Vulgar Fraction: Meaning, Steps & Solved Questions

Vulgar fraction in maths, also called a common or simple fraction, is written as a/b, where a and b are integers and b is not equal to 0. Vulgar fractions can be proper fractions (numerator < denominator), improper fractions (numerator ≥ denominator), and mixed fractions (whole number + proper fraction). Recurring decimals can also be converted into vulgar fractions.

Shivam Singh25 Oct, 2025

Vulgar Fraction: A vulgar fraction, also known as a common or simple fraction, is a way of writing a part of a whole using two whole numbers separated by a horizontal line. The top number is called the numerator, which shows how many parts are taken, and the bottom number is called the denominator, which indicates into how many parts the whole is divided. For example, 3/4 is a vulgar fraction that represents three parts out of four equal parts of a whole. This type of fraction is widely used in everyday mathematics to represent proportions, ratios, and parts of objects or quantities.

Vulgar Fraction

A vulgar fraction is a type of fraction written with one number (called numerator) placed above another number (called denominator) separated by a horizontal line. It is the ordinary way of writing fractions that you see in everyday math. The numerator represents how many parts are taken, while the denominator represents the total parts. These fractions can be proper (numerator smaller than denominator) or improper (numerator larger or equal).

Vulgar Fraction Example

An example of a vulgar fraction is $43$ , which means three parts out of four equal parts. Another example is $107$ , meaning seven out of ten parts. These fractions are commonly used to represent parts of a whole in simple fraction form.

What is Vulgar Fraction?

A vulgar fraction is simply a fraction written in the usual way with numbers above and below a line. It is sometimes also called a common or simple fraction. The numbers must be integers, and the denominator cannot be zero. It is how parts of a whole or division of quantities are shown in everyday math.

Vulgar Fraction Definition

The definition of a vulgar fraction is a rational number expressed as $b a$ , where $a$ (numerator) and $b$ (denominator) are integers, with $b \neq= 0$ . This fraction shows division of a whole into equal parts and the number of those parts we take. It is the standard form for fractions in most math contexts.

Vulgar Fraction Meaning

Vulgar fraction means the common method of representing fractions using two whole numbers separated by a line. It distinguishes from decimal or other specialized fractions. The term vulgar means "common," referring to its simple and widely used form in basic mathematics.

Vulgar Fraction Questions

Vulgar fraction questions usually ask to perform operations like addition, subtraction, multiplication, or division with fractions written as $b a$ . They may also involve simplifying fractions, converting between mixed and improper fractions, or comparing their sizes.

Vulgar Fraction Steps

The basic steps to solve vulgar fraction problems include finding a common denominator (for addition or subtraction), simplifying the numerator and denominator by their greatest common divisor, and converting improper fractions to mixed numbers if required. Understanding these steps helps in handling most fraction-related math problems easily.

What are Numerators and Denominators in Vulgar Fractions

Numerator and denominator are the two important parts of a vulgar fraction. The numerator shows how many parts of the whole we have, while the denominator shows how many equal parts the whole is divided into. For example, if a circular wheel is divided into 6 equal parts and 5 parts are shaded, this can be written as the vulgar fraction 5/6.

Here, 5 is the numerator, showing the shaded parts, and 6 is the denominator, showing the total parts of the whole. Understanding what are numerators and denominators is very important because they help us know exactly what a vulgar fraction represents.

Vulgar Fractions: Important Rules

Vulgar fractions are an important part of maths, and there are some simple rules to remember when solving questions based on them. These rules help us add, subtract, multiply, divide, and simplify vulgar fractions in the right way.

1. Value Stays the Same when Multiplied or Divided by the Same Number.

If both the numerator and denominator of a vulgar fraction are multiplied or divided by the same number (except zero), the value of the fraction stays unchanged. For example, 6/8 can be simplified to 3/4 by dividing both numerator and denominator by 2.

2. Simplifying Vulgar Fractions

A vulgar fraction can be simplified only when the numerator and denominator have a common factor. Simplifying makes fractions easy to solve while keeping their value the same.

3. Adding Vulgar Fractions

To add vulgar fractions, the denominators should be the same. Keep the denominator the same and add the numerators. For example, 2/5 + 1/5 = 3/5.

4. Subtracting Vulgar Fractions

To do subtraction of vulgar fractions, the denominators must also be the same. For example, 4/7 − 2/7 = 2/7.

5. Multiplying Vulgar Fractions

To multiply vulgar fractions, multiply the numerators to get the new numerator and multiply the denominators to get the new denominator. For example, 2/3 × 3/4 = 6/12 = 1/2 after simplification.

6. Dividing Vulgar Fractions

To divide by a vulgar fraction, multiply by its reciprocal (interchange the numerator and denominator). For example, 3/5 ÷ 2/7 = 3/5 × 7/2 = 21/10.

7. Denominator Cannot Be Zero

A vulgar fraction’s denominator should never be zero because dividing by zero is not possible in maths.

Read More: Perimeter of Square

Steps to Convert Recurring Decimals to Vulgar Fractions

When a decimal number has repeating digits, they are called recurring decimals. To convert recurring decimals into vulgar fractions, we use these steps:

Check the recurring part: Make sure the number has only repeating digits after the decimal point. For example, in 0.333…, the digit 3 repeats.
For one repeating digit: If there is only one repeating digit, put that digit as the numerator and 9 as the denominator. For example, 0.777… becomes 7/9.
For two repeating digits: If there are two repeating digits, put them as the numerator and 99 as the denominator. For example, 0.4545… becomes 45/99, which can be simplified to 5/11.
For three repeating digits: If there are three repeating digits, put them as the numerator and 999 as the denominator. For example, 0.363636… becomes 363/999, which can be simplified to 121/333.

Vulgar Fraction Examples

Find some vulgar fractions examples here that will help you understand how to solve questions in exams:

Example 1: Find the vulgar fraction for the repeating decimal 0.6 (0.666…).

Solution:

Here, only one digit (6) repeats. So, put the repeating digit as the numerator and 9 as the denominator: 0.666… = 6/9

Simplify: 6/9 = 2/3

Hence, the vulgar fraction is 2/3.

Example 2: Write 3/4 as a vulgar fraction and check its value.

Solution:

3/4 is already a vulgar fraction with numerator 3 and denominator 4.

Its value is 0.75 when written as a decimal.

Example 3: Riya ate 3 pieces of a cake that was cut into 8 equal parts. Write the fraction showing the part of the cake she ate.

Solution:

Total parts of cake = 8 (denominator).
Parts eaten = 3 (numerator).

Therefore, the vulgar fraction showing the cake eaten is 3/8.

Read More: Successor and Predecessor

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Vulgar Fraction FAQ

What is vulgar fraction?

A vulgar fraction represents the part of a whole number using two integers: one above the other, separated by a line. The top number is called the numerator, and the bottom number is the denominator.

Are vulgar fractions the same as improper fractions?

No. Vulgar fractions include both proper and improper fractions. A proper fraction has a numerator smaller than the denominator, while an improper fraction has a numerator equal to or larger than the denominator.

How to add vulgar fractions?

To add vulgar fractions, make sure the denominators are the same. Then, we can add the numerators. For example, 2/5 + 1/5 = 3/5.

How are proper fractions different from vulgar fractions?

A proper fraction is a type of vulgar fraction where the numerator is smaller than the denominator. All vulgar fractions are written in the form numerator/denominator, but not all are proper fractions.