Fraction Calculator
Perform high-precision fraction arithmetic, mixed number calculations, multi-fraction operations, and fraction reductions with complete step-by-step proofs.
Calculation Result
Step-by-Step Calculation Breakdown
Standard Fraction Arithmetic Formulas & Properties
Mathematical laws for addition, subtraction, cross-multiplication, and reduction.
| Operation | Algebraic Formula | Method Description | Example Proof | Action |
|---|---|---|---|---|
| Addition (+) | a/b + c/d = (ad + bc) / bd | Find LCD, add scaled numerators | 2/7 + 3/8 = 37/56 | |
| Subtraction (−) | a/b - c/d = (ad - bc) / bd | Find LCD, subtract scaled numerators | 5/6 - 1/4 = 7/12 | |
| Multiplication (×) | (a/b) × (c/d) = (a × c) / (b × d) | Multiply across numerators & denominators | 2/3 × 3/5 = 6/15 = 2/5 | |
| Division (÷) | (a/b) ÷ (c/d) = (a/b) × (d/c) | Multiply by the reciprocal of the second | 3/4 ÷ 2/5 = 15/8 = 1 7/8 | |
| Simplification | Divide top & bottom by GCD(a, b) | Reduces to lowest coprime terms | 18/24 (GCD 6) = 3/4 |
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Frequently Asked Questions
Everything you need to know about decimal conversions, accuracy, and formulas.
01How do you add or subtract fractions with unlike denominators?▼
To add or subtract fractions with different denominators: 1) Find the Lowest Common Denominator (LCD), which is the Least Common Multiple (LCM) of the denominators. 2) Multiply the numerator and denominator of each fraction by the factor required to make its denominator equal to the LCD. 3) Add or subtract the numerators while keeping the common denominator. 4) Simplify the resulting fraction using the Greatest Common Divisor (GCD) and convert to a mixed number if improper.
02How do you multiply fractions?▼
To multiply two fractions, multiply the numerators straight across to get the new numerator, and multiply the denominators straight across to get the new denominator. For example: (2/3) × (4/5) = (2 × 4) / (3 × 5) = 8/15. If either operand is a mixed number, first convert it into an improper fraction.
03How do you divide fractions?▼
To divide fractions, multiply the first fraction by the reciprocal (inverse) of the second fraction (flip the numerator and denominator of the divisor). For example: (3/7) ÷ (2/5) = (3/7) × (5/2) = (3 × 5) / (7 × 2) = 15/14 = 1 1/14.
04How do you convert a mixed number to an improper fraction?▼
Multiply the whole number by the denominator, add the numerator, and place the result over the original denominator. For example, for 2 3/4: (2 × 4 + 3) / 4 = 11/4.
05How do you simplify a fraction to its lowest terms?▼
Find the Greatest Common Divisor (GCD) of the numerator and denominator using the Euclidean algorithm, then divide both the numerator and denominator by that GCD. If the GCD is 1, the fraction is already in its simplest form.