Multiplication — Definition, Formula & Examples
Multiplication is a math operation that finds the total when you combine equal groups. For example, 4 × 3 means four groups of three, which gives you 12.
Multiplication is a binary arithmetic operation on two numbers, called factors, that produces a third number called the product. For whole numbers, equals the sum of added to itself times.
Key Formula
Where:
- = First factor (number of groups)
- = Second factor (size of each group)
- = Product (the result)
How It Works
To multiply two numbers, you combine equal-sized groups. If you have 5 bags with 6 apples in each bag, you multiply to find you have 30 apples total. The order of the factors does not change the product — this is called the commutative property, so . Multiplying any number by 1 gives back that same number, and multiplying any number by 0 always gives 0.
Worked Example
Problem: A classroom has 7 rows of desks with 4 desks in each row. How many desks are there in total?
Identify the factors: There are 7 rows (groups) and 4 desks in each row (group size).
Multiply: Combine 7 groups of 4: 4 + 4 + 4 + 4 + 4 + 4 + 4 = 28.
Answer: There are 28 desks in the classroom.
Why It Matters
Multiplication is used every day — calculating prices at a store, measuring areas of rooms, and figuring out how long repeated tasks take. It also forms the foundation for division, fractions, and algebra.
Common Mistakes
Mistake: Confusing multiplication with addition when the numbers are close together (e.g., thinking 3 × 4 = 7).
Correction: Remember that multiplication means repeated addition of equal groups, not a single addition. 3 × 4 means 4 + 4 + 4, which equals 12, not 3 + 4.