Kids Math

Basic Laws of Math

**Commutative Law of Addition**
The Commutative Law of Addition says that it doesn't matter what order you add up numbers, you will always get the same answer. Sometimes this law is also called the Order Property.

Examples:

x + y + z = z + x + y = y + x + z

Here is an example using numbers where x = 5, y = 1, and z = 7

5 + 1 + 7 = 13

7 + 5 + 1 = 13

1 + 5 + 7 = 13

As you can see, the order doesn't matter. The answer comes out the same no matter which way we add up the numbers.

**Commutative Law of Multiplication**
The Commutative of Multiplication is an arithmetic law that says it doesn't matter what order you multiply numbers, you will always get the same answer. It is very similar to the communtative addition law.

Examples:

x * y * z = z * x * y = y * x * z

Now let's do this with actual numbers where x = 4, y = 3, and z = 6

4 * 3 * 6 = 12 * 6 = 72

6 * 4 * 3 = 24 * 3 = 72

3 * 4 * 6 = 12 * 6 = 72

**Associative Law of Addition**
The Associative Law of Addition says that changing the grouping of numbers that are added together does not change their sum. This law is sometimes called the Grouping Property.

Examples:

x + (y + z) = (x + y) + z

Here is an example using numbers where x = 5, y = 1, and z = 7

5 + (1 + 7) = 5 + 8 = 13

(5 + 1) + 7 = 6 + 7 = 13

As you can see, regardless of how the numbers are grouped, the answer is still 13.

**Associative Law of Multiplication**
The Associative Law of Multiplication is similar to the same law for addition. It says that no matter how you group numbers you are multiplying together, you will get the same answer.

Examples:

(x * y) * z = x * (y * z)

Now let's do this with actual numbers where x = 4, y = 3, and z = 6

(4 * 3) * 6 = 12 * 6 = 72

4 * (3 * 6) = 4 * 18 = 72

**Distributive Law**
The Distributive Law states that any number which is multiplied by the sum of two or more numbers is equal to the sum of that number multiplied by each of the numbers separately.

Since that definition is a bit confusing, let's look at an example:

a * (x +y + z) = (a * x) + (a * y) + (a * z)

So you can see from above that the number a times the sum of the numbers x, y, and z is equal to the sum of the number a times x, a times y, and a times z.

Examples:

4 * (2 + 5 + 6) = 4 * 13 = 52

(4 *2) + (4*5) + (4*6) = 8 + 20 + 24 = 52

The two equations are equal and both equal 52.

**Zero Properties Law**
The Zero Properties Law of multiplication says that any number multiplied by 0 equals 0.

Examples:

155 * 0 = 0

0 * 3 = 0

The Zero Properties Law of addition says that any number plus 0 equals the same number.

155 + 0 = 155

0 + 3 = 3

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