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8.1 Ratio and Proportion Slide #1 Computing Ratios If a and b are two quantities that are measured in the same units, then the ratio of a to be is a/b. The ratio of a to be can also be written as a:b. Because a ratio is a quotient, its denominator cannot be zero. Ratios are usually expressed in simplified form. For instance, the ratio of 6:8 is usually simplified to 3:4. (You divided by 2) Slide #2 Ex. 1: Simplifying Ratios a. Simplify the ratios: 12 cm b. 6 ft 4 cm 18 ft Slide #3 c. 9 in. 18 in. Ex. 1: Simplifying Ratios a. Simplify the ratios: 12 cm b. 6 ft 4m 18 in Solution: To simplify the ratios with unlike units, convert to like units so that the units divide out. Then simplify the fraction, if possible. Slide #4 Ex. 1: Simplifying Ratios a. Simplify the ratios: 12 cm 4m 12 cm 12 cm 4m 4∙100cm 12 400 Slide #5 3 100 Ex. 1: Simplifying Ratios Simplify the ratios: b. 6 ft 18 in 6 ft 6∙12 in 18 in 18 in. 72 in. 18 in. Slide #6 4 1 4 Using Proportions An equation that equates two ratios is called a proportion. For instance, if the ratio of a/b is equal to the ratio c/d; then the following proportion can be written: Means Slide #7 Extremes = The numbers a and d are the extremes of the proportions. The numbers b and c are the means of the proportion. Properties of proportions 1. CROSS PRODUCT PROPERTY. The product of the extremes equals the product of the means. If = , then ad = bc Slide #8 Properties of proportions 2. RECIPROCAL PROPERTY. If two ratios are equal, then their reciprocals are also equal. If = , then b a = To solve the proportion, you find the value of the variable. Slide #9 Ex. 5: Solving Proportions 4 x 4 x 4 x = = = 5 7 Write the original proportion. 7 5 Reciprocal prop. 28 5 4 Multiply each side by 4 Simplify. Slide #10 Ex. 5: Solving Proportions 3 2 = y+2 y 3y = 2(y+2) 3y = 2y+4 y = 4 Write the original proportion. Cross Product prop. Distributive Property Subtract 2y from each side. Slide #11