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Natural numbers

A group of numbers that include 1,2, 3,.....

0,1,2,3,4,5...

Whole Numbers

Integers

the set of positive whole numbers and their opposites(negative numbers) and 0

Rational numbers

Numbers that include integers, wholes, and natural numbers.

Irrational Numbers

any number that cannot be expressed as a fraction.

real numbers

Any Number

1,2,3,4...

counting (natural)

no pattern

Irrational numbers

0!!!,1,2,3,4...

Whole numbers

Substitution property

a(b) = (ab)

1/-a = -1/a

Property of reciprocals of the opposite of a number

commutative property of addition

If the order of the terms changes, the sum stays the same.

ab=ba

Commutative Property of Multiplication

associative property of addition

When the grouping of terms changes, the sum stays the same.

(a∙b)c = a (b∙c)

Associative property of multiplication

a (-1) = -a

Multiplicative property of -1

a∙1 = a

Identity Property of Multiplication

a∙ ¹⁄a = 1

Property of Reciprocals (Inverse property of Multiplication)

a∙0 = 0

Multiplicative property of zero

a + (-a) = 0

Property of Opposites (Inverse property of addition)

Definition of Division

a ⁄ c + b ⁄ c = a+b ⁄ c or a ⁄ c - b ⁄ c = a-b ⁄ c

-(X+Y) = (-X) + (-Y)

Property of the opposite of a sum

Definition of Substraction

a + (-b) = a-b

a=a, x+3=x+3

Property of Equality-Reflexive

Property of Equality-Symmetric

If a=b then b=a if x=3 then 3=x

Property of Equality-Transitive

If a=b and b=c then a=c

Real Number (R)

Any type of number

Rational Number (Q)

Can be expressed as a ratio; terminating decimal, or repeating decimal.

Irrational Number (I)

Is a non terminating decimal, or does not repeat; 3.14 or a square root that cant be squared.

Integers (Z)

Any positive or negative number (as long as it isn't a decimal)

Natural Number (N)

Starting from 1, and increasing by 1; 1,2,3,4,5...... (negatives or 0 is not included)

Whole Numbers (W)

Includes all natural numbers AND 0

Commutative

Changing the order of the factors does not change the product.

associative

Changing the grouping of the factors does not change the product.

Identity

The product of any number and one is that number.

Inverse

a + (-a) = 0 = (-a) + a OR a * 1/a = 1 = 1/a * a; a cant be 0

Closure

(a + b) and (a * b) is a real number

Distributive

This is done by breaking a large fact into two smaller known facts.

Prime number

A number that can only be divided by 1 and itself. The numbers left at the bottom of the tree

Composite number

a number with more than two factors.

sum

the answer to an addition problem

difference

the answer to a subtraction problem

product

the answer to a multiplication problem

quotient

the answer to a division problem

Whole Numbers

Zero and the counting numbers 1, 2, 3, 4, 5, 6, and so on. If a number has a negative sign, a decimal point, or a part that's a fraction, it is NOT a whole number.

Imaginary numbers

A subset of the complex number system. A number which can be written in the form a + bi where b ≠ 0 and i represents the square root of -1.

Consecutive integers

Integers that follow each other in order with a difference of 1 between every two numbers. Ex. 7, 8, 9. Represented by n, n+1, n+2, n + 3 ...

Reflexive Property of Equality

Any number equals itself. x = x

Symmetric Property of Equality

For all real numbers x and y, if x = y, then y = x.

Transitive Property of Equality

For all real numbers x, y, and z , if x = y and y = z, then x = z.

Addition Property of Equality

For all real numbers x, y, and z, if x = y, then x + z = y + z.

Subtraction Property of Equality

For all real numbers x, y, and z, if x = y, then x - z = y - z.

Multiplication Property of Equality

For all real numbers x, y, and z, if x = y, then xz = yz.

Division Property of Equality

For all real numbers x, y, and z, if x = y, and z ≠ 0, then x/z = y/z. You can divide each side of an equation by the same non-zero number and not change its truth value.

Substitution Property of Equality

For all real numbers x and y, if x = y , then y can be substituted for x in any expression and vice versa.

Distributive Property of Equality

For all real numbers x, y, and z, x(y + z) = xy + xz.