Numerator and Denominator: Definition, Difference, Types of Fraction
A numerical term that symbolizes one part divided into equal parts is a fraction in mathematics. The divisible quantities can be represented by separating the values with a horizontal line. To know what is numerator and denominator? Read the proceeding explanations. The number placed above it is known as a numerator, and the number set below is known as a denominator.
The horizontal line separating the numerator from the denominator is the vinculum. This horizontal line is also used to represent division operations. However, a fraction is somewhat different. Even though division operations also have a numerator and a denominator, the numerator is treated as a dividend, and the denominator is treated as a divisor.
What is a Fraction?
In simple terms, a fraction represents the portion of a thing as a whole. For example, if a bar of chocolate is divided into ten equal pieces, then each chocolate piece will be represented as 1/10. This representation shows us the value of one piece of chocolate as a portion of the whole bar of chocolate.
Fractions are a convenient way to distribute the numbers. Hence, making the calculation faster. On the other hand, fractions are also represented through decimal values. Nonetheless, fractions look simpler and are easily understandable. But, what is numerator and denominator?
A nice way of identifying a fraction is by looking for a horizontal line that separates the numerator and the denominator. This horizontal line makes it understandable that the value placed above it is a numerator and the value placed below it is a denominator.
The numerator signifies the total parts taken, and the denominator indicates the entire parts as a whole.
For example, if ⅖ is a fraction, then
2 is a numerator, and 5 is a denominator.
Types of Fractions
Based on the numeric value of the numerator and denominator, fractions can be of two kinds.
- Improper fractions
- Proper fractions
Improper fractions – In this type of fraction, the numerator has a greater value than the denominator. Solving mixed fractions results in improper fractions.
For example- 7/2, 11/5, 7¾, and so on.
Proper fractions – In proper fractions, the numerator has a lower value than the denominator. These are called proper fractions because they are easily divisible.
For example – 3/8, 2/9, 6/7, and so on.
What is a Numerator?
In a fraction, two numerical values are separated by a horizontal line. In this representation of a fraction, the numerator is the value placed above this horizontal line.
A numerator signifies the parts taken from the total parts. In other words, a numerator is divided by a denominator to simplify a fraction.
A numerator can represent selected or removed parts from the total number of elements. For example, if a square is cut into four equal pieces and one among them is removed, the fraction of the remaining parts of the square can be represented as ¾.
Common examples of the numerator
| Fraction | Numerator | Denominator |
| 7/11 | 7 | 11 |
| (2 + 5)/ 14 | (2 + 5) | 14 |
| 2q/3c | 2q | 3c |
| 8/(18 – 4) | 8 | (18 – 4) |
| 7/6 | 7 | 6 |
What is a Denominator?
The numerical value placed below the horizontal line is known as a denominator. The value of a denominator represents the total number that an object is divided into.
While the numerator shows the selected parts, the denominator shows all the parts. For example – if a pizza has a total of 6 slices and someone eats one, then the fraction representing the leftover slices of the pizza is expressed as 5/6. Here, 6 is a denominator representing the total number of pizza slices.
Common examples of the denominator
| Fractions | Denominator |
| 12/5 | 5 |
| 11/3 | 3 |
| 2/10 | 10 |
| 3x/2y | 2y |
| 2m + n/5 | 5 |
| p – q/7 | 7 |
Why Are Numerators and Denominators Important for Learning Math?
A numerator and denominator form a fraction. A fraction is important in understanding the relations between different values. A fractional representation of numeric values helps understand the nature and interactions of the numeric values.
Fractions are applicable not only in academics but also in real life. The numerator and denominator values help to understand the nature of the fraction. By knowing the numerator and denominator values, one can understand the total output of the fractional value.
Fractions help divide time, material, food, and other physical and non-physical entities.
Can a Numerator be 0?
You may see a fraction where the numerator is 0. It is a special case where the resulting value of the fraction also becomes 0 when the numerator is 0.
It also signifies that no matter what the value of the denominator is, the resulting simplification of the fraction will be 0 if the numerator is 0.
What Will Be the Value of the Fraction If the Denominator Is?
Generally speaking, a denominator is never supposed to be 0. It is because the denominator represents the total number of a thing, and when this total number is 0, the fraction does not exist.
In other words, the fractions where the denominator is 0 are termed undefined.
What Is the Difference Between the Numerator and the Denominator in a Fraction?
Even though the numerator and denominator are parts of the same fraction, they still hold different significance.
Refer to the table below to understand the difference between a numerator and a denominator.
| For example, 11/3, where 3 is the denominator. | Denominator |
| The value placed above the horizontal line in a fraction is called a numerator. It signifies the number of parts taken out of the whole. | The numeric value below the vinculum of a fraction is called the denominator. It represents the total number of equal parts as a whole. |
| If the numeric value of the numerator is zero, then the resulting value of the complete fraction is also equal to zero. | The value of a denominator can never be zero. It is because zero parts of something can never make up a whole. |
| If the value of the numerator is greater than or equal to the value of the denominator, then the fraction is called an improper fraction. | The fraction is a proper fraction when the denominator is greater than the numerator. |
| The numerator of a fraction also acts as a dividend. | The denominator of a fraction also acts as a divisor. |
| For example, 11/3, here 11 is the numerator. | For example, 11/3, here 3 is the denominator. |
What Difference Can a Denominator Make in a Fraction?
A denominator appears at the bottom of a fraction. It signifies that its value can certainly impact the resulting value of the whole fraction.
Not all fractions have a denominator that has a greater value than the numerator. And depending upon the value of a denominator; fractions can be of two types –
- Proper fraction
- Improper fraction
To understand the above types of fractions, one can take a look at the examples given below.
- 15/23 – This is a proper fraction. It is because the denominator has a greater value than the numerator. Here, 15 denotes the value of the numerator, and 23 indicates the value of the denominator.
- 3/8- This is a proper fraction. The greater numeric value of the denominator makes this fraction a proper fraction. Here, 3 is the numerator, and 8 is the denominator.
- 13/7- This is an improper fraction. It is because the value of the denominator is less than that of the numerator. Here, 13 is the numerator, and 7 is the denominator.
- 6/5- It is an improper fraction. The value of the denominator is 5, which is less than the value of the numerator, 6.
Some Examples of Proper Fractions
In proper fractions of fractions, the value of the numerator is always less than the value of the denominator. These types of fractions are usually easy to solve.
Some examples of proper fractions are – 7/11, 3/7, 2/6, 23/47, and so on.
Some Examples of Improper Fractions
Improper fractions refer to fractions in which the value of the numerator is always greater than the value of the denominator. These are complex types of fractions that are formed by the simplification of mixed fractions.
Examples of mixed fractions are – 4¾, 7⅞, 5⅝, 3⅔, 9¾, and so on.
Examples of improper fractions are- 15/4, 7/4, 17/9, 13/11, 18/5, and so on.
Summary
Numerators and denominators are the essential values that help in understanding the nature of a fraction. Knowing these values helps better understand the given fraction and see whether it is a proper or an improper fraction. From the above explanation, it is clear what is numerator and denominator. It is easy to identify which value of a given fraction is a numerator or a denominator.
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