Math Project 1

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Whole Numbers

Multiplying

Exponents

Repeated multiplying of the same number may be reduced to a superscript of the amount of times the number appears in the equation. This is read, "to the [#]th power."

n x n x n = n^3

Cubed

Multiplying a number by itself three times.

n x n x n

Squared

Multiplying a number by itself once.

n x n

Identity Property of One

Any number multiplied by one will result in the original number.

n x 1 = n

Multiplication Property of Zero

Any number multiplied by zero results in zero.

n x 0 = 0

Changing the grouping of factors does not change the product.

(ab)c = a(bc)

Changing the order of factors does not change the product.

ab = ba

Subtracting

Because it represents repeated addition, multiplication may be distributed over subtraction separated by parentheses.

3(4 - 3) = (4 - 3) + (4 - 3) + (4 - 3)

Therefor,

a(b - c) = ab - ac

Altering the order of numbers will yield different results.

a - b =/= b - a

Adding

Distributive Property

Because it represents repeated addition, multiplication may be distributed over other addition separated by parentheses.

3(2 + 3) = (2 + 3) + (2 + 3) + (2 + 3)

Therefor,

a(b + c) = ab + ac

Associative Property

Added numbers may be grouped in any way with the same result.

(a + b) + c = a + (b + c)

Identity Property of Zero

Any number added to zero will always result in the original number.

a + 0 = a

Commutative Property

Numbers may be added in any order with the same result.

a + b = b + a

Terms

Like Terms

Combining Like Terms

Variable Term

Constant Term

Order of Operations

4. Add & Subtract

After all other operations have been completed, addition and subtraction equally share the lowermost priority; they must be fulfilled from left to right.

3. Multiply and Divide

After parentheses and exponents have been fulfilled, multiplication and division equally share the next priority; they must be fulfilled from left to right.

2. Exponents

Numbers with exponents must be multiplied before they may be used for other operations.

1. Parentheses

Operations contained between the symbols ( and ) must supercede other operations.

Dividing

Not Distributive

Remainder

A remainder occurs when whole numbers do not divide evenly, and is signified with an R.

13/4 = 3R1

Dividing by Zero

Zero may be divided by any non-zero number, and will always result in zero.

0/n = 0

No number may be divided by zero; the result is undefined.

n/0 = ???

Dividing by One

Any non-zero number divided by itself is one.

n/n = 1

Any number divided by one remains unchanged.

n/1 = n

Not Commutative

Altering the order of numbers will yield different results.

a/b =/= b/a