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.
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 Questions
- Write 5 × 4 as repeated addition and find the answer.
- What is 7 × 0?
- What is 9 × 1?
- Draw an array to represent 3 × 5.
- If there are 6 bags each containing 8 apples, how many apples are there altogether?