Algebra Ch 11 (1)

# Algebra Ch 11 (1) - 11.1 Problem Solving Using Ratios and...

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11.1 Problem Solving Using Ratios and Proportions 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 ___________ games lost = 7 games _______ 3 games = 7 __ 3

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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 60 gallons of gas. What is your fuel efficiency in miles per gallon? Rate = 120 miles ________ 60 gallons = ________ 20 miles 1 gallon Your fuel efficiency is 20 miles per gallon. 11.1 Problem Solving Using Ratios and Proportions
An equation in which two ratios are equal is called a proportion . A proportion can be written using colon notation like this a:b::c:d or as the more recognizable ( and useable ) equivalence of two fractions. a ___ ___ = b c d 11.1 Problem Solving Using Ratios and Proportions

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a:b::c:d a ___ b c d When Ratios are written in this order, a and d are the extremes , or outside values, of the proportion, and b and c are the means , or middle values, of the proportion. Extremes Means 11.1 Problem Solving Using Ratios and Proportions
To solve problems which require the use of a proportion we can use one of two properties. The reciprocal property of proportions. If two ratios are equal, then their reciprocals are equal. The cross product property of proportions. The product of the extremes equals the product of the means 11.1 Problem Solving Using Ratios and Proportions

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x 35 3 5 = 35 3 5 = x 105 5 = x 11.1 Problem Solving Using Ratios and Proportions 21 = x
9 6 2 = x x = 6 2 9 x 6 18 = x = 3 11.1 Problem Solving Using Ratios and Proportions

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Solve: 1 2 1 - = x x x – 1 = 2 x x = –1 x x 2 ) 1 ( 1 = - 11.1 Problem Solving Using Ratios and Proportions
Solve: x x x 1 1 2 - = + x 2 = -2 x - 1 x 2 +2 x + 1= 0 ) 1 2 ( 1 2 + - = x x 11.1 Problem Solving Using Ratios and Proportions ( x + 1)( x + 1)= 0 ( x + 1) = 0 or ( x + 1)= 0 x = - 1

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11.2 Problem Solving Using Percents Percent means per hundred
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## This note was uploaded on 01/12/2011 for the course MAT 116 A MAT 116 A taught by Professor Hawkins during the Spring '10 term at University of Phoenix.

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Algebra Ch 11 (1) - 11.1 Problem Solving Using Ratios and...

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