What types of fractions does this calculator support?

This calculator supports common fractions (a/b), mixed numbers (w a/b), and improper fractions. You can also perform operations with multiple fractions.

How do you add or subtract fractions?

To add or subtract a/b and c/d, use a common denominator: (a/b) ± (c/d) = (ad ± bc) / bd, then simplify the result if possible.

How do you multiply or divide fractions?

Multiplication: (a/b) × (c/d) = (ac)/(bd). Division: (a/b) ÷ (c/d) = (a/b) × (d/c) = (ad)/(bc). Then simplify the result.

How do you convert a mixed number to an improper fraction?

Convert w a/b to an improper fraction using (w × b + a) / b. Example: 2 1/3 = (2×3+1)/3 = 7/3.

Fraction Calculator

4 modes: fraction operations, simplify, mixed → improper, improper → mixed.

Auto-calculate

Enter values

Education

How many fractions?

Fraction to simplify

Mixed number

Improper fraction

Result

CalcCore

Choose a mode and click “Calculate”.

Fraction Calculator — How It Works

The CalcCore fraction calculator helps you perform fraction arithmetic, simplify fractions, and convert between mixed numbers and improper fractions. It supports both standard fractions (a/b) and mixed numbers (w a/b).

Mode 1 — Fraction Operations

This mode allows you to add, subtract, multiply, and divide fractions. The calculator automatically finds a common denominator when necessary and simplifies the final result.

Addition
a/b + c/d = (a × d + c × b) / (b × d)
Subtraction
a/b − c/d = (a × d − c × b) / (b × d)
Multiplication
a/b × c/d = (a × c) / (b × d)
Division
a/b ÷ c/d = a/b × d/c = (a × d) / (b × c)

After calculation, the result is automatically simplified and displayed both as a fraction and a mixed number if applicable.

Mode 2 — Simplify a Fraction

Simplifying a fraction means dividing both the numerator and denominator by their GCD (greatest common divisor).

GCD formula: GCD = gcd(a, b)
Simplification: a/b → (a ÷ GCD) / (b ÷ GCD)

Example: 24/36 → GCD(24,36) = 12 → 24/36 = 2/3.

Mode 3 — Mixed Number to Improper Fraction

A mixed number has the format w a/b, where w is the whole part and a/b is the fractional part.

To convert a mixed number into an improper fraction:

Formula: w a/b = (w × b + a) / b

Example: 2 1/3 = (2 × 3 + 1) / 3 = 7/3.

Mode 4 — Improper Fraction to Mixed Number

An improper fraction is a fraction where the numerator is greater than or equal to the denominator (a ≥ b).

To convert it into a mixed number, perform division with remainder:

Whole number: w = ⌊a / b⌋
Remainder: r = a mod b
Result: a/b = w r/b

Example: 29/4 → w = 7, r = 1 → 29/4 = 7 1/4.

Tips for Accurate Fraction Calculations

The denominator cannot be zero.
Simplifying fractions makes results easier to read.
When dividing fractions, multiply by the reciprocal.
Improper fractions can always be written as mixed numbers.

Frequently Asked Questions

What is a proper and improper fraction?

A proper fraction has a numerator smaller than the denominator (a < b), for example 3/5. An improper fraction has a numerator greater than or equal to the denominator, for example 9/4.

How do you simplify a fraction?

Find the greatest common divisor (GCD) of the numerator and denominator, then divide both numbers by it. Example: 18/24 → GCD = 6 → 3/4.

How do you add fractions with different denominators?

Use the formula: a/b + c/d = (a × d + c × b) / (b × d). This converts both fractions to a common denominator.

How do you divide fractions?

Division becomes multiplication by the reciprocal: a/b ÷ c/d = a/b × d/c.

How do you convert a mixed number into an improper fraction?

Multiply the whole number by the denominator and add the numerator. Formula: w a/b = (w × b + a) / b.

How do you convert an improper fraction to a mixed number?

Divide the numerator by the denominator. The quotient becomes the whole number and the remainder becomes the new numerator.

Why does the calculator show both fraction and mixed number?

Fractions are useful for precise calculations, while mixed numbers are easier to read and understand.

What happens if the denominator is zero?

A fraction with denominator 0 is undefined in mathematics, so the calculator requires a non-zero denominator.