You have already learned quite a lot about fractions. Now we will look at one way we can make solving fraction problems easier. A reciprocal of a fraction is the fraction turned upside down. The denominator switches places and goes to the top of the fraction. Let's look at this example:
The reciprocal of a whole number is always 1 over the whole number.
When we understand how reciprocals work, we will better understand how changes in parts of an equation can affect other parts of the equation.
When you change a fraction to its reciprocal in one part of an equation, you must make sure to change the rest of the equation to match. For example, look at this equation:
We will change the first fraction to its reciprocal, so we must also use the reciprocal of the second fraction. The new equation is
Remember, since the denominator in 
is greater (larger) than the top number (numerator) of the fraction, the denominator in the resulting fraction, 
, must also be greater than the top number of the fraction. Look at this equation:
This is incorrect, because one denominator is greater than the top of the fraction, while the other denominator is less (smaller) than the top of the fraction.
