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## Introduction

• Rational Number =
• A rational number is the ratio of two integers, meaning both the numerator and the denominator should be integers.
• Zero is a rational number.

## Addition and Subtraction of Rational Numbers

•  To add/subtract rational numbers with the same (like) denominators:

2. Add/subtract the numerator and keep the common denominator unchanged.

• To add or subtract rational numbers with unlike (different) denominators:

1. Find the Least Common Denominator (LCD).

To find LCD:

• List the multiples of the denominators until the least common multiple(LCM) is found. The LCM is the LCD.

OR

• Multiply the denominators of both fractions; the product will be the LCD.

2. Create an equivalent ratio by multiplying the denominator and the numerator of a rational number with the desired number that can yield the same denominators.

3. Add/Subtract the numerators (follow the rules of adding and subtracting integers), keeping the same common denominator.

E.g.

Multiples of 2: 2, 4, 6 (Stop at this number as it is the least (smallest) common multiple.)

Multiples of 3: 3, (Stop at this number because it is the least (smallest) common multiple.)

OR multiply the denominators (3 x 2) = 6.

Since the least common denominator is 6,  the denominators should be multiplied by a number that can yield 6. The numerator should also be multiplied with the same number as the denominator to create an equivalent fraction.

## Solved Examples

Example 1: Add the given rational numbers:

Find the LCD by multiplying the denominators. Create equivalent fractions by multiplying both the numerator and the denominator by the same number.

Example 2:  Subtract the given rational numbers:

Solution: Follow the rule of subtracting integers.

Find the LCD by multiplying the denominators. Create equivalent fractions by multiplying both the numerator and the denominator by the same number.