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3.9 Proportions • Goal to solve word problems involving proportions Vocabulary ratio: a comparison of two numbers through division often expressed as a fraction. Proportion: An equation that states that two ratios are equal 2 6 3 9 5 25 7 35 x 2 24 3 9 32 y 81 To Solve Proportions… • Cross multiply and set their products = to each other • Ex: a = b • c d • so ad = cb Ex 1: 3 12 5 y y = 20 Ex 2: x 7 4 6 14 x 3 Ex 3: x 5 9 3 4 4 x 20 27 4x 7 7 x 4 When to set up a proportion • Comparing units • Converting units • Has the word “per”, “ratio”, “rate”, or “out of” Steps to Solving Word Problems involving Proportions 1. Read the word problem twice 2. Identify the comparison of units and write the units in fraction form 3. Set up your proportion keeping units in proper place (convert units if need be) 4. Cross multiply 5. Set products equal to each other 6. Solve for the variable Ex 4: On a road map 3 inches represents 40 miles. If two cities are 10 inches apart on the map, how many miles is it from one to the other? inches miles 3" 10" 40mi d 3d 400 1 133 miles 3 Ex 5: The ratio of boys to girls on the swim team is 5 to 4. How many girls are on the team if there are 65 boys? boys girls 5 65 4 x 5 x 260 x 52 girls Ex 6: Ryan can type 4 pages in 15 minutes. At this rate, how many pages can he type in 2 hours? Pages min utes 60 min 1hour 120 min 2hours 4 x 15 120 480 15x x 32 pages Ex 7: A survey found that 60 out of every 85 people in a city take public transportation to work. Out of 595 people, how many take public transportation to work? public transportation total people 60 x 85 595 85x 35,700 x 420 people take public transportation Assignment Page 150 (10-24 even and 25-38 all )