Question

The following examples illustrate the inverse property of multiplication. Study the examples, then choose the statement that best describes the property.

1/5 • 5 = 1 √2 ( 1 √2 ) = 1

Inverse property of multiplication: For all real numbers except __, a • __ = 1.

Answer 1

For all real numbers a except 0, we have

a(1/a) = 1

Explanation:

Multiplication of real numbers are having the following properties:

i) commutative = ab = ba

ii) associative a(b+c) =ab+ac

iii) Multiplicative identity element exists such that for any number

a*1 =1*a = a

i.e. 1 is identity.

Inverse property is for any a not equal to 0, we have a real number such that

a*that real number = multiplicative identity

i,.e. a(a real number) = 1, a not equal to 0

In other words, there exists an 1/a for all a not equal to 0 satisfying a*1/a = 1