Ratios, proportions and percents
Mathematics, Grade 8
Ratios, proportions and percents
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Ratios, proportions and percents
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Ratios, proportions and percents
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Ratios, proportions and percents
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Study Guide Ratios, proportions and percents Mathematics, Grade 8
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RATIOS AND PROPORTIONS • Numerical proportions compare two numbers. A proportion is usually in the form of a:b or a/b. o There are 4 parts to a proportion and it can be solved when 3 of the 4 parts are known. o Proportions can be solved using the Cross Product Property, which states that the cross products of a proportion are equal. o Proportion equations can be used only when comparing equal proportions. • Similar figures have equal corresponding angles and corresponding sides that are in proportion. A proportion equation can be used to prove two figures to be similar. If two figures are similar, the proportion equation can be used to find a missing side of one of the figures. • Ratios are a comparison of two numbers that have the same units. Ratios are used to compare objects, wins and losses, sides of a figure to its area and many more. • When a ratio is known, a probability can be determined. If the numerator of a ratio is divided by the denominator of a ratio, the result is the probability of that ratio happening. • Rates are used to compare numbers that have different units. Rates are used to compare miles per hour, words per minute, price per pound and many others. o 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. o A proportion equation is used when one ratio or rate is known and only part of another ratio or rate is known. © 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.
How to use ratios and proportions • A ratio is used to compare items with the same unit. o 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. • A rate is used to compare items with different units. o 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. • 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. o For example, Jim can read 6 pages in 5 minutes, how long will it take him to read a book with 150 pages? Ex. 6 pages = 150 pages 6x = (5)(150) 5 minutes x minutes 6x = 750 x = 125, 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. • Similar figures also use proportion equations. Any object, whether a window, picture frame or pillow can be similar to another object. As long as it is stated that the two objects are similar, a proportion can be used to compare them and solve for any missing measurement. • When a ratio of an object is found, the probability of that ratio happening can also be found. For example, if 29 out of 400 people read the newspaper everyday, there is a 29/400 or .0725 probability that a person reads the newspaper everyday. © 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! 1. What is the ratio of wins to losses for the Hawks if they won 18 games and lost 3 games? 2. If Brian got paid $52 after working 8 hours, what is his hourly rate? 3. What is a better buy, a 4 lb. bag of peanuts for $2.59 or a 10 lb. bag of peanuts for $5.99? 4. 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? 5. Two pillows are similar. The smaller pillow is 8" x 10" length by width, if the larger pillow has a length of 20", wha t will the width be? 6. If eighteen people out of 30 drive to work, what is the probability that a person drives to work? What is the probability that a person does not drive to work? © 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.
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