Arithmetic Operations
Introduction to Multiplication
Multiplication is the third of the four arithmetic operations. At its heart, it is a fast, efficient way of doing something you already know how to do: addition.
Multiplication tables are among the oldest surviving mathematical documents. Babylonian clay tablets recording multiplication facts date back nearly 4,000 years, and ancient Chinese mathematicians used a rhyming "Nine-Nine Song" (still taught in some schools today) to memorise products up to 9 × 9 as early as the Warring States period. The × symbol itself is much newer — it was introduced by the English mathematician William Oughtred in 1631, in a book that also popularised several other symbols still used in algebra today.
What Does Multiplication Mean?
When you multiply, you are adding the same number repeatedly a certain number of times.
The two numbers being multiplied are called factors. The result is called the product.
The Multiplication Symbol
Multiplication can be written in three ways:
| Notation | Meaning |
|---|---|
| 4 × 3 | Using the times sign |
| 4 · 3 | Using a dot (common in algebra) |
| 4(3) or (4)(3) | Using brackets (no symbol) |
A Visual Model – Arrays
An array is a rectangular arrangement of objects. It shows multiplication visually.
Key Facts
- Multiplying by 1 always gives the same number: 7 × 1 = 7.
- Multiplying by 0 always gives 0: 9 × 0 = 0.
- Order does not matter: 4 × 3 = 3 × 4 = 12 (commutative property).
Why Learn Multiplication?
- Faster than repeated addition for large numbers.
- Essential for division, fractions, algebra, and almost every area of mathematics.
- Used constantly in everyday life: prices, areas, speeds, recipes.
Key Takeaways
- Multiplication is repeated addition.
- The numbers being multiplied are factors; the answer is the product.
- Multiplying by 0 gives 0; multiplying by 1 leaves the number unchanged.
- Order does not change the product.
Practice: Multiply These Numbers
A fresh multiplication fact appears every time. If you get it wrong (or leave it blank), we'll show it as repeated addition.