1. Proper fractions; in this type of fraction, the numerator is smaller than the denominator e.g. ½, 2/3 etc.
2. Improper fractions: in this type of fraction, the numerator is larger than the denominator e.g. 3/2, 4/3 etc.
3. Mixed fractions: this is a type of fraction which is combined with a whole number e.g. 1½ , 2¾ etc.

Addition of fractions

Common fractions can be added directly only if they have a common denominator. Example:

Evaluate; ¾ + 2/5

Solution

LCM (4, 5)= 20, convert both fractions to fractions with 20 as the denominator and then add their numerators:

¾ + 2/5= 15/20 + 8/20= 23/20= 1320 

Subtraction of fractions

Common fractions can be subtracted directly only if they have a common denominator. Example;

Evaluate 238 - 1512

Solution

238 – 1512

=19/8 – 17/12         (write each fraction as an improper fraction)

=57/24 – 34/24 (express both fractions as fractions with common denominator)

=23/24          (find the difference between the numerators)

Multiplication of fractions

To multiply any two fractions, first convert the fractions to improper fractions, then multiply the two numerators and denominators. Example;

Evaluate; 312 × 235

Solution

=7/2 x 13/5

=91/10

=9110

Division of fractions

To divide one fraction (the dividend) by another fraction (the divisor), multiply the dividend by the reciprocal of the divisor. If necessary first express both fractions as improper fractions. Example:

Evaluate 225÷16

Solution

225=125

= 12/5 ÷ 1/6

= 12/5 x 6/1

=72/5 = 1425

Equivalent fractions

Equivalent fractions are fractions which represent the same part of a whole. Example;

The fractions 2/8, 4/16, 3/12, and 5/20 are all equivalent. Each fraction expressed in its simplest terms is equal to 1/4.