Open in App Suggest Corrections 0
We will learn how to solve different types of problems on arranging ratios in ascending order and descending order. When a ratio is expressed in fraction or in decimal we first need to convert the ratio into whole number to compare the ratios. The order of a ratio is important to compare two or more ratios. By reversing the antecedent and consequent of a ratio are different ratio is obtained. Solved problems on comparing and arranging ratios in ascending and descending order: 1. Compare the ratios 1\(\frac{1}{3}\) : 1\(\frac{1}{5}\) and 1.6 : 1.2 Solution: 1\(\frac{1}{3}\) : 1\(\frac{1}{5}\) and 1.6 : 1.2 = \(\frac{4}{3}\) : \(\frac{6}{5}\) and \(\frac{16}{10}\) : \(\frac{12}{10}\) = \(\frac{4}{3}\) × 15 : \(\frac{6}{5}\) × 15 and \(\frac{16}{10}\) × 10 : \(\frac{12}{10}\) × 10 = 20 : 18 and 16 : 12 = \(\frac{20}{18}\) and \(\frac{16}{12}\) = \(\frac{10 × 2}{9 × 2}\) and \(\frac{4 × 4}{3 × 4}\) = \(\frac{10}{9}\) and \(\frac{4}{3}\) = 10 : 9 and 4 : 3 Now, \(\frac{10}{9}\) and \(\frac{4}{3}\) are to be compared. L.C.M. of 9 and 3 = 9 \(\frac{10}{9}\) = \(\frac{10 × 1}{9 × 1}\) and \(\frac{4}{3}\) = \(\frac{4 × 3}{3 × 3}\) = \(\frac{10}{9}\) and \(\frac{12}{9}\) Since, \(\frac{10}{9}\) < \(\frac{12}{9}\) Therefore, 10 : 9 < 4 : 3 Hence, 1\(\frac{1}{3}\) : 1\(\frac{1}{5}\) < 1.6 : 1.2 2. Compare the ratios 14 : 23, 5 : 12 and 61 : 92 in
ascending order. Solution: Given ratios can be written as \(\frac{14}{23}\), \(\frac{5}{12}\) and \(\frac{61}{92}\) L.C.M. of the denominators 23, 12 and 92 = 276 \(\frac{14}{23}\) = \(\frac{14 × 12}{23 × 12}\) = \(\frac{168}{276}\) \(\frac{5}{12}\) = \(\frac{5 × 23}{12 × 23}\) = \(\frac{115}{276}\) and \(\frac{61}{92}\) = \(\frac{61 × 3}{92 × 3}\) = \(\frac{183}{276}\) Since, \(\frac{115}{276}\) < \(\frac{168}{276}\) < \(\frac{183}{276}\) Therefore, \(\frac{5}{12}\) < \(\frac{14}{23}\) < \(\frac{61}{92}\) Hence, 5 : 12 < 14 : 23 < 61 : 92 3. Arrange the ratios 1 : 3, 5 : 12, 4 : 15 and 2 : 3 in descending order. Solution: Given ratios can be written as \(\frac{1}{3}\), \(\frac{5}{12}\), \(\frac{4}{15}\) and \(\frac{2}{3}\) L.C.M. of the denominators 3, 12, 15 and 3 = 60 \(\frac{1}{3}\) = \(\frac{1 × 20}{3 × 20}\) = \(\frac{20}{60}\) \(\frac{5}{12}\) = \(\frac{5 × 5}{12 × 5}\) = \(\frac{25}{60}\) \(\frac{4}{15}\) = \(\frac{4 × 4}{15 × 4}\) = \(\frac{16}{60}\) and \(\frac{2}{3}\) = \(\frac{2 × 20}{3 × 20}\) = \(\frac{40}{60}\) Since, \(\frac{40}{60}\) > \(\frac{25}{60}\) > \(\frac{20}{60}\) > \(\frac{16}{60}\) Therefore, \(\frac{2}{3}\) > \(\frac{5}{12}\) > \(\frac{1}{3}\) > \(\frac{4}{15}\) Hence, 2 : 3 > 5 : 12 > 1 : 3 > 4 : 15. ● Ratio and proportion 10th Grade Math From Arranging Ratios to HOME
Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.
Writing the given ratios in fraction `(2)/(3), (17)/(21), (11)/(14), (5)/(7)`LCM of 3, 21, 14, 7 = 42 Converting the given ratio as equivalent `(2)/(3) = (2 xx 14)/(3 xx 14) = (28)/(42) ; (17)/(21) = (17 xx 2)/(21 xx 2) = (34)/(42)` `(11)/(14) = (11 xx 3)/(14 xx 3) = (33)/(42) ; (5)/(7) = (5 xx 6)/(7 xx 6) = (30)/(42)` `(28)/(42), (30)/(42), (33)/(42), (34)/(42)`or`(2)/(3), (5)/(7), (11)/(14), (17)/(21)`or 2 : 3 ; 5 : 7 ; 11 : 14 and 17 : 21. |