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Ratio - A ratio compares two quantities by division. Ratios can be simplified just like fractions. 18 15 ÷ 3 3 = 5 6 Simplify - 4 10 6 5 = = 2 10 25 18 8 = = Ratios compare like quantities - Sometimes the quantities appear different but are like. One example would be measurement. 12 inches = 1 foot When simplifying ratios involving measurement the units must be the same. 3 feet = 1 yard 36 inches = 1 yard 2 yards 9 feet 12 inches = 1 foot 3 feet = 1 yard 36 inches = 1 yard Example - Simplify the ratio 2 yards to 9 feet. x feet per yard = 6 feet 9 feet ÷ 3 = 3 Let's convert yards to feet. Every yard = 3 feet, so multiply 4 yards x 3 feet per yard. So 4 yards = 12 feet. 36 inches = 1 yard 12 inches = 1 foot 3 feet = 1 yard Write the ratio 4 yards to 15 feet in simplest form. You have to convert the measurements to the same unit. 15 feet 4 yards x 3 ft./yd. ft. = ft. ÷ 3 3 = Let's convert inches to feet. Every foot = 12 inches, so divide 36 in. by 12 in. per ft. So 36 inches = 3 feet. 36 inches = 1 yard 12 inches = 1 foot 3 feet = 1 yard Write the ratio 36 inches to 15 feet in simplest form. Convert the measurements to the same unit. 15 feet 36 in. ÷ 12 in./ft. ft. = ft. ÷ 3 3 = When two ratios are set equal to each other they form a proportion. Two ratios are said to be proportional is their cross products are equal. Does 3 x 24 = 9 x 8? 3 8 = ? 24 9 15 15 x 45 = ? yes or no? 18 6 = 6 x ? = ? 75 75 x 100 = ? yes or no? 8 4 = 4 x ? = ? 7 7 x 2 = ? yes or no? 6 21 = 21 x ? = ? |