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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

Advanced Kids Math Subjects

Multiplication
Intro to Multiplication
Long Multiplication
Multiplication Tips and Tricks

Division
Intro to Division
Long Division
Division Tips and Tricks

Fractions
Intro to Fractions
Equivalent Fractions
Simplifying and Reducing Fractions
Adding and Subtracting Fractions
Multiplying and Dividing Fractions

Decimals
Decimals Place Value
Adding and Subtracting Decimals
Multiplying and Dividing Decimals 		Statistics
Mean, Median, Mode, and Range
Picture Graphs

Algebra
Order of Operations
Exponents
Ratios
Ratios, Fractions, and Percentages

Geometry
Polygons
Quadrilaterals
Triangles
Pythagorean Theorem
Circle
Perimeter
Surface Area

Misc
Basic Laws of Math
Prime Numbers
Roman Numerals
Binary Numbers


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