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6.1 – Ratio and Proportion Ratio: is the quotient of two numbers or quantities. The ratio of a number a to a number b can be written several ways. a a :b a to b b Write the ratio of 3 parts of oil to 7 parts of gasoline. 3 7 Write the ratio of 40 minutes to 1 hour. 40 4 60 6 2 3 6.1 – Ratio and Proportion Write the ratio of 1.68 to 4.8. 1.68 100 100 4.8 168 480 7 20 10 meters 6 meters 8 meters Using the dimensions of the triangle, write (1) the ratio of the smallest side to the longest side and (2) the ratio of the longest side to the perimeter. (1) 6 3 10 5 (2) 10 10 5 24 10 8 6 12 6.1 – Ratio and Proportion Proportion: is an equation setting two ratios equal. a c b d The method of cross products is used to solve proportions. a c b d ad bc Solve for x. 3 63 8 x 3 x 63 8 21 63 8 x 3 1 x 168 6.1 – Ratio and Proportion Solve for x. 2x 1 x 3 7 5 52 x 1 7 x 3 10 x 5 7 x 21 7x 7x 3 x 5 21 5 5 3 x 26 3 x 26 3 3 26 x 3 6.1 – Ratio and Proportion Mixing 5 ounces of isopropyl alcohol per 16 gallons of gasoline can increase the amount of octane. How many gallons of gasoline can be treated with an 8 ounce bottle of isopropyl alcohol? Set up the proportion. 5 ounces 8 ounces 16 gallons x gallons 5 x 16 8 5 x 128 5 5 x 25.6 gallons 6.1 – Ratio and Proportion On construction scaled drawings, 1 inch corresponds to 4 feet in the 1 field. How long is a wall if its length on the plans is 4 inches? 4 1 17 4 4 4 Set up the proportion. 17 inches 1 inch 4 4 feet x feet 17 x 4 4 x 17 feet 6.2 – Percents, Decimals and Fractions Percent: A method to describe a portion. It is based on “per hundred” and % is used to denote a percent. Of 100 students in a club, 27 of them are freshmen. What percent of the students are freshman? 27 100 27% Thirty-one out of one hundred executives are in their forties. What percent are in their forties? 31 100 31% 6.2 – Percents, Decimals and Fractions Writing Percents as a Decimal or Fraction Convert from a percent to a decimal: drop the % sign and multiply by 0.01. 49% 49 0.01 0.49 82% 0.82 175% 175 0.01 1.75 1.5% 0.015 3.5% 3.5 0.01 0.035 600% 6 0.46% 0.46 0.01 0.0046 6.2 – Percents, Decimals and Fractions Writing Percents as a Decimal or Fraction Convert from a percent to a fraction: drop the % sign and multiply by 1/100. 1 49% 49 100 49 100 1 175% 175 100 175 100 7 4 1 3 .5 35 7 3.5% 3.5 100 100 1000 200 0.46% 0.46 1 0.46 46 23 100 100 10000 5000 6.2 – Percents, Decimals and Fractions Writing Decimals or Fractions as Percents Convert from a decimal or fraction to a percent: multiply by 100% and simplify if necessary. 0.14 0.14 (100%) 14% 1.75 1.75(100%) 175% 0.057 0.057 (100%) 0.5 0.5 (100%) 5.7% 50% 6.2 – Percents, Decimals and Fractions Writing Decimals or Fractions as Percents Convert from a decimal or fraction to a percent: multiply by 100% and simplify if necessary. 3 25 3 300 100% % 25 25 9 40 90 900 9 % % 100% 4 40 40 1 5 2 11 1100 % 100% 2 2 12% 550% 22.5% 6.2 – Percents, Decimals and Fractions Writing Decimals or Fractions as Percents Write 3/17 as a percent. Round the answer to the nearest hundredth percent. 3 17 3 300 100% % 17 17 17.647% 17.65% Provincetown’s budget for waste disposal increased by 1¾ times from last year’s budget. What percent increase is this? 3 7 1 4 4 700 7 % 100% 4 4 175%