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Explore two parts of a fraction called the numerator and denominator. Discover what these two numbers represent as you further your understanding of fractions.
Numerator and Denominator
The first time you saw a fraction, you probably noticed that there were two numbers involved: a top number and a bottom number. You may have wondered what these numbers are and what they represent. These two numbers are called a numerator and a denominator, and they both represent different things. The simplest way to define a numerator and a denominator is the following:
Numerator: the top number of a fraction
Denominator: the bottom number of a fraction
Consider these examples.
The fraction 4/7 has a top number 4 and a bottom number 7. Therefore, the numerator is 4, and the denominator is 7.
The fraction 10/3 has a top number 10 and a bottom number 3. Thus, the numerator is 10, and the denominator is 3.
What Do the Numerator and Denominator Represent?
It’s time to explore what the numerator and the denominator represent in a fraction. One way dictionary.com defines a fraction is as ‘a part as distinct from the whole of anything; portion or section.’ In other words, a fraction represents a part of a whole. In a fraction, the denominator represents the number of equal parts in a whole, and the numerator represents how many parts are being considered.
You can think of a fraction as p/q is as p parts, which is the numerator of a whole object, which is divided into q parts of equal size, which is the denominator. For example, in the fraction 5/9, the numerator is 5 and the denominator is 9, so the fraction 5/9 means 5 parts of a whole object, which is divided into 9 parts of equal size.
Pizza Example
For a more concrete example, imagine you are at a get-together with a couple of your friends. You decide to order a pizza and, when it is delivered, it has already been cut into 8 equal slices.
Assume your friend takes 3 slices of this pizza, and you want to determine what the numerator and the denominator would be in the fraction representing those 3 slices. In this case, the slices are the parts, and the pizza is the whole. You see that 8 pieces makes up the whole pizza, so this would be the denominator, which is the number of equal parts in the whole. Since your friend took 3 slices, you are considering 3 parts of the whole, so 3 would be the numerator. Thus, you determine that you would represent 3 slices of this pizza using the fraction 3/8. That is, 3 slices of the pizza represent 3/8 of the pizza.
 
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