# Basic Arithmetic : Reciprocals

## Example Questions

### Example Question #1 : Manipulation Of Fractions

What is the reciprocal of ?

Explanation:

To get the reciprocal of a fraction, you simply switch the numerator and the denominator.

In our case our numerator is  and our denominator is .

So  becomes .

### Example Question #1 : Reciprocals

Compute:

Explanation:

We will need to rewrite this in order to eliminate the negative exponent in the problem.

Because the denominator has a negative exponent, that is the same as having a positive exponent in the numerator. Therefore we can rewrite the problem as follows and then multiply.

### Example Question #2 : Reciprocals

Evaluate:

Explanation:

To divide a term by a fraction, take the reciprocal of the fraction.

Then mutiply both terms.

### Example Question #3 : Reciprocals

What is the sum of the reciprocal of  and ?

Explanation:

To find the reciprocal of a fraction, flip the numerator and the denominator.

Thus, the reciprocal of  is .

Then we need to find the sum of 4 and 7, which is 11.

### Example Question #4 : Manipulation Of Fractions

What is the reciprocal of  multiplied by the reciprocal of ?

Explanation:

To find the reciprocal of a fraction, we simply need to switch the numerator and the denominator: for example, the reciprocal of a fraction  is .

With integers, it helps to remember that all integers are really fractions with a denominator of :

, and

The reciprocals of these numbers are  and  respectively.

Therefore, to solve the problem, we first need to find the reciprocals of  and . If we keep in mind that , we can determine that the reciprocals are  and , respectively. The product of these two numbers is: