106 LearnersLast updated on July 4th, 2025
Unit Fraction
A unit fraction is a type of fraction where the numerator is always 1 and the denominator is a natural number. It is written in the form 1/p, where p is a natural number; for example, 1/2, 1/5, 1/9. It is used to understand how a whole object is divided into equal parts.
What is a Unit Fraction?
A fraction is a type of number that represents a part of a whole and is written in the form p/q. A unit fraction is a type of fraction where the numerator is always 1 and the denominator can be any natural number. The word ‘unit’ means one, which is why the fraction with 1 as the numerator is called a unit fraction. For example, 1/4, 1/23, and 1/45.
Difference Between Unit and Non-Unit Fractions
The fractions can be classified into unit fractions and non-unit fractions based on the numerator and denominator. Let’s understand the difference between unit fractions and non-unit fractions.
| Unit Fraction | Non-Unit Fraction |
| The numerator of a unit fraction is always 1 | The numerator of a non-unit fraction is greater than 1 |
| A unit fraction is always a proper fraction | A non-unit fraction can be a proper or an improper fraction |
| Example: 1/2, 1/5, 1/7 | Examples: 2/5, 6/7, 8/3 |
How to Multiply Unit Fractions
The multiplication of a unit fraction follows the same rules as fractions. We can multiply a unit fraction with a whole number, another unit fraction, or a non-unit fraction. When multiplying two unit fractions, we first multiply the numerators and then the denominators. It can be expressed as 1/a × 1/b = (1 × 1)/(a × b),
For example,
1/5 × 1/7 = (1 × 1)/(5 × 7) = 1/35
How to Add Unit Fractions
When adding unit fractions, there are two cases based on the denominator. That is, whether the denominators are the same or not.
- Adding unit fractions with the same denominators:
When the denominator is the same, we add the numerators and the denominator is kept unchanged; then the answer is simplified if necessary.
For example, 1/5 + 1/5 = (1 + 1)/5 = 2/5.
- Adding unit fractions with different denominators:
When adding unit fractions with different denominators, convert the fractions to equivalent fractions. First, we need to find the least common multiple of the denominators. If the fractions have the same denominators, then just by adding the numerators, the result is obtained.
For example, 1/8 + 1/6
The least common denominator of 8 and 6 is 24.
Multiplying 1/8 with 3/3, 1/8 × 3/3 = 3/24
Multiplying 1/6 with 4/4, 1/6 ×4/4 = 4/24
So adding 3/24 and 4/24, 3/24 + 4/24
= (3 + 4)/24 = 7/24.
How to Subtract Unit Fractions
The subtraction of a unit fraction is similar to the addition, and instead of adding, we subtract. For example, subtract 1/5 from 1/2
1/2 - 1/5, as the fractions have different denominators, we find the least common denominator of 2 and 5
The LCM of 2 and 5 is 10
To convert the fraction to equivalent fractions,
we multiply 1/2 with 5/5, that is 1/2 × 5/5 = 5/10
we multiply 1/5 with 2/2, that is 1/5 × 2/2 = 2/10
5/10 - 2/10 = (5 - 2)/10 = 3/10
How to Divide Unit Fractions by a Whole Number
Dividing a unit fraction by a whole number is done by multiplying the fraction by the reciprocal of the whole number. By following these steps, you can divide a unit fraction by a whole number.
Step 1: Take the reciprocal of the whole number
Step 2: Change the division to the multiplication of the first fraction by the reciprocal of the whole number
For example, 1/5 ÷ 4
To divide ⅕ by 4, we multiply ⅕ by the reciprocal of 4.
The reciprocal of 4 is 1/4
That is 1/5 ÷ 1/4 = 1/5 × 1/4
= 1/20
Common Mistakes and How to Avoid Them in Unit Fractions
Errors are common among students when working on unit fractions. So let’s learn a few common mistakes and the ways to avoid them.
Mistake 1
Confusing unit fractions with proper fractions.
Students often confuse proper fractions with unit fractions, for example, think of 2/5 as a unit fraction instead of a proper fraction. So always remember that the unit fraction has 1 as the numerator, and in a proper fraction, the numerator is smaller than the denominator.
Mistake 2
Assuming that a larger denominator means a larger fraction
Sometimes students assume that a larger denominator means a larger fraction. For instance, 1/8 is larger than 1/4, as 8 is greater than 4, but it is wrong because 1/8 is smaller than 1/4. As the denominator divides the whole into more parts.
Mistake 3
Confusing whole numbers with fractions
Students often think that whole numbers and fractions are interchangeable; for example, students assume that ½ is the same as 2. Any whole number can be written as a fraction, for example, 2 as 2/1.
Mistake 4
Mixing up the numerator and the denominator
Confusion between the numerator and denominator is common. So, always identify the numerator and denominator using visual aids. Also, remember that the number above the fraction bar is the numerator and the number below the fraction bar is the denominator. In p/q, p is the numerator and q is the denominator.
Mistake 5
Not finding the common denominator while adding and subtraction
For adding or subtracting fractions with different denominators, first find the common denominator and then do the operations.
Real-world applications of Unit Fraction
In real life, we use unit fractions in different fields such as cooking, shopping, math, physics, and so on. Here are the applications of unit fractions:
- We use fractions when dividing an object among a group. For example, to cut a cake into equal slices, such as 1/4, 1/6, etc.
- In cooking and baking, to measure the ingredients, we mostly use unit fractions, for example, 1/2 cup of sugar, 1/4 teaspoon, etc.
- To calculate the discount in shopping, we use unit fractions, for example, ½ off.
Solved Examples of Unit Fractions
Problem 1
Write the fraction representing the shaded part of each circle. Identify which fractions can be classified as unit fractions.
The unit fractions are 1/4 and 1/5
Explanation
A unit fraction is a fraction that has 1 as a numerator.
In the first circle, the fraction is 1/4; it is a unit fraction as the numerator is 1.
In the second circle, the fraction is 3/6, as the numerator is 3, which is not a unit fraction.
In the third circle, the fraction is 1/5, which is a unit fraction.
Problem 2
Find the sum of 1/8 and 1/3?
1/8 + 1/3 = 11/24
Explanation
To find the sum of 1/8 +1/3, we need to find the common denominator of 8 and 3
The least common denominator of 8 and 3 is 24
Multiplying 1/8 by 3/3; 1/8 × 3/3 = 3/24
Multiplying 1/3 by 8/8; 1/3 × 8/8 = 8/24
3/24 + 8/24 = 11/24
Problem 3
Subtract 1/2 - 1/5?
1/2 - 1/5 = 3/10
Explanation
As both fractions have different denominators, we first find the common denominator of 2 and 5
The least common denominator of 2 and 5 is 10
Multiplying 1/2 by 5/5, 1/2 × 5/5 = 5/10
Multiplying 1/5 by 2/2, 1/5 × 2/2 = 2/10
5/10 - 2/10 = 3/10
Problem 4
Find the product of 1/9 and 1/4?
1/9 × 1/4 = 1/36
Explanation
Multiplying the numerator and denominator that is
1/9 × 1/4 = (1 × 1) / (9 × 4)
=1/36
Problem 5
Find the value 1/4 ÷ 1/2?
1/4 ÷ 1/2 = 1/2
Explanation
To divide a fraction, we multiply the first fraction by the reciprocal of the second fraction.
So, 1/4 ÷ 1/2 = 1/4 × 2/1
=2/4 = 1/2
FAQs on Unit Fraction
1.What is a unit fraction?
2.How to identify a unit fraction?
3.Is 3/4 a unit fraction?
4.Why is 1/4 a unit fraction?
5. What are some examples of unit fractions?
6.How can children in United States use numbers in everyday life to understand Unit Fraction?
7.What are some fun ways kids in United States can practice Unit Fraction with numbers?
8.What role do numbers and Unit Fraction play in helping children in United States develop problem-solving skills?
9.How can families in United States create number-rich environments to improve Unit Fraction 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.
