Multiplication and Laws of Multiplication
Grade 5 Mathematics — Working with Large Numbers
What You'll Learn
In this lesson, you will master multiplication with large numbers (thousands, ten-thousands, hundred-thousands, and millions), understand the laws of multiplication, and learn strategies to make calculations easier!
1. What is Multiplication?
Definition
Multiplication is one of the four basic arithmetic operations (along with addition, subtraction, and division). It is a shortcut for repeated addition — finding the total when combining equal groups.
Example with Large Numbers:
Instead of adding 1,000 five times:
1,000 + 1,000 + 1,000 + 1,000 + 1,000 = 5,000
We simply write:
5 × 1,000 = 5,000
Interactive visualization — available in the full lesson
2. Definition of Product
The Product of Numbers
- The product of numbers a and b is the result of multiplying them together
- Multiplication can be thought of as adding a number to itself b times
- a × b means "a added to itself b times" or "b groups of a"
| Expression | Meaning | Result |
|---|---|---|
5 × 1,000 |
5 groups of 1,000 | 5,000 |
8 × 10,000 |
8 groups of 10,000 | 80,000 |
3 × 100,000 |
3 groups of 100,000 | 300,000 |
Formula
a × b = Product
The product is the answer when we multiply two or more numbers together.