Chapter 4 Rates, Ratio, and Proportions.

Ratio- Is the comparison of two quantities that have the same units, often written in fraction form.Is the comparison of two quantities that have 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 Ratio The ratio of 15 hours to 20 hours. 15 hours 20 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

Rates is the comparison of two quantities with different units. is the comparison of two quantities with different units. Unit Rate- is the rate whose denominator value equals one. (Divide)

Examples of Unit Rates A car traveled 301 miles in 7 hours. Find the unit rate. 301 / 7 = 43 miles per hour

Example 2- Unit Rate You spend $4.00 for 15 tablets. Find the unit rate / 15 = $ 0.27 per tablet =.2666 repeats

Example 3- Unit Rate You spend $6150 on 150 shares. Find the unit rate / 150 =$41 per share

Proportions 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 1 Determine if the two ratios form a proportion 7= x 35 = 70 7 x 10 = 70 YES

Example 2 3 ½ = 5 ¼ ½ x 12 = 42 5 ¼ x 8 = 42 YES

Example = x 5 = x 3 = 12.9 NO Validation is not required

Solving 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 2 5 = N x 5 = / 12 =60

Example = n x 4.3 = / 10 =2.795

Application 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? = 6400 N 6400 x 3 = / 192= 100

Example 2 If 2 ½ inches on a map represent 48 miles, what distance does 6 inches represent? 2 ½ 48 = 6N6N 6 x 48 = / 2 ½ =115.2

Example 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 = ½ x 3 = / 2 = 11.2 Round to 11 feet

Example 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? 3232 = N 10 3 x 10 =30 30 / 2 =15