ALGEBRAIC PROPERTIES COMMUTATIVE PROPERTIES Commutative When Property of
ALGEBRAIC PROPERTIES
COMMUTATIVE PROPERTIES �Commutative �When Property of Addition adding two or more numbers or terms together, order is NOT important. �a +b=b+a � 2 + 7 = 7 + 2
COMMUTATIVE PROPERTIES �Commutative Property of Multiplication �When multiplying two or more numbers or terms together, order is NOT important. �a *b=b*a � 3 * 5 = 5 * 3
COMMUTATIVE PROPERTIES �Subtraction and Division are NOT commutative as shown below. � 7 – 2 ≠ 2 – 7, since 5 ≠ -5 � 50 ÷ 10 ≠ 10 ÷ 50, since 5 ≠ 0. 2
ASSOCIATIVE PROPERTIES �Associative Property of Addition �When adding three or more numbers or terms together, grouping is NOT important. �(a + b) + c = a + (b + c) �(5 + 2) + 6 = 5 + (2 + 6)
ASSOCIATIVE PROPERTIES �Associative �When Property of Multiplication multiplying three or more numbers or terms together, grouping is NOT important. �(a * b) * c = a * (b * c) �(5 * 2) * 6 = 5 * (2 * 6)
ASSOCIATIVE PROPERTIES �Subtraction and Division are NOT associative as shown below: � (5 – 2) – 3 ≠ 5 – (2 – 3), since 0 ≠ 6 � (20 ÷ 4) ÷ 2 ≠ 20 ÷ (4 ÷ 2), since 2. 5 ≠ 10
IDENTITY PROPERTIES �Identity Property of Addition �Adding zero to any expression gives the same expression. �a +0=a � 6 + 0 = 6
IDENTITY PROPERTIES �Identity Property of Multiplication �Multiplying any expression by one gives the same expression. � 1 *a=a � 1 * 6 = 6
INVERSE PROPERTIES �Additive Inverse Property �For every number a there is a number –a such that a + (-a) = 0. �A common name used for the additive inverse is the opposite. That is, -a is the opposite of a. � 3 + (-3) = 0 and -5 + 5 = 0
INVERSE PROPERTIES �
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