Ratio Lesson 4-1 and Proportion

Objectives Use ratios and rates to solve real-life problems. Solve proportions.

Ratios A ratio is the comparison of two numbers written as a fraction. For example: Your school’s basketball team has won 7 games and lost 3 games. What is the ratio of wins to losses? Because we are comparing wins to losses the first number in our ratio should be the number of wins and the second number is the number of losses. The ratio is ___________ games won _______ 7 games __ 7 = = games lost 3 games 3

Rates In a ratio, if the numerator and denominator are measured in different units then the ratio is called a rate. A unit rate is a rate per one given unit, like 60 miles per 1 hour. Example: You can travel 120 miles on 6 gallons of gas. What is your fuel efficiency in miles per gallon? ________ 120 miles ________ 20 miles Rate = = 6 gallons 1 gallon Your fuel efficiency is 20 miles per gallon.

Unit Analysis Writing the units when comparing each unit of a rate is called unit analysis. You can multiply and divide units just like you would multiply and divide numbers. When solving problems involving rates, you can use unit analysis to determine the correct units for the answer. Example: How many minutes are in 5 hours? 5 hours • 60 minutes ________ = 300 minutes 1 hour To solve this problem we need a unit rate that relates minutes to hours. Because there are 60 minutes in an hour, the unit rate we choose is 60 minutes per hour.

Do you know a way to solve when two fractions equal each other??? Proportion An equation in which two ratios are equal is called a proportion. ___ ___ a c = b d Do you know a way to solve when two fractions equal each other???

Cross Multiply and Divide! Do you remember that? Proportion Cross Multiply and Divide! Do you remember that? Example: Use the cross multiply property.

Proportion Example: Use the cross multiply property.

Proportion Example: Use the cross multiply property.

Proportion Example: Use the cross product property.

You Try It! CHALLENGE: If the average person lives for 75 years, how long would that be in seconds?

You Try It! If the average person lives for 75 years, how long would that be in seconds? To solve this problem we need to convert 75 years to seconds. We can do this by breaking the problem down into smaller parts by converting years to days, days to hours, hours to minutes and minutes to seconds. There are 365.25 days in one year, 24 hours in one day, 60 minutes in 1 hour, and 60 seconds in a minute. Multiply the fractions, and use unit analysis to determine the correct units for the answer.