RATIO AND PROPORTION

The ratio of two quantities of the same units is a fraction that one quantity is of the other.

The ratio a : b represents a fraction a/b . The first term of a ratio is called antecedent while the second term is known as consequent. Thus, the ratio 5 : 7 represents 5/7 with antecedent 5 änd consequent 7.

The multiplication or division of each term of a ratio by a same non-zero number does not affect the ratio.

Thus 4:5 = 8:10 = 12:15 = 16:20 etc.

**Proportion :** The equality of two ratios is called Proportion.

If a : b = c: d, we write, a:b :: c:d and we say that a, b, c, d are in proportion.

In a proportion, the first and fourth terms are known as extremes, while second and third terms are known as means.

We have, ** Product of Means • Product of Extremes**

**Fourth Proportional:** If a: b = c: d, then d is called the fourth proportional to a, b, c.

**Third Proportional:** The third proportional to a, b is the fourth proportional to a, b, b.

**Mean Proportional :** Mean proportional between a and b is √ab.

**Comparison of Ratios** : We say that (a: b) > (c : d) if a / b > c / d

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

**Some More Definitions:**

(i) a^{2} : b^{2} is called the duplicate ratio of a: b.

(ii) √a :√b is called sub-duplicate ratio of a:b.

(iii) a³ : b³ is called triplicate ratio of a:b.

(iv) If a/b=c/d then a+b/a-b=c+d/c-d (Componendo & dividendo)

**Variation :** We say that x is directly proportional to y

if x = ky for some constant k and we write, x y,

Also, we say that x is inversely proportional to y,

if x=k/y for some constant k and we write x is inversely propotional to y.