Fractions are numbers that express partial quantities of numbers. To know fractions, it's important to understand the two categories of numbers that make up fractions. A fraction is a way of expressing how the two basic parts of a fraction -- the numerator and the denominator -- relate to each other. Once you understand numerators and denominators, you'll be able to use fractions easily.

## Numerator and Denominator

**The numerator and denominator** of a fraction are the two numbers that make the fraction. The numerator is the top number of a fraction. The denominator is the bottom number. Suppose you have the fraction 2/3. The numerator is 2, and the denominator is 3. A common trick for remembering numerator and denominator is to associate the *n* in the word *numerator* with north, to remember that the numerator is on top, and the *d* in the word *denominator* to signify that the denominator is *down* or below the numerator.

Sometimes, when using fractions, youâ€™ll see two fractions that have different denominators that you have to add or multiply. Two or more fractions that have different denominators are known as **unlike denominators.** When you work with fractions that have unlike denominators, you have to convert them to a common denominator.

## What Do the Numerator and Denominator Signify?

**The denominator of a number shows** what fraction of 1 a fraction is counting. For example: 1/4 means one-quarter. The 4 signifies that you are splitting 1 into four parts. Similarly, 1/2 is one-half, and 1/3 is one-third. **The numerator shows** how many divisions are being counted. So, 2/4 is two quarters, 3/4 is three quarters and 4/4 is four quarters.

Numerator and denominator also signify division. **A fraction is equal** to its numerator divided by its denominator. Usually, doing this division will produce a decimal. For example, 1/4 is equal to 0.25. This also means that a fraction like 4/4, which has the same number as the numerator and denominator, is equal to 1.

## Improper Fractions

**The numerator of a fraction can be larger than the denominator.** If the numerator is larger, then the fraction is larger than 1 -- and is called an *improper fraction*. For example, the fraction 7/4 is 7 fourths. If you can divide an improper fraction's numerator evenly by its denominator, then the improper fraction is equal to a whole number. For instance, the improper fraction *18/6* is equal to the whole number *3.*

An improper fraction that has a denominator of 1 will always be equal to its numerator. So, the improper fraction of *7/1* = *7*. This is true because dividing a number by 1 will always give you the original whole number.

## Mixed Fractions

**Since an improper fraction is larger than 1,** you can also express it as a *mixed fraction,* such as 4 3/5. A mixed fraction is equal to the whole number outside of the fraction plus the fraction. For example, take the fraction *7/4.* If you divide the fraction, you find that 4 goes into 7 once, and has a remainder of 3. Place the quotient of the division outside the fraction, and set the remainder as the new numerator. The denominator stays the same. So, since 4 went into 7 one time with a remainder of 3, then the improper fraction *7/4* equals the mixed fraction *1 and 3/4.*

**You can convert a mixed fraction** into an improper fraction, using the reverse process. To convert a mixed fraction into an improper fraction, multiply the number outside the fraction by the denominator, then add it to the numerator. For example, take the mixed fraction *3 and 1/6.* First, multiply 3 times 6 to get 18. Then, add *3* to the numerator of *18,* which results in *19.* So, the mixed number *3 and 1/6* equals the improper fraction *19/6.*