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What is a Mixed Number in Maths?

A mixed number is a whole number combined with a proper fraction. The whole number part represents complete units, and the fraction part represents a portion of one additional unit. For example, 2¾ contains the whole number 2 and the proper fraction ¾.

Mixed numbers express values that fall between two consecutive integers. The value 2¾ sits between 2 and 3 on a number line. Every mixed number has 3 components: a whole number, a numerator (top number of the fraction), and a denominator (bottom number of the fraction).

Mixed Numeral Formula

The mixed numeral formula converts between mixed numbers and improper fractions. This conversion is the first step in every mixed number calculation.

Conversion Chart

To add or subtract mixed numbers, follow these 4 steps. This conversion chart applies to every addition and subtraction problem involving mixed number fractions.

Step One: Convert the Mixed Numbers to Improper Fractions

Multiply the whole number by the denominator, then add the numerator. Place the result over the original denominator. Repeat for each mixed number in the problem.

Example: 1⅔ → (1 × 3 + 2) / 3 = 5/3 and 1¾ → (1 × 4 + 3) / 4 = 7/4

Step Two: Convert to Fractions with Matching Denominators

Find the least common denominator (LCD) of the two fractions. Multiply each fraction's numerator and denominator by the factor needed to reach the LCD.

Example: LCD of 3 and 4 is 12. Convert 5/3 → 20/12 and 7/4 → 21/12.

Step Three: Add or Subtract the Numerators

Once the denominators match, add or subtract the numerators and keep the common denominator.

Example: 20/12 + 21/12 = 41/12

Step Four: Simplify the Improper Fraction

Find the greatest common factor (GCF) of the numerator and denominator. Divide both by the GCF to reduce. Then convert back to a mixed number using long division.

Example: 41/12 → GCF(41, 12) = 1, already reduced. 41 ÷ 12 = 3 remainder 5 → 3 ⁵⁄₁₂

Performing Arithmetic Operations on Mixed Numbers

Mixed number arithmetic requires converting to improper fractions first. There are 4 operations: addition, subtraction, multiplication, and division. Each operation follows the same starting step — convert mixed numbers to improper fractions — but the calculation method differs.

Adding Mixed Numbers

To add mixed numbers, convert both to improper fractions, find a common denominator, add the numerators, then simplify.

Equation to Add Fractions

Example

Add 1 ²⁄₆ and 2 ¹⁄₄

Convert: 1 ²⁄₆ = 8/6 and 2 ¹⁄₄ = 9/4

Apply formula: (8 × 4 + 9 × 6) / (6 × 4) = (32 + 54) / 24 = 86/24

Simplify: GCF(86, 24) = 2, so 86/24 = 43/12 = 3 ⁷⁄₁₂

Subtracting Mixed Numbers

To subtract mixed numbers, convert both to improper fractions, find a common denominator, subtract the numerators, then simplify.

Equation to Subtract Fractions

Example

Subtract 2 ¹⁄₄ from 1 ²⁄₆

Convert: 1 ²⁄₆ = 8/6 and 2 ¹⁄₄ = 9/4

Apply formula: (8 × 4 − 9 × 6) / (6 × 4) = (32 − 54) / 24 = −22/24

Simplify: GCF(22, 24) = 2, so −22/24 = −11/12

Multiplying Mixed Numbers

To multiply mixed numbers, convert both to improper fractions, multiply numerators together, multiply denominators together, then simplify.

Equation to Multiply Fractions

Example

Multiply 1 ²⁄₆ by 2 ¹⁄₄

Convert: 1 ²⁄₆ = 8/6 and 2 ¹⁄₄ = 9/4

Multiply: (8 × 9) / (6 × 4) = 72/24

Simplify: 72/24 = 3/1 = 3

Dividing Mixed Numbers

To divide mixed numbers, convert both to improper fractions, flip the second fraction (reciprocal), then multiply and simplify.

Equation to Divide Fractions

Example

Divide 1 ²⁄₆ by 2 ¹⁄₄

Convert: 1 ²⁄₆ = 8/6 and 2 ¹⁄₄ = 9/4

Flip and multiply: (8 × 4) / (6 × 9) = 32/54

Simplify: GCF(32, 54) = 2, so 32/54 = 16/27

Common Use Cases for a Mixed Number Calculator

A mixed number calculator serves 3 primary use cases:

Simplifying Fractions

To simplify a fraction, divide both the numerator and denominator by their greatest common factor (GCF). The GCF is the largest number that divides evenly into both values.

To simplify a mixed number fraction, follow these 4 steps:

1. Take the fraction part (e.g., ⁴⁄₈).
2. Find the GCF of the numerator and denominator → GCF(4, 8) = 4.
3. Divide both by the GCF: 4 ÷ 4 = 1, 8 ÷ 4 = 2 → ¹⁄₂.
4. Recombine with the whole number → 3½.

A fraction is fully simplified when the GCF of numerator and denominator equals 1. The mixed numeral calculator at the top of this page simplifies every result automatically.