Numerator in Mathematics

Numerator is one of two parts of any fraction, where the other part is the denominator. Numerator and Denominator combined define any fraction in mathematics, where the numerator is the top part of the fraction representing the number of equal parts considered, while the denominator is the bottom part representing the total number of equal parts the whole is divided into. Together, they express the relative portion or value of the part being considered within the whole.

Thus, to comprehend fractions, you must first understand the notions of numerator and denominator. In this article, we will look at what the numerator is, how it is used in division, how it is used in fractions, and how it is related to the denominator.

What is a Numerator?

A ratio or any fraction consists of two parts, a Numerator (the part above the line) and a Denominator (the part below the line).

In simple words, you can say that a numerator is the number above the fraction bar, which is divided by the denominator, the number below the bar. For example, in the fraction 3/5, the numerator is 3, and the denominator is 5. Here, the numerator tells us how many equal parts of the whole we are considering.

Numerator Definition

The numerator is the top part of a fraction or a ratio and it represents the number of parts that you have or are considering.

Numerator Examples

Below are some examples on numerators:

• Pizza Slices: You have a pizza divided into 8 equal slices, and you’ve eaten 4 of them. What is the numerator in the fraction that represents the slices you’ve eaten?
• Sharing Marbles: You want to give your friend 3 out of the 6 marbles you have. What is the numerator in the fraction that represents the marbles you’re giving your friend, and what fraction of marbles are you left with?
• Cooking and Recipes: In a recipe for cookies, it states you need 2/3 cups of sugar. What does the numerator (2) in this fraction indicate?
• String Segments: You have divided a piece of string into 7 equal segments. If you plan to use 2 of these segments for your project, what is the numerator in the fraction that represents the segments you’re utilizing, and what is the ratio of the segments you’re left with to the total segments?
• Sharing Colored Pencils: You have a bunch of colored pencils, including 5 red, 7 blue, and 12 green. You decide to give 2 red and 3 blue pencils to friend A and 2 blue and 6 green pencils to friend B. What is the numerator in the fraction that represents the total pencils you have after sharing with friend A, and what fraction of the total number of pencils did you give to friend B?

Numerator in Division

When it comes to division, the numerator plays a crucial role in determining how many times one number can be divided by another. In a division expression, such as 56 ÷ 7, the numerator (56) is the dividend, representing the total quantity to be divided into parts. It helps us understand how many parts can be obtained from the whole.

Conside the below example,

Your class teacher have 12 pencils and she wants to divide them equally between 3 groups.

Here, Total number of pencils (quantity) are 12 (Dividend), also called numerator and needs to be divided in 3 equal parts so the expression becomes 12 ÷ 3 = 4.

Read More about Division.

Numerator in Fractions

Numerators are essential components of fractions. They help us express parts of a whole or a group. A Numerator of a fraction will represent the number of parts selected or removed from the total quantity.

Consider the below example,

If you have a pizza divided into 8 equal slices and you’ve eaten 3 of them, the fraction 3/8 represents the numerator (3), signifying the number of slices you’ve consumed out of the total.

Important Points about Numerator

• The fraction as a whole becomes zero regardless of the value of the denominator if the numerator is equal to zero. To provide an example, 0/50 = 0, 0/3 = 0, and so on.
• If the numerator’s value is equal to the denominator, then the fraction’s value will be equal to 1. For example, 16/16 = 1, since numerator is 16 which is equal to denominator.
• If the value numerator is greater than the denominator, then the fraction becomes an improper fraction. For example, 7 / 9 is an improper fraction.

Numerator and Denominator

The relationship between the numerator and denominator is crucial when discussing fractions, division, ratios, proportions etc. When combined, these two components make it possible to represent and understand numbers. The number of components you have or are considering is shown by the numerator, which is located above the fraction bar. The total number of equal pieces that make up the whole or the group is represented by the denominator, which is situated underneath the fraction bar.

When combined, they create a fraction of whole part, a ratio of parts, a division of parts or a proportion of two parts, that allows us to compare amounts, depict proportions accurately, and carry out mathematical operations. A thorough grasp of numerator and denominator, and their applications may be obtained by working together with these terms, whether you’re splitting a pizza, measuring components in a recipe, or any other mathematical problem.

• Fractions: In Fractions, Numerators are essential components. They help us express parts of a whole or a group.

• Ratios: In ratios, the numerator is the part of the comparison you are interested in.

• Proportions: When dealing with proportions, the numerator helps us determine how two ratios relate with each other.

Numerator Vs Denominator

The key differences between numerator and denominator are listed in the following table:

Aspect	Numerator	Denominator
Definition	The upper part of a fraction or a ratio, indicating the number of parts under consideration.	The lower part of a fraction, signifying the total number of equal parts forming the whole or the group.
Position	Positioned above the fraction bar. Positioned before the colon in ratio Positioned before the division sign	Positioned below the fraction bar. Positioned after the colon in ratio Positioned after the division sign.
Role	Specifies the quantity of parts under consideration in a fraction. Specifies the quantity of the first quantity in a ratio. Represents the dividend in a division operation. Represents the first quantity in a proportion.	Determines how many parts the whole is divided into in a fraction. Specifies the quantity of the second quantity in ratio Represents the divisor in a division operation. Represents the second quantity in a proportion.
Example	In Fraction 3/5, the numerator is 3. In the ratio 2:3, the numerator is 2. In Division 56 ÷ 7, the numerator is 56. In Proportion of 2:3 = 4:6, the numerator in both ratios is 2 and 4, respectively.	In Fraction 3/5, the denominator is 5. In the ratio 2:3, the denominator is 3. In Division 56 ÷ 7, the denominator is 7. In Proportion of 2:3 = 4:6, the denominator in both ratios is 3 and 6, respectively.

Applications of Numerators

• Cooking and Recipes: The numerator is frequently used when following recipes, where you need to determine the quantity of ingredients. For example, if a recipe calls for 2/3 cup of flour, the numerator (2) tells you how much flour you need in relation to the total cup.
• Measurement and Conversions: In everyday measurements, numerators are commonly employed. If you are traveling and need to convert 3/4 of a mile into feet, you will focus on the numerator (3) to calculate the distance in feet.
• Financial Calculations: In financial transactions, such as calculating sales tax or discounts, numerators come into play. For example, if a store offers a 20% discount on a 50 rupees item, you’ll use the numerator (20) to calculate the amount saved.

Read More,

• Addition of Fractions
• Subtracting Fractions
• Multiplication of Fractions

Practise Questions on Numerator

Question 1: If you have a pizza divided into 8 equal slices and you’ve eaten 4 of them, what is the numerator in the fraction that represents the slices you’ve eaten?

Question 2: You have a bag of marbles, and you want to give your friend 3 out of the 6 marbles you have. What is the numerator in the fraction that represents the marbles you’re giving your friend? What fraction of marbels are you left with?

Question 3: In a recipe for cookies, it says you need 2/3 cups of sugar. What does the numerator (2) in this fraction indicates?

Question 4: You have divided a piece of string into 7 equal segments. If you plan to use 2 of these segments for your project, what is the numerator in the fraction that represents the segments you’re utilizing, and what is the ratio of the segments you’re left with to the total segments?

Question 5: You have a bunch of colored pencils, 5 red, 7 blue and 12 green. You decide to give 2 red and 3 blue pencils to friend A and 2 blue and 6 green pencils to friend B, What is the numerator in the fraction that represents the total pencils you have after sharing with friend A and fraction of total no. pencils you gave to friend B?

Numerator – FAQs

1. What is meaning of Numerator?

A numerator is one of the two components of a fraction. The numerator is the top part of the fraction, representing the number of parts under consideration.

2. What is the Numerator in Division?

In division, the numerator represents the dividend, which is the number to be divided by another number, called the divisor.

3. How do you remember the Numerator and Denominator in a Fraction?

In a fraction, the upper part represents the numerator, while the lower part represents the denominator. For example, in the fraction 6 / 17, the numerator is 6, and the denominator is 17.

4. Is the numerator bigger than the denominator?

Yes, in some fractions, the numerator can be larger than the denominator, and such fractions are called improper fractions.

5. Do you divide the Numerator by the Numerator?

To perform division with fractions, you convert it into multiplication by taking the reciprocal of the second fraction and then multiply the numerators and denominators.

6. Can we Rationalise the Numerator?

Yes, you can rationalize the numerator of a fraction by multiplying both the numerator and denominator by a suitable expression that eliminates radicals or complex terms in the numerator. But, general convention states that we only rationalise the denominator not numerator.

7. What is Negative Numerator?

For any fraction -a/b, where both a and b are integers, -a is called the negative numerator, as it is the numerator with the negative sign. It is not necessary for the negative sign to be with the numerator only. It can also be written with the denominator as well.