The numbers a, b, c, d being positive, comparison of ratios a b , c d can be done using following rules :
(i) If ad > bc then a/b > c/d
(ii) If ad < bc then a/b < c/d
(iii) If ad = bc then a/b = c/d
Compare the following pairs of ratios
Ex (1) 4/9 ,7/8 , Solution : 4 *8 ? 7 *9 32 < 63 \ 4 9 7 8
Ex (2) 13 8 7 5 , 13 ´ ´ 5 8 , ? 7 65 56? 65 56 > \ 13 8 7 5
Comparing ratios is a fundamental concept in mathematics that involves analyzing the relationship between two or more quantities. Ratios are typically expressed as fractions or in the form of "a:b" where "a" and "b" are numbers representing quantities. Comparing ratios is essential in various fields, including mathematics, science, finance, and everyday life.
Here are some key points about comparing ratios:
Equality of Ratios: Two ratios are said to be equal if their corresponding fractions are equal. For example, the ratios 2:3 and 4:6 are equal because both reduce to the fraction 2/3.
Comparing Simple Ratios: When comparing two simple ratios, you can cross-multiply to see which ratio is larger. For instance, if you have ratios A:B and C:D, compare AD and BC. If AD > BC, then A:B > C:D.
Common Multiplier: To compare ratios with different denominators, find a common multiple of the denominators. Then, convert both ratios to equivalent ratios with the common denominator.
Solving Proportions: Ratios can also be used in solving proportions, where you compare two equal ratios. For example, if you have a/b = c/d, then ad = bc.