Ratio And Proportion

What is ratio?

The ratio of two quantities a and b in the same unit's, is the fraction a/b and we write it as a : b. In the ratio, a : b, we call a as the first term or antecedent and b, the second term or consequent. For ex: The ratio 5 : 9 represents 5/9 with antecedent = 5, consequent = 9.

Rule: The multiplication or division of each term of a ratio by the same non-zero number does not affect the ratio.
For ex: 4 : 5 = 8 : 10 = 12 : 15 etc. Also, 4 : 6 = 2 : 3

What is proportion?

The equality of two ratios is called proportion. If a : b = c : d, we write, a : b : : c : d, then d is called the fourth proportion. Here a and d are called extremes, while b and c are called mean terms.

Product of means = Product of extremes.

Thus, a : b : : c : d <⇒ ( b× c) = (a × d)

• Fourth Proportional : If a : b = c : d, then d is called the fourth proportional to a, b, c
• Third Proportional: If a : b = b : c, then c is called the third proportional to a and b.
• Mean Proportional : Mean Proportional between a and b is √ab

Comparison of Ratios: We say that (a : b) > (c : d) <⇒ a/b > c/d

Compounded Ratio: The compounded ratio of the ratios (a : b), (c : d), (e : f) is (ace : bdf).

Duplicate ratio of (a : b) is (a²:b²)
Sub Duplicate ratio of (a : b) is (√a : √b )
Triplicate ratio of (a : b) is (a³ : b³)
Sub triplicate ratio of (a : b) is (a^1/3 : b^1/3)
If a/b = c/d, then (a+b)/(a-b) = (c+d)/(c-d) (compound and dividend)

Variation:

1.  We say that x is directly proportional to y, if×= ky for some constant k and we write,×∝ y.
2.  We say that x is inversely proportional to y, if xy = k for some constant k and we write,×∝ 1/y.