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Fraction Arithmetic Calculator

Add, subtract, multiply, or divide two fractions and get the result simplified, as a mixed number, and as a decimal.

Simplified Fraction
23/20
Mixed Number
1 3/20
Decimal Value
1.150000
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Calculation Guide & Reference

Fraction Arithmetic Mathematics

Fraction calculator adds, subtracts, multiplies, or divides two fractions and shows the result simplified, as a mixed number, and as a decimal.

Standardized Mathematical Formula
a/b + c/d = (ad + bc) / bd

To add or subtract fractions, convert them to a common denominator (bd) first. To multiply, multiply numerators and denominators directly. To divide, multiply by the reciprocal of the second fraction.

Variables:
a/b:First fraction
c/d:Second fraction
How It Works (Step-by-Step)
  • 1Enter both fractions and choose an operation (+, βˆ’, Γ—, Γ·).
  • 2View the result simplified to lowest terms, as a mixed number, and as a decimal.
Real-World Numerical Example
Adding 3/4 + 2/5

Add the fractions 3/4 and 2/5.

β€’Common denominator: 4 Γ— 5 = 20.
β€’Numerator: (3 Γ— 5) + (2 Γ— 4) = 15 + 8 = 23.
β€’Result: 23/20, which cannot be simplified further (GCD = 1).
β€’As a mixed number: 1 3/20. As a decimal: 1.15.
Result: 3/4 + 2/5 = 23/20 = 1 3/20 = 1.15.
Calculation Best Practices & Tips
Examine the discriminant (bΒ² - 4ac) before solving quadratics to instantly know if roots are real, distinct, repeated, or complex.
In statistical analysis, always check both the mean and median to identify if data distribution is skewed by outliers.
When calculating percentage changes, ensure you divide by the original starting baseline value: ((New - Old) / Old) * 100.

Frequently Asked Questions (FAQ)

Convert both fractions to a common denominator (multiplying the two denominators together always works), add the numerators, then simplify the result to lowest terms.

Multiply the first fraction by the reciprocal (flipped version) of the second β€” dividing by a/b is the same as multiplying by b/a.

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