AMSCO'S Geometry. New York - Rye High School

The Real Numbers and Their Properties 5When three numbers are multiplied, two are multiplied first and thentheir product is multiplied by the third. The product does not dependon which two numbers are multiplied first. This property is called theassociative property of multiplication. For all real numbers a, b, and c:a (b c) (a b) c4. Identity PropertyWhen 0 is added to any real number a, the sum is a. The real number 0is called the additive identity. For every real number a:a 0 a and 0 a aWhen 1 is multiplied by any real number a, the product is a. The realnumber 1 is called the multiplicative identity. For every real number a:a 1 a and 1 a a5. Inverse PropertyTwo real numbers are called additive inverses if their sum is the additiveidentity, 0. For every real number a, there exists a real number a suchthat:a (a) 0Two real numbers are called multiplicative inverses if their product isthe multiplicative identity, 1. For every real number a 0, there exists a real1number a such that:6. Distributive Propertya ? 1 a 5 1The distributive property combines the operations of multiplication andaddition. Multiplication distributes over addition. For all real numbers a, b,and c:a(b c) ab ac and (a b)c ac bc7. Multiplication Property of ZeroZero has no multiplicative inverse. The multiplication property of zerodefines multiplication by zero. For all real numbers a and b:ab 0 if and only if a 0 or b 0.