3.8 Algebra I

We SayAlgebraically The ratio of a to b if a and b are measured in the same unit a/b is a ratio If a and b are measured in different units a/b is called a rate if a/b represents a rate and b=1 then a/b represents a unit rate.

Write a Ratio 1. The tennis team won 10 of its 16 matches. Find the ratio of their wins to losses. 2. You run a 10 kilometer race in 50 minutes. What is your average speed in kilometers per minute?

Ratios are not always…  Ratios are not always written as fractions, you have seen them in a couple other ways as well. What are some other ways we see ratios?

Finding a rate  A ratio compares two quantities measured in the same unit  A rate compares two quantities that have different units.

Examples  You kept a record of the number of miles you drove in your truck and the amount of gasoline used for two months. What was the average mileage for a gallon of gasoline? Round your result in miles per gallon (mi/gal) to the nearest tenth. Number of miles Number of gallons

Unit Analysis  Writing the units when comparing each quantity of rate is called unit analysis. You can multiply and divide units just like you multiply and divide numbers. When solving a rate problem, you can use unit analysis to help determine the units of the rate.

Convert using Unit Analysis  3 hours to minutes  72 inches to feet  8 pounds to ounces  84 days to weeks

 Use the average mileage 24.2 mi/gal from the previous example, to find the number of miles you can drive on a full 18-gallon tank of gas. Round your answer to the nearest mile.

 You are visiting Mexico and want to exchange $150 for pesos. The rate of currency exchange is Mexican pesos per US dollar on the day you exchange the money. How many pesos will you receive? Round to the nearest whole number.

Assignment  Pg #12-18, 24, 25, 28-31, 34, 35, 44-48, 52-59