# How to Add and Subtract Rational Numbers

A rational number constitutes a fundamental category of numbers, encompassing values that can be expressed as a precise quotient of two integers. In this article, we will explore how two rational numbers can be added or subtracted together.

## A Step-by-step Guide to Add and Subtract Rational Numbers

Here is a step-by-step guide to adding and subtracting rational numbers:

### Step 1: Grasping the Notion of Rational Numbers

Embarking on our mathematical expedition, the initial stage demands an astute understanding of the notion of rational numbers. A rational number is essentially any number that can be denoted as a quotient or fraction, where the numerator and the denominator are both integers, and the denominator is not zero.

### Step 2: Recognizing the Principle of Common Denominators

Following the foundational comprehension, the second step involves the cognition of an important mathematical principle: for addition or subtraction of fractions, the denominators must be the same, or ‘common’. If the denominators are disparate, the fractions cannot be directly added or subtracted.

### Step 3: Ensuring Common Denominators

In cases where the denominators are different, it becomes imperative to manipulate the fractions to have common denominators. This is achieved by finding the least common multiple (LCM) of the denominators and then adjusting the fractions accordingly.

### Step 4: Adjusting the Numerators

When adjusting the fractions to have common denominators, it is crucial to also adjust the numerators. If you multiply or divide the denominator of a fraction, you must do the same to the numerator. This ensures that the value of the fraction remains the same, although its appearance may change.

### Step 5: Performing the Addition or Subtraction

Now that the fractions have common denominators, the arithmetic operation can be performed. In addition, combine the numerators and place the sum over the common denominator. For subtraction, subtract the second numerator from the first, placing the difference over the common denominator.

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