# AG 1 BM 21-22 Properties of Real Numbers

AG 1 BM 21-22 Properties of Real Numbers

## Terms

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- addition property of equality
- that allows one to add the same quantity to both sides of an equation. This, along with the multiplicative property of equality, is one of the most commonly used properties for solving equations. Ex: If a = b, then a + c = b + c
- symmetric property
- If if a = b then b = a. This is one of the equivalence properties of equality.
- multiplicative identity
- If you multiply any quantity by one, the resulting quantity remains the same. Ex: a ( 1 )=a
- multiplication property of equality
- If two numbers are equal then the product of these two numbers and another number is also equal. Ex: If a = b, then c ( a )= c ( b )
- additive inverse
- The opposite of a number. When a number is added to its additive inverse, the sum is zero. Ex: a + -a = 0
- zero product property
- if the product of two factors is zero, then at least one of the factors must be zero. Ex: If ab = 0, then a = 0 or b = 0.
- additive identity
- If you add zero to any quantity, the resulting quantity remains the same. Ex: a + 0 = a
- substitution property
- if a = b, then a can be substituted for b in any equation or inequality. Ex: If c = a + 2, then c = b + 2
- multiplicative inverse
- Reciprocal of a number. When a number is multiplied by its multiliped by its multiplicative inverse , the products is always one. The reciprocal of is .
- associative property of addition
- The sum stays the same when the grouping of addends or factors is changed. Ex: ( a + b ) + c = a + ( b + c) or ( a b ) c = a ( b c)
- distributive property
- The product of a number and the sum or difference of two numbers is equal to the sum or difference of the two products. Ex: c ( a + b) = ac + bc
- commutative property
- The sum stays the same when the order of the addends or factors is changed Ex: a + b = b + a or ab =ba