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Proper Fraction Calculator with Steps

Add, subtract, multiply, and divide fractions with step-by-step visual solutions. Features GCD simplification and mixed number handling.

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Category Math & Algebra
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About

Fraction arithmetic often trips up students and professionals alike because, unlike decimals, it requires finding common grounds before combining values. This tool handles the heavy lifting of finding the Least Common Multiple (LCM) and Greatest Common Divisor (GCD) to perform precise calculations. It visualizes the process step-by-step, showing how the common denominator is derived and how the final result is simplified to its lowest terms. It supports both proper fractions and mixed numbers, making it essential for checking homework or scaling carpentry measurements.

fractions math homework algebra mixed numbers

Formulas

To simplify a fraction to its lowest terms, we divide both the numerator and denominator by their Greatest Common Divisor (GCD).

a ÷ GCD(a,b)b ÷ GCD(a,b)

Reference Data

OperationFormulaExample
Addition
ab + cd
Find LCD, scale numerators, add.
Subtraction
ab − cd
Same as addition, subtract numerators.
Multiplication
ab × cd = acbd
Multiply straight across.
Division
ab ÷ cd = adbc
Flip second fraction (reciprocal) and multiply.

Frequently Asked Questions

This tool automatically converts mixed numbers (e.g., 1 1/2) into improper fractions (e.g., 3/2) before calculating. The result is then converted back to a mixed number if possible.
You cannot add slices of different sizes. A common denominator ensures all "slices" (fractions) represent the same portion size, allowing you to simply add the count of slices (numerators).
GCD stands for Greatest Common Divisor. It is the largest number that divides evenly into two other numbers. We use it to simplify fractions (e.g., 4/8 becomes 1/2 because 4 is the GCD).