Rational Number Operations

Understanding Rational Numbers

A rational number is any number that can be expressed as a fraction $\frac{a}{b}$, where $a$ and $b$ are integers, and $b \neq 0$.

Examples of rational numbers include:

• $\frac{1}{2}$
• $-\frac{3}{4}$
• $5$ (which can be written as $\frac{5}{1}$)

Basic Operations with Rational Numbers

Addition and Subtraction

To add or subtract rational numbers, follow these steps:

1. Find a common denominator: Make the denominators the same.
2. Add or subtract the numerators: Keep the common denominator.
3. Simplify the fraction: If possible, reduce the fraction to its simplest form.

Multiplication

To multiply rational numbers:

1. Multiply the numerators: Multiply the top numbers.
2. Multiply the denominators: Multiply the bottom numbers.
3. Simplify the fraction: Reduce the fraction if possible.

Division

To divide rational numbers:

1. Flip the second fraction: Take the reciprocal of the divisor.
2. Multiply: Follow the steps for multiplication.
3. Simplify: Reduce if possible.