Reciprocals

All the following hands give the same result





More generally so do these hands



Whatever the number x is declared as

 

We have already seen that the solution to can be found from

How about  ? We already know that the solution is since we know 

The rules for solving gives that so we have that

This is true for any number x


What about something like  ? This comes from the solution to

and

When  then

When then

The solution to is 

A new name when One is divided by a number the you get the reciprocal of the number

The reciprocal of 6 is               

The reciprocal of is 6               

The reciprocal of is                

The reciprocal of is                

You form the reciprocal of a fraction by swapping over the numerator and denominator.
The product of a number and its reciprocal is always One.

In Dividing Fractions

We found that

 

Instead of dividing by a fraction we multiply by the reciprocal of the fraction.

Further Example