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# Kids Math

## Basic Laws of Math

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

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

 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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