How to Use the Fraction Calculator
- Select the arithmetic operation: Addition (+), Subtraction (-), Multiplication (×), or Division (÷).
- Enter the numerator and denominator for Fraction 1 and Fraction 2 (and optional whole numbers for mixed numbers).
- Instantly view the simplified result in both proper/improper fraction and mixed number formats, alongside the decimal equivalent.
- Follow the detailed step-by-step mathematical working including LCM of denominators and GCD simplification.
- Compare two different fraction equations side-by-side using the Compare mode.
- Export the complete step-by-step solution to PDF or Excel.
Fraction Rules & Simplification Formulas
Fraction operations follow exact algebraic rules: 1. Addition & Subtraction: • Must have a common denominator. • Find Least Common Multiple: LCD = LCM(d1, d2) • Adjusted Numerator: (n1 × LCD/d1) ± (n2 × LCD/d2) • Result = Adjusted Numerators / LCD 2. Multiplication: • Multiply straight across: (n1 × n2) / (d1 × d2) 3. Division: • Multiply by the reciprocal of the second fraction: (n1 / d1) ÷ (n2 / d2) = (n1 × d2) / (d1 × n2) 4. Simplification & Mixed Numbers: • Simplify by dividing numerator and denominator by Greatest Common Divisor: GCD(n, d). • Mixed Number = Math.floor(n / d) and Remainder / d.
Example 1: Adding Unlike Fractions (1/2 + 2/3)
Operation: Add | Fraction 1: 1/2 | Fraction 2: 2/3
LCD of 2 & 3 = 6 1/2 = 3/6 and 2/3 = 4/6 3/6 + 4/6 = 7/6
7/6 = 1 1/6 (Decimal: 1.1667)
Example 2: Subtracting Mixed Numbers (2 3/4 - 1 1/2)
Operation: Subtract | 2 3/4 - 1 1/2
Convert to improper: 11/4 - 3/2 LCD = 4: 11/4 - 6/4 = 5/4
5/4 = 1 1/4 (Decimal: 1.25)
Example 3: Multiplying Fractions (3/8 × 4/9)
Operation: Multiply | 3/8 × 4/9
Numerators: 3 × 4 = 12 Denominators: 8 × 9 = 72 Reduce via GCD(12, 72) = 12: 12÷12 / 72÷12 = 1/6
1/6 (Decimal: 0.1667)
Algebra Tips & Techniques
- ✓Always convert mixed numbers to improper fractions before performing multiplication or division.
- ✓When adding or subtracting, finding the Lowest Common Multiple (LCM) keeps numbers smaller and easier to simplify.
- ✓To divide fractions, remember the rhyme: "Dividing fractions, don’t be shy, flip the second and multiply!"
- ✓The Greatest Common Divisor (GCD) allows you to reduce any fraction to its simplest irreducible form in a single division step.
Common Arithmetic Mistakes
- ✗Adding denominators directly (e.g. 1/2 + 1/2 is not 2/4 = 1/2, it is 2/2 = 1).
- ✗Forgetting to invert the second fraction when dividing.
- ✗Setting a denominator equal to 0, which is undefined in mathematics.
- ✗Failing to simplify the final fraction to lowest terms.