Properties of Real Numbers IN WORDS ISN Page 32 You have learned properties of real numbers starting in 4th grade. 8th grade math pulls them all together so that we can justify our steps when solving equations. Let’s review. 1) Addition Property of Equality: IN WORDS: If you add the same number on both sides of an equation, the two sides remain equal. 2) Subtraction Property of Equality: IN WORDS: If you subtract the same number on both sides of an equation, the two sides remain equal. 3) Multiplication Property of Equality: IN WORDS: If you multiply the same number on both sides of an equation, the two sides remain equal. 4) Division Property of Equality: IN WORDS: If you divide the same number on both sides of an equation, the two sides remain equal. 5) Associative Property of Addition: IN WORDS: The way in which addends are grouped does not change the sum. 6) Associative Property of Multiplication: IN WORDS: The way in which factors are grouped does not change the sum. 7) Commutative Property of Addition: IN WORDS: The order in which numbers are added does not change the sum 8) Commutative Property of Multiplication: IN WORDS: The order in which numbers are multiplied does not change the sum 9) Identity Property of Addition (Additive Identity) IN WORDS: The sum of an addend and zero is the addend. 10) Identity Property of Multiplication (Multiplicative Identity) IN WORDS: The product of a factor and 1 is the factor. 11) Inverse Property of Addition (Additive Inverse) IN WORDS: The sum of a number and its additive inverse is zero. 12) Inverse Property of Multiplication (Multiplicative Inverse) IN WORDS: The product of a number and its multiplicative inverse is 1. 13) Distributive Property: Not available in just words. We will practice on the back 14) Zero Product Property: IN WORDS: The product of a factor and zero is zero. There are a lot of properties to know. Use flashcards to help you remember them. Always do your assigned homework, and complete the notes on the back. Properties of Real Numbers EXAMPLES ISN Page 32 Match the property on the left with its example on the right. 1) Addition Property of Equality: Example: A a + (b + c) = (a + b) + c 2) Subtraction Property of Equality: Example: B 2 + (3+4) = (2+3) + 4 a+0=a 4+0=4 3) Multiplication Property of Equality: Example: 4) Division Property of Equality: Example: D 5) Associative Property of Addition: Example: a C (b c) = (a a 1=a b) c 4 1=4 2 (3 4) = (2 3) 6) Associative Property of Multiplication: Example: 7) Commutative Property of Addition: Example: E a b=b a 4 8) Commutative Property of Multiplication: Example: 9) Identity Property of Addition (Additive Identity) Example: a G 4 2(x + 2) = 2x + 4 4(x – 1) = 4x - 1 F 10) Identity Property of Multiplication (Multiplicative Identity) Example: 3=3 0=0 4 0=0 11) Inverse Property of Addition (Additive Inverse) Example: 12) Inverse Property of Multiplication (Multiplicative Inverse) Example: H a + (-a) = 0 3 + (-3) = 0 13) Distributive Property: Example: J 14) Zero Product Property: Example: a+b=b+a 1+4=4+1 3x = 6 3 3 K x-2=6 x-2+2=6+2 L x+1=5 x + 1 -1 = 5 - 1 M N A a 1 a =1 x 2 5 2 2 3 1 =1 3 4

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# Properties of Real Numbers IN WORDS ISN Page 32 You have