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Real Numbers and their properties
8/7/2023
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Real Numbers and Their Properties I. Properties of Real Numbers A. Closure Property Addition Closure • Example: 5 + 3 = 8 (Both 5 and 3 are real numbers, and their sum is also a real number) • Multiplication Closure ● Example: 2*4=8 (Both 2 and 4 are real numbers, and their product is also a real number) B. Commutative Property • Addition Commutativity • Example: 7 + 9 = 9+7 (Changing the order of addition does not affect the result) • Multiplication Commutativity ● Example: 3 * 5 = 5 * 3 (Changing the order of multiplication does not affect the result) C. Associative Property • Addition Associativity • Example: (3 + 4) + 2 = 3 + (4 + 2) (Changing the grouping of numbers during addition does not affect the result) • Multiplication Associativity • Example: (2*3)* 5 = 2 * (3 * 5) (Changing the grouping of numbers during multiplication does not affect the result) D. Identity Property • Additive Identity • Example: 6 + 0 = 6 (The sum of any real number and zero is the number itself) • Multiplicative Identity • Example: 5*1 = 5 (The product of any real number and one is the number itself) E. Inverse Property . Additive Inverse • Example: 8+ (-8)= 0 (The sum of a real number and its additive inverse is zero) • Multiplicative Inverse ●...
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Alternative transcript:
Example: 3* (1/3) = 1 (The product of a real number and its multiplicative inverse is one) F. Distributive Property • Distributive Property of Multiplication over Addition • Example: 4 * (3 + 2) = 4 * 3 + 4 * 2 (Multiplication distributes over addition) II. Examples of Real Numbers and Their Properties • Example 1: Addition and Multiplication with Positive Real Numbers • 5+3=8 • 2*4=8 • Example 2: Commutativity and Associativity 7+9=9+7 •(3+4) +2=3+(4+2) ● Example 3: Identity and Inverse • 6 +0=6 • 5*1=5 .8+(-8)= 0 • Example 4: Distributive Property • 4* (3+2) = 4 * 3+4 * 2