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# Algebra1: Properties

### Includes the name, words, and examples

Substitution Property of Equality If two quantities are equal, then one quantity can be replaced by the other; If k = 2, then k + 1 can be written as 2 + 1
Commutative Property of Addition The order in which numbers are added does not change the sum; 3 + 4 = 4 + 3
Commutative Property of Multiplication The order in which numbers are multiplied does not change the product; 3 x 4 = 4 x 3
Associative Property of Addition The way in which numbers are grouped when added does not change the sum; (3+4) + 5 = 3 + (4=5)
Associative Property of Multiplication The way in which numbers are grouped when multiplied does not change the product; (3x4) x 5 = 3 x (4x5)
Additive Identity When 0 is added to any number, the sum is the number; 3 + 0 = 0 + 3 = 3
Additive Inverse The sum of any number and its additive inverse is 0; 3 + (-3) = 0
Multiplicative Identity When any number is multiplied by 1, the product is the number; 3 x 1 = 1 x 3 = 3
Multiplicative Inverse The product of and its multiplicative inverse is 1; 3/4 x 4/3 = 1 so 3/4 and 4/3 are multiplicative inverses
Multiplicative Property of Zero When any number is multiplied by 0, the product is 0; 3 x 0 = 0 x 3 = 3
Reflexive Property of Equality Any quantity is equal to itself; 7 = 7, 2 + 3 = 2 + 3
Symmetric Property of Equality If one quantity equals a second quantity, then the second quantity also equals the first; If 10 = 4 + 6, then 4 + 6 = 10
Transitive Property of Equality If one quantity equals a second quantity and the second quantity equals a third quantity, then the first equals the third; If 3 + 5 = 8 and 8 = 2 (4) then 3 + 5 = 2 (4)
Distributive Property To multiply a number by a sum, multiply each number inside the parentheses by the number outside the parentheses; 3 (4 + 2) = 3 x 4 + 3 x 2, (5 + 3) 2 = 5 x 2 + 3 x 2
Created by: secretyou