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Last updated on July 4th, 2025

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Unit Fraction

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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.

Unit Fraction for US Students
Professor Greenline from BrightChamps

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.

Professor Greenline from BrightChamps

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

 

Professor Greenline from BrightChamps

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
 

Professor Greenline from BrightChamps

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.
Professor Greenline from BrightChamps

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
 

Professor Greenline from BrightChamps

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 
 

Max Pointing Out Common Math Mistakes

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

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 Confusing unit fractions with proper fractions.

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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

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Assuming that a larger denominator means a larger fraction

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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

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Confusing whole numbers with fractions

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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

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Mixing up the numerator and the denominator

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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

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Not finding the common denominator while adding and subtraction
 

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For adding or subtracting fractions with different denominators, first find the common denominator and then do the operations. 

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Professor Greenline from BrightChamps

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.  
     
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Solved Examples of Unit Fractions

Ray, the Character from BrightChamps Explaining Math Concepts
Max, the Girl Character from BrightChamps

Problem 1

Write the fraction representing the shaded part of each circle. Identify which fractions can be classified as unit fractions.

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

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. 
 

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

Problem 2

Find the sum of 1/8 and 1/3?

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

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
 

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

Problem 3

Subtract 1/2 - 1/5?

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

 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 
 

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

Problem 4

Find the product of 1/9 and 1/4?

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

1/9 × 1/4 = 1/36

Explanation

Multiplying the numerator and denominator that is
1/9 × 1/4 = (1 × 1) / (9 × 4)
=1/36
 

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

Problem 5

Find the value 1/4 ÷ 1/2?

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

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

Max from BrightChamps Praising Clear Math Explanations
Ray Thinking Deeply About Math Problems

FAQs on Unit Fraction

1.What is a unit fraction?

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2.How to identify a unit fraction?

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3.Is 3/4 a unit fraction?

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4.Why is 1/4 a unit fraction?

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5. What are some examples of unit fractions?

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6.How can children in United States use numbers in everyday life to understand Unit Fraction?

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7.What are some fun ways kids in United States can practice Unit Fraction with numbers?

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8.What role do numbers and Unit Fraction play in helping children in United States develop problem-solving skills?

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9.How can families in United States create number-rich environments to improve Unit Fraction skills?

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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.

Max, the Girl Character from BrightChamps

Fun Fact

: She loves to read number jokes and games.

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