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NUMERICAL PROPORTIONS • Numerical proportions compare two numbers. The numbers can have the same units such as a ratio or the numbers can have different units such as rates. A proportion is usually in the form of a:b or a/b. • Ratios are used to compare objects, wins and losses, sides of a figure to its area and many more. • Rates are used to compare miles per hour, words per minute, price per pound and many others. A unit rate is when the denominator of a proportion is one. Miles per hour is an example of a unit rate. When comparing different unit rates, a better buy decision can be made. • A proportion equation is used when one ratio or rate is known and only part of another ratio or rate is known. • There are 4 parts to a proportion and it can be solved when 3 of the 4 parts are known. • Proportion equations can be used only when comparing equal proportions. • Proportion equations can be used to make dimensional analysis in regards to photo enlargement, room dimensions, etc. How to use numerical proportions: • A ratio is used to compare items with the same unit. For example, if School A won 18 out of 24 games, the ratio of winning games to total games would be 3/4. To compare this to School B that won 36 out of 48 games, the ratio would have to be found. The ratio of winning games to total games for School B is also 3/4. Therefore both schools have the same ratio of winning games to total games. © Copyright NewPath Learning. All Rights Reserved. Permission is granted for the purchaser to print copies for non-commercial educational purposes only. Visit us at www.NewPathLearning.com.

Another example: If there are 10 cats and 5 dogs in a neighborhood, the ratio of cats to dogs is 10:5 or 10/5 or 10 to 5. • A rate is used to compare items with different units. For example, if Renee drove 135 miles in 3 hours, her average speed would be 45 miles per hour. • A unit rate is used to determine what a rate would be in one hour, one pound, one ounce etc. When comparing two products, the unit rate can be used to determine the better buy or cheaper price. Example: Which is the better buy? $1.99 for a half dozen apples or $2.49 for a dozen apples $1.99 = x $2.49 = x 6 1 12 1 x = .33 for one apple x = .21 for one apple This is the better buy. • The proportion equation is used to compare items and is used when one ratio or rate is known and only part of another ratio or rate is known. There are 4 parts to a proportion and it can be solved when 3 of the 4 parts are known. For example, Jim can read 6 pages in 5 minutes. How long will it take him to read a book with 150 pages? Example: 6 pages = 150 pages (5)(150) = 6x 5 minutes x minutes 750 = 6x 125 = x, so 125 minutes or about 2 hours • With proportional equations, it is very important that the correct units are lined up in order to find the correct result. © Copyright NewPath Learning. All Rights Reserved. Permission is granted for the purchaser to print copies for non-commercial educational purposes only. Visit us at www.NewPathLearning.com.

Try This! What is the ratio of wins to losses for the Hawks if they won 12 games and lost 4 games? If Brian got paid $52 after working 8 hours, what is his hourly rate? What is a better buy: a 4 lb. bag of peanuts for $2.59 or a 10 lb. bag of peanuts for $5.99? A recipe for lemonade needs 10 lemons to serve 15 people, if 36 people are coming to a party, how many lemons are needed to make lemonade? A photograph is 8" x 10" length by width, if the photographer wants to enlarge the picture to have a length of 20", wha t will the width be? © Copyright NewPath Learning. All Rights Reserved. Permission is granted for the purchaser to print copies for non-commercial educational purposes only. Visit us at www.NewPathLearning.com.