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A group of numbers that include 1,2, 3,.....
the set of positive whole numbers and their opposites(negative numbers) and 0
Numbers that include integers, wholes, and natural numbers.
any number that cannot be expressed as a fraction.
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.
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
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.
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
Changing the order of the factors does not change the product.
Changing the grouping of the factors does not change the product.
The product of any number and one is that number.
a + (-a) = 0 = (-a) + a OR a * 1/a = 1 = 1/a * a; a cant be 0
(a + b) and (a * b) is a real number
This is done by breaking a large fact into two smaller known facts.
A number that can only be divided by 1 and itself. The numbers left at the bottom of the tree
a number with more than two factors.
the answer to an addition problem
the answer to a subtraction problem
the answer to a multiplication problem
the answer to a division problem
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.
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.
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.