Properties of Multiplication

Have you ever looked at a math problem and thought it looked too hard to solve in your head? The properties of multiplication are like secret shortcuts that make multiplying numbers much easier and faster. Let's learn the three main properties!

The Commutative Property

The commutative property tells us that you can multiply numbers in any order, and the product (the answer) will always be the same.

Rule: $a \times b = b \times a$

Example: What is $8 \times 5$? It is exactly the same as $5 \times 8$. Both equal $40$. If you forget a multiplication fact, try flipping the numbers around!

The Associative Property

The associative property says that when you are multiplying three or more numbers, it doesn't matter how you group them. You can move the parentheses around to make the math easier.

Rule: $(a \times b) \times c = a \times (b \times c)$

Example: Rewrite $4 \times 7 \times 25$ to make it easier to compute. Instead of multiplying $4 \times 7$ first, we can group $4$ and $25$ together because $4 \times 25$ is a friendly number ($100$). $4 \times 7 \times 25 = (4 \times 25) \times 7$ $100 \times 7 = 700$

The Distributive Property

The distributive property lets you break apart a larger number into smaller, easier numbers (usually tens and ones), multiply each part, and then add them together.

Rule: $a \times (b + c) = (a \times b) + (a \times c)$

Example: Use the distributive property to find $6 \times 48$. Break $48$ into $40 + 8$. $6 \times 48 = 6 \times (40 + 8)$ Now, multiply $6$ by both parts: $(6 \times 40) + (6 \times 8) = 240 + 48 = 288$

Putting It All Together

Let's use properties to calculate $5 \times 36 \times 2$. Using the commutative property, we can swap the $36$ and the $2$: $5 \times 2 \times 36$ Using the associative property, we group $5$ and $2$ first: $(5 \times 2) \times 36$ $10 \times 36 = 360$

By using these properties, a difficult problem becomes a quick mental math trick!