# Ratio

The ratio of two quantities a and b in the same units, is the fraction 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.

**Eg.**The ratio 5 : 9 represents 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.

**Eg.**4 : 5 = 8 : 10 = 12 : 15. Also, 4 : 6 = 2 : 3.

# 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.

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 x c) = (a x d).

**Fourth Proportional:**

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

**Third Proportional:**

a : b = c : d, then c is called the third proportion to a and b.

**Mean Proportional:**

Mean proportional between a and b is ab.

**Comparison of Ratios:**

We say that (a : b) > (c : d) .

**Compounded Ratio:**

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

**Duplicate Ratios:**

**Duplicate ratio of (a : b) is (a**

^{2}: b

^{2}).

^{3}: b

^{3}).

^{1/3}: b

^{1/3}).

**Variations:**

**We say that x is directly proportional to y, if x = ky for some constant k and we write, x y.**

We say that x is inversely proportional to y, if xy = k for some constant k and

we write,