104 LearnersLast updated on July 4th, 2025
Types of Fractions
Fractions represent a part of a whole and are expressed as p/q, where p and q are the numerator and denominator, respectively. Fractions are categorized into different types based on the values and relationships of the numerator and denominator. Let’s learn more about them in this topic.
What are Fractions?
In mathematics, there are different types of numbers based on their properties; a fraction is one such type. A fraction is a way of representing part of a whole or group of objects using numbers. The fraction is written in the form p/q, where p is the numerator, q is the denominator, separated by a fractional bar (/). Denominators represent the number of equal parts that make up a whole. The numerator tells us how many parts we have from the whole.
What are the Different Types of Fractions?
There are different kinds of fractions, and the type depends on the relationship between the numerator and the denominator. The values of the numerator and denominator can also determine the type of fraction. Let’s see the different types of fractions here:
- Proper Fraction
- Improper Fraction
- Mixed Fraction
- Like Fraction
- Unlike Fraction
- Equivalent Fraction
- Unit Fraction
Proper Fraction: When the numerator of the fraction is less than the denominator, then it is called a proper fraction. For example, 6/15, 5/12, 9/17, etc.
Improper Fraction: In improper fractions, the numerator is greater than the denominator, for example, 8/5, 9/7, etc.
Mixed Fraction: The fraction with a mix of a whole number and a proper fraction is the mixed fraction. It can be represented as 657, where 6 is the whole number and 5/7 is the proper fraction. For example, 159, 327, 349, etc.
Like Fractions: If the denominators of two or more fractions are the same, then they are called like fractions. For example, 1/5, 2/5, 3/5, 4/5, 5/5.
Unlike Fraction: If the fractions have different denominators, then they are called unlike fractions, such as 1/3, 5/6, 5/9,
Equivalent Fractions: Two or more fractions with different numbers but the same value when simplified are called equivalent fractions. For example, 2/6, 3/9, and 4/12 are all different fractions, but they can be simplified to ⅓.
Unit Fraction: Unit fractions are fractions whose numerator is always 1. Example: 1/2, 1/6, and 1/9.
How to Convert Improper Fraction to Mixed Fraction?
For converting improper fraction to mixed fraction, few steps need to be followed. The first step is to divide the numerator by the denominator, and the resulting quotient will be the whole number. The remainder from the division will become the new numerator, and the divisor will be the denominator.
For example, let’s convert 11/4. The quotient is 2, the remainder is 3, and the divisor is 4. So, 11/4 in mixed fraction can be written as
2 3/4.
How to Convert Mixed Fraction to Improper Fraction?
The mixed fraction is the mixture of a whole number and a proper fraction, so to convert a mixed fraction to an improper fraction. We first multiply the denominator by the whole number and then add the product to the numerator. The sum is the new numerator, and the denominator will remain the same.
For example, let’s convert 325 to an improper fraction. To convert, first we multiply the whole number by the denominator, that is 3 × 5 = 15. Now adding the numerator to the product, that is 15 + 2 = 17. So, 325 can be written as 17/5.
Common Mistakes and How to Avoid Them in Types of Fractions
When working on fractions, it can be tricky for students, especially when doing the basic arithmetic operations. So let’s learn some common mistakes and the ways to avoid them in fractions.
Mistake 1
Confusing proper fractions with improper fraction
Students tend to be confused with the proper and improper fractions when identifying them. When the numerator is less than the denominator, then it is a proper fraction, that is 2/5, 6/7, 2/9, etc. The fractions where the numerator is greater than the denominator are improper fractions
Mistake 2
Errors when converting the mixed fraction to an improper fraction
When converting the mixed fractions to improper fractions, students tend to make errors. To avoid these mistakes, you should be careful when converting mixed fractions to improper fractions.
Mistake 3
Adding and subtracting without a common denominator
Sometimes students add or subtract the fractions without a common denominator, which is an error. When adding or subtracting fractions, we should first check if the fractions have the same denominators. If not, the LCD must be determined before continuing with the addition or subtraction.
Mistake 4
Errors while dividing fractions
When dividing fractions, we should multiply by the reciprocal of the second fraction instead of dividing the fractions. This is because dividing by a number and multiplying by its reciprocal is the same. Students usually forget to take the reciprocal of the second fraction, which will lead to errors. To avoid this, students should first take the reciprocal of the second fraction and multiply the fractions.
Mistake 5
Incorrectly simplifying the fraction
There are certain rules to be followed while simplifying fractions, such as finding the GCF and dividing by common factors. Failing to do so will result in miscalculations.
Real-world Applications of Types of Fractions
We use fractions to represent measurements like weight and height. Let’s discuss some real-life applications of fractions:
- In cooking, we use fractions to measure ingredients, such as ½ cup of sugar, 234 cups of flour, and so on.
- We use fractions to represent that 15 minutes is equal to ¼ hour, and 45 minutes is equal to ¾ hour.
- To mention the score of a test, we use fractions, that is, the mark they scored out of the total mark. For example, 25/50, 6/10.
- In shops, they use fractions to show the discount or pricing. We use fractions, that is, ½ price.
Solved Examples of Types of Fractions
Problem 1
Convert the improper fraction 23/6 into a mixed fraction
23/6 in mixed fraction can be written as 3 5/6
Explanation
To convert a fraction to a mixed fraction we first divide the fraction, that is 23 ÷ 6
So, the quotient is 3 and the remainder is 5
So, 23/6 can be represented as 3 5/6
Problem 2
Classify the following fractions as proper or improper fractions 8/15, 12/7, 5/4, 17/9, and 4/9
Here, the proper fractions are 8/15 and 4/9 and the improper fraction are 12/7, 5/4, and 17/9
Explanation
The proper fractions are the fractions when the numerator is less than its denominator
The improper fractions are the fractions where the numerator is greater than the denominator
So, 8/15 and 4/9 are proper fractions as the numerator is less than the denominator
12/7, 5/4, and 17/9 are improper fractions as the numerator is greater than the denominator
Problem 3
Convert 3 2/5 to an improper fraction?
3 2/5 can be represented as 17/5
Explanation
To convert a mixed fraction we first multiply the whole number with the denominator
That is, 3 × 5 = 15
Adding the product with a numerator
That is 15 + 2 = 17
So, 3 2/5 can be written as 17/5
Problem 4
Find the sum of 2/9 + 4/9
The sum of 2/9 + 4/9 = 2/3
Explanation
Adding the numerator, that is 2 + 4 = 6
As the denominator of both fractions are same, it will be the same for the sum also
So, 2/9 + 4/9 = 6/9
It can be simplified as 2/3
Problem 5
Find the product of 3/4 × 5/6
The product of 3/4 × 5/6 = 5/8
Explanation
Multiply the numerator
That is 3 × 5 = 15
Multiply the denominator
That is 4 × 6 = 24
So, 3/4 × 5/6 = 15/24
It can be simplified as 5/8
FAQs on Types of Fractions
1.What are fractions?
2.What are the different types of fractions?
3.What are the parts of fractions?
4.What are the parts of fractions?
5.What is the inverse of a fraction?
6.What is a proper fraction?
7.How can children in Singapore use numbers in everyday life to understand Types of Fractions?
8.What are some fun ways kids in Singapore can practice Types of Fractions with numbers?
9.What role do numbers and Types of Fractions play in helping children in Singapore develop problem-solving skills?
10.How can families in Singapore create number-rich environments to improve Types of Fractions skills?
Hiralee Lalitkumar Makwana
About the Author
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
Fun Fact
: She loves to read number jokes and games.
