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.

4 × 3 means "four groups of three" = 3 + 3 + 3 + 3 = 12

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.

3 rows of 4 dots = 4 × 3 = 12

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.

Calculate the product.