Understanding the Numerator in a Fraction

Suppose we ordered a medium size pizza. Usually, it is divided into 6 equal parts. Now a person eats 2 slices. If he wants to answer how much he ate of the whole pizza then what would be his answer? 

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The concept of Fractions helps to answer such questions. Fractions are the mathematical way to represent a part of an object. It has two components. The first one is the numerator and the second one is the denominator. For example \[\frac{3}{4}\]. This fraction contains 3 which is the numerator, 4 which is the denominator and the line separating them.

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What is a Numerator?

Most of us have questions like what is a numerator or what is the meaning of a numerator during our lower grade. In this section, we’ll see the numerator's meaning with its significance.

Numerator’s meaning is enumerate.It’s pronunciation is [ nōō′mə-rā′tər ]. It comes from the Latin word “enumerate”, which means to count something. We still use this word in modern English. There is one more to get as it is a contraction of the words ‘number’ and ‘tor’.

Numerator Definition: The numerator is the upper part of the fraction. It enumerates the fractional unit that is taken into consideration. In other words, how much part we are considering something whole. The numerator of a fraction tells us the count of equally divided parts that are taken under consideration. For an example consider \[\frac{2}{3}\]. It means we did 3 equal parts of something and we are considering only 2 of it.

Significance of the Numerator is Bigger than the Denominator?

Since the numerator tells us the count which is taken under consideration of something whole, so many students make the misconception that numerator can’t be bigger than the denominator. And even till now, whatever fractions we have used, all of them have the numerator less than the denominator. Which is not always true.

So is it possible to have the numerator bigger than the denominator? Fraction something like \[\frac{5}{3}\]. And even if it is possible, what is its significance?

Let us try to understand this with our conventional understanding. In fraction \[\frac{5}{3}\], 3 is the denominator and 5 is the numerator. Denominator 3 indicates that something whole is divided into 3 equal parts. Whereas the numerator 5 indicates that we are considering 5 of those equal divided parts. So, If 3 parts make a whole and we are considering 5 then we must be having a whole object plus 2 more of the equally divided parts. So, \[\frac{5}{3}\] is the same as 1 + \[\frac{2}{3}\]. There is another way to represent this is 1 \[\frac{2}{3}\]. This can be read out as “one and two-third”. 

The summary of this explanation is to know or understand that a fraction with the numerator bigger than the denominator means a number that is greater than one. This might be the reason for the subdivision of fractions. Which we’ll see in the next section.

Misconceptions about Numerator: 

Many students think the numerator will always be smaller than the denominator which is not always true and this has been a misconception among students. As we discussed in the previous section, the numerator is not necessarily smaller than the denominator and this gives further subdivision of fractions into subparts. One is proper and another one is improper fractions.

Proper fractions are fractions in which the numerator is less than or smaller than the denominator. For an example consider \[\frac{1}{3}\]. Here, the numerator is 1 which is less than the denominator which is 3. 

Improper fractions are fractions in which the numerator is not smaller than the denominator. In other words, the numerator is greater than the denominator. For an example consider \[\frac{7}{5}\]. Here, the numerator is 7 which is greater than the denominator which is 5.

Significance of Denominator Less than One.

Till now we have only discussed denominators greater than one. Now the next brain-teaser question will be what if the denominator is less than one. Let’s understand this with an example. Consider \[\frac{2}{0.5}\]. It simply means we are considering half for something as a whole.

Do you know?

1. The fraction with 1 as the numerator is called the unit fraction.

2. The fraction will become zero if the numerator is zero. And this is regardless of the denominator. For example \[\frac{0}{12}\], \[\frac{0}{1}\] and 0. These all are equal.

3. The word numerator comes from the lain word numerātor, which means counter and this can be seen in modern English also.

4. If the denominator is the same as the numerator then the value of the fraction will become 1. It means \[\frac{2}{2}\], \[\frac{35}{35}\], \[\frac{7}{7}\] and so on, all are equal to one.