Fraction Arithmetic Calculator (+, −, ×, ÷)
Add, subtract, multiply, and divide fractions with step-by-step common denominators and simplification.
Fraction Calculator — interactive calculator, computed instantly in your browser.
Mastering Fraction Arithmetic: Addition, Subtraction, Multiplication & Division
Finding Common Denominators: Visual Area Model (3/4 + 2/5)
Key Takeaway: Before fractions can be added or subtracted, they must be converted into like terms with a matching common denominator (LCD).
A fraction represents a numerical part of a whole, expressed as a ratio $\frac{a}{b}$, where $a$ is the numerator (the number of equal parts selected) and $b$ is the denominator (the total number of equal parts into which the whole is divided).
1. The Four Fundamental Fraction Operations
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Addition ($+$): Convert both fractions to their Least Common Denominator (LCD), add their numerators, and reduce:
\frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd}
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Subtraction ($- $): Convert to LCD, subtract the second numerator from the first, and simplify:
\frac{a}{b} - \frac{c}{d} = \frac{ad - bc}{bd}
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Multiplication ($\times$): Multiply numerators directly across, multiply denominators directly across:
\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}
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Division ($\div$): Invert the second fraction (find its reciprocal) and perform standard multiplication:
\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c} = \frac{ad}{bc}
2. Mixed Numbers vs. Improper Fractions
When working with mixed numbers like $2\frac{3}{4}$, always convert to an improper fraction prior to calculation:
🔗 Fraction & Rational Number Suite
Mastering fraction arithmetic requires finding Least Common Denominators (LCD) and Greatest Common Divisors (GCD). Access our ➗ Math & Statistics Hub for full fraction utilities.
Convert fractions to decimals or solve mixed number operations with the specialized tools below.
Frequently Asked Questions (Fraction Calculator)
Dividing by zero is mathematically undefined. A fraction represents dividing a whole into equal parts; dividing into zero parts has no logical or mathematical quantity.
LCD (Least Common Denominator) is the smallest common multiple used to combine fractions with different denominators. GCF (Greatest Common Factor) is the largest integer that divides evenly into both numerator and denominator to reduce a fraction to lowest terms.
Divide the numerator by the denominator. The whole number quotient becomes the whole integer part, the remainder becomes the new numerator, and the denominator stays identical.