# The product of the reciprocal of 2 consecutive integers is 1/30. What are the numbers?

##### 2 Answers

There are two possibilities:

#5# and#6# #-6# and#-5#

#### Explanation:

#1/5*1/6 = 1/30#

#1/(-6)*1/(-5) = 1/30#

There are two possibilities:

#### Explanation:

Call the two integers

The reciprocals of these two integers are

The product of the reciprocals is

Thus, we know that

Multiply both sides by

However, this doesn't really solve the problem: we have to address that fact that the integers are consecutive. If we call the first integer

To solve

If

#1/(-6)xx1/(-5)=1/30#

If

#1/5xx1/6=1/30#