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pPreAlg Number Prop
PreAlgebra Number Properties
| Term | Definition | |
|---|---|---|
| Commutative Property of Addition | The order in which two numbers are added does not matter | a + b = b + a |
| Commutative Property of Multiplication | The order in which two numbers are multiplied does not matter | a x b = b x a |
| Associative Property of Addition | States that the way in which numbers are grouped when more than two numbers are added does not matter (grouping symbols) | (a + b) + c = a + (b + c) |
| Associative Property of Multiplication | States that the way in which numbers are grouped when more than two numbers are multiplied does not matter (grouping symbols) | (a x b) x c = a x (b x c) |
| Identity Property of Addition (Addition Property of Zero) | Shows that 0 added to a number is equal to that number | a + 0 = a |
| Identity Property of Multiplication (Multiplication Property of One) | Shows that a number multiplied by 1 is equal to that same number | a x 1 = a |
| Inverse Property of Addition | Shows that a number added to its opposite is equal to 0 | a + (-a) = 0 |
| Inverse Property of Multiplication | Shows that a number multiplied by its reciprocal is equal to 1 | a/b x b/a = 1 |
| Distributive Property | States that every term of a sum or difference inside parentheses is multiplied by whatever is outside the parentheses | a(b + c) = a x b + a x c or a(b - c) = a x b - a x c |
| Addition Property of Equality | States that two sides of an equation remain equal if the same number is added to both sides of the equation | If a = b, then a + c = b + c |
| Subtraction Property of Equality | States that two sides of an equation remain equal if the same number is subtracted from both sides of the equation | If a = b, then a - c = b - c |
| Multiplication Property of Equality | States that two sides of an equation remain equal if both sides of the equation are multiplied by the same number | If a = b, then a x c = b x c |
| Division Property of Equality | States that two sides of an equation remain equal if both sides of the equation are divided by the same number | If a = b and c does not equal 0, then a/c = b/c |
| Multiplication Property of Zero | Shows that a number multiplied by 0 is 0 | a x 0 = 0 |
| Product of Powers Property | To multiply numbers with exponents that have the same base, add the exponents and keep the base the same | a^m⋅a^n = a^(m + n) |
| Quotient of Powers Property | To divide numbers with exponents that have the same base, subtract the exponent of the denominator from the exponent of the numerator and keep the base the same | a^m /a^n = a^(m − n), a ≠ 0 |
| Power of a Power Property | To simplify a number with an exponent that is raised to a power, multiply the exponents | (a^m)^n = a^(mn) |
| Addition Property of Inequality | States that two sides of an inequality remain balanced if the same number is added to both sides | If a > b, then a + c > b + c. |
| Subtraction Property of Inequality | States that two sides of an inequality remain balanced of the same number is subtracted from both sides | If a > b, then a − c > b − c. |
| Power of a Product Property | To simplify a product raised to a power, raise each factor to the power | (ab)^m = (a^m)( b^m) |
| Zero Exponents | A base with an exponent of 0 equals 1 | a^0 = 1, a ≠ 0 |
| Negative Exponents | For any integer n and any nonzero number a, a^(−n) is the reciprocal of a^n. | a^(−n) = 1/a^n , a ≠ 0 |
Created by:
PRO Teacher
shelleypruit
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