The Pillars of Arithmetic
Arithmetic is the oldest and most elementary branch of mathematics. It forms the absolute foundation upon which all other mathematical disciplines—such as algebra, geometry, and calculus—are built. At its core, arithmetic is the study of numbers and the traditional operations that we perform on them: addition, subtraction, multiplication, and division.
Order of Operations (PEMDAS / BODMAS)
When solving complex arithmetic expressions, mathematical operations must be executed in a very specific, universally agreed-upon sequence. This ensures that everyone who solves the same equation arrives at the exact same answer.
- P / B (Parentheses / Brackets): Always calculate the expressions inside parentheses first.
- E / O (Exponents / Orders): Next, resolve any powers, square roots, or indices.
- M & D / D & M (Multiplication and Division): Perform these operations from left to right as they appear in the equation.
- A & S / A & S (Addition and Subtraction): Finally, perform addition and subtraction, strictly from left to right.
Real-World Applications
While basic, arithmetic is the mathematical language of daily life. We use it subconsciously when determining the best discount at a grocery store (percentages), splitting a restaurant bill among friends (division), adjusting recipes for more guests (fractions and ratios), or managing a household budget. Developing strong mental arithmetic skills significantly enhances problem-solving speed in higher-level academia.