Fraction Calculator

Math

Perform fraction addition, subtraction, multiplication, and division with mixed numbers, simplifying, and step-by-step solutions.

Result

3 20

Simplified Fraction: 23/20

Mixed Number: 1 3/20

Decimal Form: 1.15

Percentage: 115%

Step-by-Step Solution

1 Find common denominator (LCD)

LCD(4, 5) = 20

Convert both fractions to have denominator 20.

2 Scale numerators

15/20 + 8/20

Multiply 3 by 5 and 2 by 4.

How This Calculator Works

A fraction represents a numerical quantity that is not a whole number, written as a numerator over a non-zero denominator (a/b). The numerator denotes how many equal parts are taken, while the denominator specifies the total number of parts dividing the whole. Our Fraction Calculator supports mixed numbers, proper and improper fractions, automatic Least Common Denominator (LCD) finding, and reduction to simplest form using the Greatest Common Divisor (GCD).

📐 Fundamental Fraction Arithmetic Operations

a/b ± c/d = (a·d ± b·c)/(b·d) | (a/b) × (c/d) = (a·c)/(b·d) | (a/b) ÷ (c/d) = (a·d)/(b·c)

a/b: First fraction with numerator a and denominator b ≠ 0

c/d: Second fraction with numerator c and denominator d ≠ 0

LCD: Least Common Denominator, equal to LCM(b, d)

GCD: Greatest Common Divisor, used to reduce the result to lowest terms

Key Mathematical Rules & Properties

Common Denominator Rule

You can only directly add or subtract fractions that share the same denominator. If denominators differ, convert both fractions using their Least Common Denominator (LCD).

Division via Reciprocal

Dividing by a fraction is equivalent to multiplying by its reciprocal (inverting the numerator and denominator): (a/b) ÷ (c/d) = (a/b) × (d/c).

Simplification / Reduction

Divide both numerator and denominator by their Greatest Common Divisor: a / GCD and b / GCD.

Mixed Numbers Conversion

To convert mixed number W a/b to an improper fraction: (W × b + a) / b.

✎

Worked Example: Adding Unlike Fractions

Calculate 1/2 + 1/3 and simplify the result.

Identify denominators: 2 and 3. Find LCD: LCM(2, 3) = 6.
Convert 1/2: multiply numerator and denominator by 3 → 3/6.
Convert 1/3: multiply numerator and denominator by 2 → 2/6.
Add numerators over common denominator: (3 + 2) / 6 = 5/6.
Check GCD(5, 6) = 1. The fraction 5/6 is already in simplest form.

Final Answer: 5/6 (Decimal: 0.8333...)

Frequently Asked Questions

Why can the denominator of a fraction never be zero?

Division by zero is mathematically undefined. A fraction represents dividing a quantity into equal parts; you cannot divide something into zero parts.

What is the difference between proper and improper fractions?

A proper fraction has a numerator strictly smaller than its denominator (e.g. 3/4). An improper fraction has a numerator greater than or equal to its denominator (e.g. 7/4 or 5/5) and can be converted into a mixed number.

How do you convert a decimal into a fraction?

Write the decimal digits over the appropriate power of 10 based on place value (e.g., 0.75 = 75/100). Then divide both numbers by their GCD (75 ÷ 25 = 3, 100 ÷ 25 = 4 → 3/4).

Can negative fractions have the minus sign in the denominator?

Standard mathematical convention places the negative sign in the numerator or in front of the fraction (-a/b), rather than in the denominator (a/-b), though both represent the exact same negative value.

Understanding your calculation

Method, example and limitations

How the calculation works

Fraction arithmetic uses a common denominator for addition and subtraction, multiplies numerators and denominators for products, and reduces the result by their greatest common factor.

Example to check

1/2 + 1/3 = 3/6 + 2/6 = 5/6. Multiplying 2/3 by 3/4 gives 6/12, which reduces to 1/2.

Before using the result

A denominator cannot be zero. Division by a zero fraction is undefined. Keep mixed-number notation distinct from multiplication.

Calculation methodology · Report a result that needs review