# Math's: Number System: Mathematical Operations on Rational Numbers

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## Mathematical Operations on Rational Numbers

### Addition of Rational Numbers

**The following rule is applied to add two or more rational numbers:**

When the rational numbers have the same denominator- The numerators are added, and the denominator is the same as the common denominator.

When the rational numbers have different denominators- Firstly, their denominators are made equal by taking their equivalent forms and then the numerators are added to get the numerator of the sum and the denominator is the same as the resultant common denominators.

### Subtraction of Rational Numbers

The rule is similar to that of addition.

1. Add the following rational numbers.

(i) (ii)

Solution: (i)

(ii)

2. Simplify the following:

(i) (ii)

Solution: (i)

(ii)

## Multiplication of Rational Numbers

## Division of Rational Numbers

3. Simplify the following.

(i)

(ii)

Solution: (i)

(ii)

## Converting Rational Numbers into Decimal Numbers

Rational numbers can be converted into decimal numbers by long division.

4. Convert the following rational numbers into decimal numbers.

(i) (ii)

Solution:

## Converting Decimal Numbers into Rational Numbers

5. Express the following decimal numbers into rational numbers.

(i) 0.64 (ii) 0.333….

Solution: (i)

(ii)