What Are Mixed Numbers? Definition With Examples

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. 

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Definition of Mixed Fraction

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

Example:

Convert 3 1⁄2 to an improper fraction:

(3 × 2) + 1 = 6 + 1 = 7

So, 3 1⁄2 = ⁷⁄2

Read More- Subtraction Table - Definition, Chart, Examples

Converting Improper Fractions to Mixed Numbers

An improper fraction has a numerator (top number) that is bigger than the denominator (bottom number). Examples include 12/5, 23/11, and 7/2.

You can convert an improper fraction into a mixed fraction by following these simple steps:

Step 1: Divide the numerator by the denominator.

Step 2: Write down the quotient (the result of the division) as the whole number.

Step 3: The remainder becomes the numerator of the fraction. The denominator stays the same.

Step 4: Write the final answer in the following form:

Mixed Number = Quotient followed by Remainder over Divisor

or

Quotient  R⁄D

here:

• Quotient is the whole number part

• R is the remainder

• D is the divisor (original denominator)

Example: Convert 12/7 into a mixed fraction.

Divide 12 by 7: 

12 ÷ 7 = 1 with a remainder of 5

Write it as: 1 5⁄7

So, 12/7 =   1 5⁄7

Converting a Mixed Fraction to an Improper Fraction

A mixed fraction can also be changed back to an improper fraction using this method:

Step 1: Multiply the whole number by the denominator.

Step 2: Add the numerator to the result.

Step 3: Keep the same denominator.

Step 4: Write your answer as an improper fraction.

Example: Convert 2 2⁄5  into an improper fraction.

Multiply 2 × 5 = 10

Add 10 + 2 = 12

Keep the denominator the same. 

So, 2 2⁄5  = 12/5

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Operations on Mixed Fractions

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

Step 2: Multiply the numerators

Step 3: Multiply the denominators

Step 4: Simplify the result

Read More - Multiplication of Fractions: Definition, Calculation Methods , and Examples

Example: Multiply  2 1⁄7 ×  4 5⁄7

Convert:
2 1⁄7  = 15/7
4 5⁄7 = 33/7

Multiply:  (15 × 33) / (7 × 7) = 495 / 49

So,   2 1⁄7 ×  4 5⁄7 = 495/49 =  10 5⁄49

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4. Division of Mixed Fractions

To divide:

Step 1: Convert both to improper fractions

Step 2: Keep the first fraction

Step 3: Flip the second fraction (take its reciprocal)

Step 4: Multiply the two fractions

Step 5: Simplify if needed

Read More- Division of Fractions - Definitions, Steps and Examples

Example: Divide 3 1⁄5  ÷ 5 3⁄5

Convert:
3 1⁄5  = 16/5

5 3⁄5 = 28/5

Flip and multiply: 16/5 ÷ 28/5 = 16/5 × 5/28 = 80/140

Simplify: 80/140  = 8/14 = 4/7

3 1⁄5  ÷ 5 3⁄5 = 4/7

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