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A mixed number includes a whole part and a fraction, while a proper or improper fraction has no whole number.
Can every improper fraction be written as a mixed number?
Yes, every improper fraction can be converted into a mixed number.
Can a mixed number be negative?
Yes, a mixed number can be negative, for example, –2 1⁄2.
Why are mixed numbers useful?
They make it easier to understand quantities greater than one, especially in real-life contexts like cooking or measuring.
What Are Mixed Numbers? Definition With Examples
Mixed numbers are made of whole and fractional parts. Learn how to add, subtract, multiply, divide and convert them into improper fractions with examples.
Nikita Aggarwal4 Jun, 2025
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Mixed numbers, or mixed fractions, are numbers that include both a whole number and a proper fraction. They are used to show values that are more than a whole but not quite a full unit.
For example, instead of writing the improper fraction 17⁄5, we can express it as the mixed number 3 2⁄5. This means 3 whole parts and 2 out of 5 parts of another.
Mixed numbers are useful in everyday situations like measuring ingredients, tracking time, or understanding distances.
In this blog, we will explore what mixed numbers are, how to convert between improper fractions and mixed numbers, and how to add, subtract, multiply, or divide them easily.
What is a Mixed Fraction?
A mixed fraction is just another term for a mixed number. It is the combination of a whole number and a proper fraction. The terms “mixed number” and “mixed fraction” are used interchangeably in mathematics. For example, 4 2⁄3 is a mixed fraction, where 4 is the whole part and ⅔ is the fractional part.
A mixed fraction is a number consisting of a non-zero whole number and a proper fraction. The fractional part always has a numerator smaller than its denominator.
For example:
3 3⁄4 → Here, 3 is the whole number and 3⁄4 is the proper fraction.
5 1⁄5 → Here, 5 is the whole number and 1⁄5 is the proper fraction.
The definition of mixed fraction aligns closely with the concept of representing more-than-whole values without converting everything into improper fractions.
Mixed Fraction Structure
A mixed fraction has two parts:
A whole number
A fraction (which includes a numerator and a denominator)
Here,
A whole number shows how many complete units there are.
The numerator is the top number of the fraction. It tells you how many parts you have.
The denominator is the bottom number. It shows how many equal parts make up one whole.
Example: In the mixed fraction 2 3⁄4,
2 is a whole number
3 is a numerator
4 is a denominator
Mixed Fraction Example
Mixed fractions appear frequently in real-life situations where measurements involve both whole units and parts of a unit.
For example, if you eat 2 whole pizzas and half of another, you can express this as a mixed fraction. Half of a pizza is 1⁄2, so the total amount eaten is 2 ½ pizzas.
Another common situation is running. If you complete 3 full kilometers and then run 1⁄4 kilometer more, the total distance is a mixed fraction, i.e., 3 ¼ kilometers.
In another case, when reading, if you finish 5 books and read one-third of the sixth, the total can be written as 5 ⅓ books.
These mixed fraction examples show how fractional values are often used with whole numbers in everyday measurements. They make it easier to describe amounts more accurately.
Mixed Fraction Formula
Working with mixed fractions involves formulas, especially when converting them to improper fractions for easier calculation. This step is important when performing operations like addition, subtraction, multiplication, or division.
Mixed Fraction to Improper Fraction Formula:
Improper Fraction = (Whole Number × Denominator) + Numerator/ Denominator
Mixed fractions can be added, subtracted, multiplied, and divided. To make it easier, we usually convert them into improper fractions first. Let’s look at each operation one by one with examples.
1. Addition of Mixed Fractions
To add mixed fractions:
Step 1: Convert both to improper fractions
Step 2: Add the fractions normally
Step 3: Convert the result back to a mixed fraction (if needed)
Example: Add 2 1⁄7 and 4 5⁄7
Convert: 2 1⁄7 = 15/7 4 5⁄7 = 33/7
Add: 15/7 + 33/7 = 48/7
Mixed form: 48 ÷ 7 = 6 remainder 6 → 6 6⁄7
So, 2 1⁄7 + 4 5⁄7 = 6 6⁄7
2. Subtraction of Mixed Fractions
To subtract mixed fractions:
Step 1: Convert both mixed fractions to improper fractions
Step 2: Subtract the fractions
Step 3: Simplify the result
Example: Subtract 4 5⁄7 − 2 1⁄7
Convert: 4 5⁄7 = 33/7 2 1⁄7 = 15/7
Subtract: 33/7 − 15/7 = 18/7
Mixed form: 18 ÷ 7 = 2 remainder 4 → 2 4⁄7
So, 4 5⁄7 − 2 1⁄7 = 2 4⁄7
3. Multiplication of Mixed Fractions
To multiply:
Step 1: Convert both mixed fractions to improper fractions
