Proper Fraction - Definition, Difference, Uses, Examples

What is Proper Fraction?

A proper fraction is a type of fraction where the numerator is smaller than the denominator. The numerator is the top number in a fraction and tells how many parts we have. The denominator is the bottom number and tells how many equal parts the whole is divided into.

For example:

• 2/3 is a proper fraction.

• 5/8 is a proper fraction.

• 7/10 is a proper fraction.

In each of these examples, the numerator is smaller than the denominator. This means the value of the fraction is always less than 1.

Difference Between Proper and Improper Fraction 

 A proper fraction is a type of fraction where the numerator, which is the top number, is smaller than the denominator, which is the bottom number. This means that the value of a proper fraction is always less than one whole. 

For example, in the fraction 4/5, the numerator is 4 and the denominator is 5. Since 4 is smaller than 5, this is a proper fraction. Proper fractions represent parts of a whole that are less than the whole amount.

On the other hand, an improper fraction is a fraction where the numerator is equal to or greater than the denominator. This means the value of the fraction is equal to or more than one whole. 

For example, in the fraction 7/4, the numerator is 7 and the denominator is 4. Since 7 is greater than 4, this is an improper fraction. Improper fractions show amounts that are more than or equal to a full whole. These types of fractions can also be written as mixed numbers, which include a whole number and a proper fraction together. 

Read more: Numerator and Denominator: Definition and Difference

How to Add Proper Fractions

When adding proper fractions, we need to check if the denominators are the same.

Case 1: Same Denominator

Proper Fraction Example: 2/5 + 1/5 = 3/5

Just add the numerators and keep the denominator the same.

Case 2: Different Denominators

Proper Fraction Example: 1/3 + 1/4

Step 1: Find the LCM (Least Common Multiple) of 3 and 4, which is 12.

Step 2: Convert both fractions to have 12 as the denominator.

• 1/3 = 4/12

• 1/4  = 3/12

Step 3: Add the numerators/

4/12 + 3/12 = 7/12

Enroll Now for Maths Online Classes

How to Subtract Proper Fractions

Subtracting proper fractions follows the same rules as addition.

Case 1: Same Denominator

Proper Fraction Example: 5/7 − 2/7 = 3/7

Case 2: Different Denominators

Proper Fraction Example: 3/4 − 1/6

Step 1: Find the LCM of 4 and 6, which is 12.

Step 2: Convert the fractions.

• 3/4 = 9/12

• 1/6 = 2/12

Step 3: Subtract the numerators.

9/12 − 2/12 = 7/12

So, when subtracting proper fractions, always find a common denominator first.

How to Multiply Proper Fractions

Multiplying proper fractions is easy. You just multiply the numerators and the denominators.

Proper Fraction Example:  2/3 × 4/5

• Numerator: 2 × 4 = 8

• Denominator: 3 × 5 = 15

2/3 × 4/5 = 8/15

That’s it. No need to find a common denominator when multiplying proper fractions.

How to Divide Proper Fractions

To divide one proper fraction by another, use the reciprocal of the second fraction and multiply.

Proper Fraction Example:  3/4 ÷ 2/5

Step 1: Find the reciprocal of the second fraction.

Reciprocal of 2/5  is 5/2

Step 2: Multiply.

3/4 × 5/2 = 15/8

Step 3: Simplify if needed.

So, dividing proper fractions means multiplying by the reciprocal.

Read more: Unit Fraction- Definition, Examples, Practice Problems

Mixed Fraction to Proper Fraction

A mixed fraction is a number that has a whole number and a proper fraction written together. It shows a value that is more than one whole. 

For example, the mixed fraction 2 and one-third is written as 2 ⅓. This means you have two whole parts and one more part out of three equal parts.

To work with mixed fractions more easily, we often convert them into improper fractions. An improper fraction has only a numerator and a denominator, and its numerator is equal to or greater than the denominator. To change a mixed fraction into a single fraction, we follow a few simple steps:

• Multiply the whole number by the denominator.
  In this case: 2 × 3 = 6

• Add the numerator of the proper fraction to that result.
  6 + 1 = 7

• Place the result over the original denominator.
  Final fraction: 7/3

So, the mixed fraction 2 ⅓ becomes 7/3 after converting. The result, 7/3, is an improper fraction because the top number is larger than the bottom number. Even though we are turning a mixed number into a single fraction, what we end up with is not a proper fraction, but an improper one.

Remember:

• You cannot directly turn a mixed fraction into a proper fraction.

• You must first convert it into an improper fraction.

• After that, you may simplify the result if possible.

Knowing how to change a mixed fraction into an improper fraction helps make solving fraction problems simpler and more accurate.

Read more: Vulgar Fraction: Meaning, Steps & Solved Questions

Proper Fractions Examples 

Let’s try a few examples to test your understanding of proper fractions and how to work with them.

1. Is 9/10 a proper fraction?
Yes. The numerator is 9 and the denominator is 10. Since 9 is less than 10, this is a proper fraction.

2. Add 1/6 + 2/3

Solution:

Step 1: Convert 2/3to have the same denominator as ⅙

The least common denominator of 6 and 3 is 6. So,

2/3 = 4/6

Step 2: Add the two fractions

1/6 + 4/6 = 5/6

5/6​ is the sum, and it is a proper fraction.

3. Multiply 3/5 × 2/7

Solution:

Step 1: Multiply the numerators: 3 × 2 = 6

Step 2: Multiply the denominators: 5 × 7 = 35

 So, 3/5 × 2/7 = 6/35

6/35 is the product, and it is a proper fraction.

4. Divide 2/3 ÷ 4/5

Step 1: Change division to multiplication by using the reciprocal of 4/5 which is 5/4.

Step 2: Multiply

2/3 × 5/ 4 =10/12

Step 3: Simplify 10/12

Divide both numerator and denominator by 2:

10/12 = 5/6

5/6 is the result, and it is a proper fraction.

5. Convert the mixed fraction 3½ to an improper fraction

Step 1: Multiply the whole number by the denominator:
3 × 2 = 6

Step 2: Add the numerator
6 + 1 = 7

Step 3: Place the result over the original denominator
7/2

3½ = 7/2 which is an improper fraction.

Make Learning Easy and Enjoyable for Your Child with CuriousJr

Does your child find it difficult to grasp new topics in maths or other subjects? Many students face this challenge, and without the right guidance, it can affect both their grades and confidence.

CuriousJr’s online school tuition classes are designed to strengthen your child’s understanding of key concepts and provide ongoing academic support.

• With a personalised curriculum for each subject, CuriousJr offers live classes in English, Math, Science, and Social Studies. Every session is guided by two expert teachers to make learning clear, interactive, and effective.

• Daily doubt-solving, homework assistance, and six days of live sessions each week help students stay consistent and engaged.

• Parents also receive regular progress updates, so you’re always informed about your child’s development. 

Book a demo class today to know more about CuriousJr online classes.