6-3 Solving Proportions notes
6-3 Solving Proportions notes
6-3 Solving Proportions notes
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Integrated ISection 6-3 <strong>Solving</strong> <strong>Proportions</strong>6-3 <strong>Solving</strong> <strong>Proportions</strong>Warm-up1. Simplify 303415/17Solve:2. 4x = 18 x = 4.53. 6x = 15 • 24 x = 604. Find 10% of 240 245. Are the ratios 8 and50 equal?9 54NoFind the Probability using a standard die:6. P(odd #) 1/27. P(3) 1/68. P(not 4) 5/69. A deck of cards is missing one card. If you pick a card, what would be the numberof possible outcomes? 516-3 <strong>Solving</strong> <strong>Proportions</strong>Proportion: a statement that two ratios are equal such as 2 x 7 = .9 3Cross Product: The products formed by multiplying the numerator of one fraction by thedenominator of the other fraction.Ex: 4 = 129 x so 4⋅x = 9⋅12Example 1Solve the proportions:a) 5 = 126 yb)2x 7 =9 3Solutiona) 5⋅y = 6⋅12 5y = 72 so y = 14.4b)2x⋅ 3= 9⋅76x= 6363x = = 10.56so x = 10.56-3 <strong>Solving</strong> <strong>Proportions</strong>
Integrated ISection 6-3 <strong>Solving</strong> <strong>Proportions</strong>Example 2Solve 19 x=4 8Solution19⋅ 8 = 4x152 = 4x152= x4x = 38Example 33000 150Solve = [Do on your own]x 3Solution3000⋅ 3 = 150x9000 = 150x9000x150x = 60Using proportions to solve problemsWe can use proportions to solve for an unknown in situations with steady rates.Example 4A work crew lays 0.5 miles of new road in 1 week. At this rate, how long will it take to lay 3miles of new road?SolutionSince the rates for laying 0.5 miles and 3 miles are the same, a proportion can be used.Let t = the number of weeks it takes to lay 3 miles of road.0.5 3 miles miles= ← =1 t weeks weeks.5t= 3⋅1t = 3(2)t = 6It will take 6 weeks to lay 3 miles of new road.6-3 <strong>Solving</strong> <strong>Proportions</strong>
Integrated ISection 6-3 <strong>Solving</strong> <strong>Proportions</strong>Example 5Three grams of oxygen unite with 24 grams of hydrogen to form water. How many grams ofoxygen unite with 1 kg of hydrogen?SolutionLet x = the number of gramsconvert 1 kg to grams….1 kg = 1000gOxygen = OxygenHydrogen Hydrogen3gxg=24g1000g3000 = 24x3000= x24x = 125It will take 125 grams.Using proportions to find percentagesUse the following proportion to solve for percentages… Let x = percentageis = xof 100Example 6What percent of 20 is 15?SolutionLet x = the percentage15 = x20 100 20 ⋅ x = 15 ⋅ 10020x = 1500x = 75%Example 76 is what percent of 80?SolutionLet x = the percentage6 = x80 100 6 ⋅ 100 = 80 ⋅ x600 = 80xx = 7.5%6-3 <strong>Solving</strong> <strong>Proportions</strong>
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