Numerator and denominator are two parts of a fraction. They represent the parts in context and the total number of equal parts that form the whole. Let us first explore the definitions and then we shall illustrate fractions including numerator and denominator with examples.
A fraction is a portion or a part of an entire object. Imagine a standard ruler which is twelve inches or a foot long, also representing a little more than thirty centimeters. The whole ruler is the object here which can be divided into many parts. You could take just two inches out of twelve, you may take fifteen centimeters out of thirty and you can take multiple smaller parts which can form the whole ruler. Every small part you form is a fraction of the whole object.
Numerator and Denominator: Definition
Numerator is a number that represents the parts of the whole being considered as taken. Denominator is a number that represents all the parts of the whole. Whenever you break an object into several parts, you would have to account for all the parts to make sense of the parts being considered or taken into the calculations. Let us use the ruler example to illustrate this.
Numerator and Denominator: Illustrated
Imagine the standard twelve inches or one foot long ruler and break it down into twelve equal parts. In here, every part is of one inch. There are twelve parts of an inch each accounting for the twelve inches or a foot. Now, let us consider a straight line that you wish to draw that runs for three inches. You may take the ruler, line it up and draw the straight line from the ‘zero’ mark to the ‘three’ mark on the ruler. This will give you a straight line of three inches. Since you have already considered that every inch is a part of the ruler which has twelve parts, you can say that the straight line is three-twelfth (3/12) of the ruler.
In the above example, three (3) is the numerator and twelve (12) is the denominator. The numerator and the denominator collectively form the fraction. Let us consider another example.
Presume a circle of any radius or diameter. The size doesn’t matter but it should be a perfect circle, not a semicircle or oval shaped object. Take a standard ruler and draw a straight line right at the middle of the circle. Take the centre of the circle and make sure you draw a straight line. Draw the line which will cut the circle in half.
Now, what do you see? You would see a circle cut in half. That gives you two parts. You may also call these halves. The two halves or parts make the full circle. Now, you can color one half or part of the circle. You have one colored half and the other as it was. If you have to represent the colored half of the circle, you would say that one part of the two parts or one half of the two halves is colored. You would represent it as 1/2. Here ‘1’ is the numerator representing the colored half and ‘2’ represents both the parts, aka halves, of the circle that you have created by initially drawing the straight line cutting through the middle of the circle.
You can take this a step further. Draw another straight line through the centre of the same circle but perpendicular to the existing straight line. This will further divide the circle into a total of four parts. You would see four equal parts of the circle, of which two equal parts would be colored because you had already colored one half of the circle. There will be two parts uncolored. Color one of the two smaller parts that are uncolored. Now, you have three colored parts and one uncolored part. There are a total of four parts that form the circle and three are colored. This can be represented in a fraction of 3/4. Here, ‘3’ is the numerator depicting the three colored parts. ‘4’ is the denominator depicting the four parts that form the circle, including the three colored and one uncolored part.
Significance of Equal Parts in a Fraction
It must be noted that when you are presenting a fraction, the numerator and denominator represents parts of a whole object and these parts are always equal. Unless you divide a whole object in equal parts, you cannot have a fraction. If you don’t have equal parts then the sum of the smaller parts taken into consideration will not lead to the actual fraction you are trying to depict. The moment you have unequal parts, the total number of parts will not form the whole object or the considered parts won’t form the true fraction of the whole.