What is the reciprocal, or multiplicative inverse, of any nonzero real number a is 1/a?

Question

Algebra 1 Vocabulary

Answer 1

The question ending up, what is the reciprocal of 1/a where a is nonzero real number?

The reciprocal number x makes 1 when any number is multiplied into it.

Therefore,  x * 1/a = 1

And multiply a on both sides,  x = a  Answer.

Simply the reciprocal of a is 1/a and the reciprocal of 1/a is a.

Answer 2

Yes, the multiplicative inverse (or reciprocal) of any non-zero real number, a, is 1/a.  The product of a number times its reciprocal is always equal to 1 (a*(1/a) = a/a = 1). 

 

Examples:

 

If a= 3, then 1/a = 1/3

3*(1/3) = 3/3 = 1

 

If a = -3/7, then 1/a = -7/3

(-3/7)*(-7/3) = 1