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Five Fraction Calculator with Steps

Calculate complex arithmetic expressions with up to 5 fractions. Features step-by-step solutions showing LCD, simplification, and mixed number conversion.

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About

Multi-step fraction problems are a staple of intermediate algebra but represent a common stumbling block due to the complexity of finding a common denominator across multiple terms. Converting to decimals simplifies the arithmetic but often introduces rounding errors that are unacceptable in academic or engineering contexts.

This calculator handles expressions involving up to five distinct fractions. It strictly follows the Order of Operations (PEMDAS), prioritizing multiplication and division sequences before addressing addition and subtraction. The engine automatically finds the Least Common Denominator (LCD) for addition/subtraction steps and reduces the final result to its simplest form by calculating the Greatest Common Divisor (GCD).

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Formulas

For a standard addition of five fractions, the Least Common Denominator (LCD) is required:

LCD = LCM(d1, d2, d3, d4, d5)

Result = 5∑i=1 (ni × LCDdi)LCD

Where n is the numerator and d is the denominator.

Reference Data

OperationRuleExample
Additionab + cd = ad + bcbd12 + 13 = 56
Subtractionab − cd = ad − bcbd34 − 14 = 12
Multiplicationab × cd = acbd23 × 34 = 12
Divisionab ÷ cd = ab × dc12 ÷ 14 = 2

Frequently Asked Questions

Division by zero is undefined in mathematics. The tool validates all inputs and will return an error if 0 is entered as a denominator or if a division operation results in a zero divisor.
Yes. You can enter negative integers in the numerator field (e.g., -5) to represent a negative fraction.
The solver parses the inputs left-to-right respecting PEMDAS. It first resolves all Multiplication and Division pairs, reducing them to temporary results. Then, it resolves Addition and Subtraction by calculating the LCD for the remaining terms.
No. For a 5-fraction calculation, all fields must be filled. If you need fewer fractions, use the 3-Fraction Calculator or enter "0/1" with a "+" operator (adding zero doesn't change the value).