casts a shadow 7 ½ feet long while the 3 foot tall evergreen tree growing next to it casts a shadow 2 feet long. To the the nearest foot, how tall is the pole barn?

7 ½

N=

2

3

7 ½ x 3 = 22.5

22.5 / 2 = 11.2

Round to 11 feet

Example 4Example 4

The school volunteers used 3 gallons of paint for two rooms. How many gallons would they need to paint 10 rooms of the same size?

3

2=

N

10

3 x 10 = 30

30 / 2 = 15