# Algebra Properties

23 cards

basic algebraic properties

Created Oct 1, 2010
by
barr04

 Shuffle Cards

# Flashcard Set Preview

 Side A Side B 1 Commutative Property of Addition For all real numbers a and b, a + b = b + a 2 Associative Property of Addition For all real numbers a, b, and c, a + (b + c) = (a + b) + c 3 Identity Property of Addition There is a unique real number 0 such that for every real number a, a + 0 = a  ... 4 Additive Inverse Property (property of opposites) For every real number a, there is a unique real number -a such that, a + (-a) = 0   ... 5 Associative Property of Multiplication For all real numbers a, b, and c, (ab)c  = a(bc) 6 Commutative Property of Multiplication For all real numbers a and b, ab = ba 7 Transitive Property of Equality For all real numbers a, b, and c, if a = b and b = c, then a = c. 8 Reflexive Property of Equality For each real number a   a = a 9 Symmetric Property of Equality For all real numbers a, b, if a = b, then b = a 10 Closure Property For all real numbers a and b, a + b  is a unique real number and ab  is a unique... 11 Property of Opposite of a Sum For all real numbers a, and b,  -(a + b) = -a + (-b) 12 Distributive property with respect to addition For all real numbers a, b, and c,  a(b + c) = ab + ac 13 Distributive property with respect to subtraction For all real numbers a, b, and c, a(b - c) = ab - ac 14 Definition of subtraction For all real numbers a and b, a - b = a + (-b)(To subtract b, add the opposite of b) 15 Identity Property of Multiplication There is a unique number 1 such that for every real number a, 1(a) = a and (a)1 = a. 16 Multiplicative Property of Zero For every real number a, a • 0 = a  and 0 • a = a. 17 Multiplicative Property of -1 For every real number a, (-1)a = -a and a(-1) = -a.When a = (-1), then (-1)(-1) = 1 18 Property of Opposites in Products For all real numbers a and b, -a(b) = -ab, a(-b) = -ab, and (-a)(-b) = ab 19 Multiplicative Inverses (reciprocals) Two numbers whose product is 1 20 Property of Reciprocals For every NONZERO number a, there is a unique number 1/a such that a • 1/a = 1 and 1/a •... 21 Property of the Reciprocal of the Opposite of a Number For every nonzero number a, -1/a = 1(-a)This is read "The reciprocal of the opposite of... 22 Property of the Reciprocal of a Product For all NONZERO numbers a and b, 1/ab = 1/a • 1/b(the reciprocal of the product of 2... 23 Definition of Division For every real number a and every NONZERO real number b, the quotient a ÷ b, or a/b, is defined...