###$$ Denominators

What is a Denominator?

A denominator is the bottom number of a fraction. The word comes from the Latin root word “denominaire” and it means “that which gives a name to”. Ancient mathematicians chose this word because the denominator of a fraction names the size of a fractional part. 

The size of a fractional part is determined by the number of parts in a whole. If there is a larger number of parts in the whole, the parts will be smaller because the whole is split into more pieces. 


The denominator of \(\frac{4}{5}\) is 5.

The denominator of \(\frac{7}{12}\) is 12.

The denominator of \(\frac{1}{2}\) is 2.

Fractions as Division

Fractions are usually interpreted as a parts of a whole. When most people see \(\frac{2}{3}\), they think of one whole split into three parts with two of the parts shaded.  

However, fractions can also be interpreted as division. For example, \(\frac{2}{3}\) could be seen as two wholes that are divided equally among three people. 

Either way, the amount represented by the fraction \(\frac{2}{3}\) is the same. There are just two different ways of thinking about it. When fractions are interpreted as division, the denominator of the fraction is the divisor of the division problem. 

When Will I Use Denominators?

Any time you add or subtract fractions, you have to find common denominators because you can’t add fractions if the fraction parts are not the same size. 

When you have a square root in the bottom of a fraction, you may be asked to rationalize the denominator before you submit your answer. 

If you have variables like x or y in a fraction, that means you are dealing with a rational expression. You can follow these rules to simplify rational expressions or you can follow these steps to solve rational equations if there is an equal sign. 

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