## Introduction to Ratio and Proportions:

**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 5/9 with antecedent = 5, consequent = 9.

**Proportion:**

Proportions is where two ratios are compared and equated.

Where a:b is a ratio and c:d is another ratio, and if they are equal,

then, they can be re-written as a:b :: c:d. { the ‘::’ sign means ‘equal to’}

Therefore, a:b = c:d

**Properties of proportions:**

(i) a:b = c:d

can be written as a/b = c/d

which implies, axd = bxc, or, ad = bc

this property helps in solving many questions

(ii) if a:b = b:c, which means this proportions between three numbers is in the form of

‘continued proportions’, as all three numbers are having a connection.

so, a/b=b/c or,

ac=bxb or,

ac=b2