Perform precise operations on simple and mixed fractions with automatic LCD finding, prime reductions, visual representations, and step-by-step working.
Quick Presets:
Fraction Arithmetic with Mixed Numbers
Fraction 1
Fraction 2
Simplify Fraction to Lowest Terms
Compare Two Fractions
Fraction A
VS
Fraction B
Decimal to Fraction
Fraction to Decimal
Fraction Result
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📝 Step-by-Step Solution Breakdown:
VISUAL PROPORTION BAR:
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LCD Method: Least Common Denominator
Mixed Fractions: Full whole + proper support
Prime Reduction: Exact GCD simplification
Decimal Precision: Up to 10 decimal digits
What is a fraction?
A fraction represents a part of a whole. It consists of a numerator (top number indicating how many parts you have) and a denominator (bottom number indicating the total number of equal parts). In fractional arithmetic, the denominator can never equal zero because division by zero is mathematically undefined.
How fraction operations work
Addition & Subtraction: Fractions must first share a common denominator before their numerators can be combined. The calculator computes the Least Common Denominator (LCD = LCM(d1, d2)), scales the numerators, performs the operation, and reduces the final fraction using the Greatest Common Divisor (GCD).
Multiplication: Multiply the numerators together and the denominators together: (a/b) × (c/d) = (a×c) / (b×d), followed by reduction.
Division: Multiply the dividend by the reciprocal (inverted form) of the divisor: (a/b) ÷ (c/d) = (a/b) × (d/c) = (a×d) / (b×c).
Frequently asked questions
How do I add two fractions?▶
Give them a common denominator (Least Common Denominator), scale each numerator, then add the numerators. For example 1/4 + 1/6 becomes 3/12 + 2/12 = 5/12.
How do I divide fractions?▶
Multiply the first fraction by the reciprocal (inverted form) of the second. For example 3/4 ÷ 1/6 = 3/4 × 6/1 = 18/4 = 4 1/2.
What is a mixed number?▶
A mixed number combines a whole number and a proper fraction, like 2 1/3. It equals 2 + 1/3, which converts to the improper fraction 7/3.
How do I convert a decimal to a fraction?▶
Write the decimal as a fraction over a power of 10 (e.g. 0.375 = 375/1000) and simplify by dividing by the greatest common divisor (GCD 125) to get 3/8.