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
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
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