Lesson 28: Multiplication Table

New Concept

Changing the order of factors does not change the product. This is the Commutative Property of Multiplication.

Why it matters

This isn't just a rule for multiplication tables; it's a fundamental law of algebra that allows you to simplify complex expressions. Mastering these properties is the difference between simply doing math and truly understanding how it works.

What’s next

Next, you'll use the multiplication table to explore this property and others, building a solid foundation for your calculations.

Property

$m \times n = n \times m$

Examples

• $9 \times 3 = 27$ is the same as $3 \times 9 = 27$.
• $6 \times 4 = 24$ is the same as $4 \times 6 = 24$.
• $12 \times 11 = 132$ is the same as $11 \times 12 = 132$.

Explanation

It's the 'order doesn't matter' rule! Swapping the numbers you multiply doesn't change the answer. Think of it like $3 \times 9$ and $9 \times 3$—both get you to 27. Easy!

Property

$1 \times n = n$

Examples

• $1 \times 25 = 25$.
• $1 \times 12 = 12$.
• $1,000,000 \times 1 = 1,000,000$.

Explanation

The number 1 is like a magic mirror. Any number multiplied by 1 sees itself as the answer. It keeps its 'identity,' which makes it the easiest multiplication fact ever!

Property

$0 \times n = 0$

Examples

• $0 \times 25 = 0$.
• $0 \times 1492 = 0$.
• $12 \times 0 = 0$.

Explanation

Zero is the ultimate party pooper of multiplication! Anything you multiply by it, no matter how big, instantly becomes zero. A million dollars times zero? You get zero dollars. Bummer!