Multiply — Definition, Formula & Examples

Multiply is the operation of combining equal groups together to find a total. When you multiply two numbers, you are adding one number to itself as many times as the other number says.

Multiplication is a binary arithmetic operation in which two values, called factors, are combined to produce a result called the product. For whole numbers, $a \times b$ equals the sum of $b$ copies of $a$ .

Key Formula

a \times b = \underbrace{a + a + a + \cdots + a}_{b \text{ times}}

Where:

$a$ = One of the two factors being multiplied
$b$ = The number of times a is added to itself

How It Works

To multiply two numbers, think of one number as the size of each group and the other as how many groups you have. For example,

4 \times 3

means 3 groups of 4, which gives 12. The order of the factors does not change the product, so

4 \times 3 = 3 \times 4

. This property is called the commutative property. Any number multiplied by 1 stays the same, and any number multiplied by 0 equals 0.

Worked Example

Problem: A classroom has 5 rows of desks with 6 desks in each row. How many desks are there in total?

Identify the factors: There are 5 rows and 6 desks in each row, so the factors are 5 and 6.

5 \times 6

Multiply: Add 6 five times: 6 + 6 + 6 + 6 + 6 = 30.

5 \times 6 = 30

Answer: There are 30 desks in total.

Why It Matters

Multiplication is essential for everyday tasks like figuring out the cost of multiple items at a store or calculating area. It also forms the foundation for division, fractions, and algebra, which you will use throughout school and beyond.

Common Mistakes

Mistake: Confusing multiplication with addition, for example thinking 3 × 4 = 7 instead of 12.

Correction: Multiplication means 3 groups of 4 (4 + 4 + 4), not 3 + 4. The result of multiplying is called the product, while the result of adding is called the sum.