169_186_CC_A_RSPC1_C12_662330.indd



2-6 Study Guide and InterventionRatios and ProportionsRatios and Proportions A ratio is a comparison of two numbers by division. The ratio of x to y can be expressed as x to y, x:y or xy . Ratios are usually expressed in simplest form. An equation stating that two ratios are equal is called a proportion. To determine whether two ratios form a proportion, express both ratios in simplest form or check cross products.Example 1: Determine whether the ratios 2436 and 1218 are equivalent ratios. Write yes or no. Justify your answer.2436 = 23 when expressed in simplest form.1218 = 23 when expressed in simplest form.The ratios 2436 and 1218 form a proportion because they are equal when expressed in simplest form.Example 2: Use cross products to determine whether1018 and 2545 form a proportion. 1018 ? 2545 Write the proportion.10(45) ? 18(25) Cross products 450 = 450 Simplify.The cross products are equal, so 1018 = 2545.Since the ratios are equal, they form a proportion.ExercisesDetermine whether each pair of ratios are equivalent ratios. Write yes or no.1. 12, 1632 2. 58, 1015 3. 1020, 25494. 2536, 1520 5. 1232, 316 6. 49, 12277. 0.12, 5100 8. 1520, 912 9. 1412, 203010. 23, 2030 11. 59, 2545 12. 7264, 9813. 55, 3020 14. 1824, 5075 15. 10075, 443316. 0.051, 120 17. 1.52, 68 18. 0.10.2, 0.450.92-6 Study Guide and Intervention (continued)Ratios and ProportionsSolve Proportions If a proportion involves a variable, you can use cross products to solve the proportion. In the proportion x5 = 1013, x and 13 are called extremes. They are the first and last terms of the proportion. 5 and 10 are called means. They are the middle terms of the proportion. In a proportion, the product of the extremes is equal to the product of the means.Means-Extremes Property of ProportionsFor any numbers a, b, c, and d, if ab = cd, then ad = bc.Example: Solve x5 = 1013.x5 = 1013 Original proportion13(x) = 5(10) Cross products13x = 50 Simplify. 13x13 = 5013 Divide each side by 13.x = 31113 Simplify.ExercisesSolve each proportion. If necessary, round to the nearest hundredth.1. -3x = 28 2. 1t = 53 3. 0.12 = 0.5x4. x + 14 = 34 5. 46 = 8x 6. x21 = 3637. 9y + 1 = 1854 8. 3d = 183 9. 58 = p2410. 4b - 2 = 412 11. 1.5x = 12x 12. 3 + y4 = -y813. a - 1812 = 153 14. 12k = 24k 15. 2 + w6 = 129Use a proportion to solve each problem.16. MODELS To make a model of the Guadeloupe River bed, Hermie used 1 inch of clay for 5 miles of the river’s actual length. His model river was 50 inches long. How long is the Guadeloupe River?17. EDUCATION Josh finished 24 math problems in one hour. At that rate, how many hours will it take him to complete 72 problems? ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download