Multiplication is adding the same number over and over.
If you want to be fancy, you can say multiplication is repeated addition.
Let's learn about five properties of multiplication.
Tip: Properties are rules that help you multiply numbers more easily.
The identity property of multiplication tells you that multiplying a number by 1 gives you the same number.
Take a look:
1 × 56 = 56
1 × 971 = 971
3,829 × 1 = 3,829
Nothing changes when you multiply a number by 1.
The zero property of multiplication tells us that any number multiplied by 0 equals zero.
65 × 0 = 0
872 × 0 = 0
0 × 34,561 = 0
No matter what number you multiply by zero, the answer will always be zero.
The commutative property of multiplication tells you that changing the order of the factors does not change the answer.
Take a look
4 × 3 = 12 = 3 × 4
The property is true even if we have three numbers we multiply together:
2 × 3 × 4 =
4 × 3 × 2
Both sides above equal 24.
The associative property of multiplication tells us that if we're multiplying three or more factors, changing the order of which we multiply first doesn't change the product, or answer.
Let's look at an example:
2 × 5 × 4 = ?
Let's try multiplying the first two factors first.
(2 × 5) × 4 = 10 × 4 = 40
Now, let's try multiplying the last two factors first.
2 × (5 × 4) = 2 × 20 = 40
The answer is the same.
So changing which of the factors we multiplied first didn't change the answer! This is the associative property of multiplication. 😀
The distributive property of multiplication helps us solve equations just like this:
8 × (5 + 7) = ?
The distributive property says that we can distribute, or hand out, the 8 x to each of the addends.
After we distribute, we end up with:
(8 × 5) + (8 × 7) =
40 + 56 =
96 ✅
Let's check if we get the same answer without distributing:
8 × (5 + 7) =
8 × 12 =
96
Yes, the answer is the same, 96.
So we see that:
8 × (5 + 7) = (8 × 5) + (8 × 7) ✅
Here's another example of the distributive property:
Great job learning about the properties of multiplication.
Do you remember all five? Complete the practice to find out.