# Fractions Calculator

> Add, subtract, multiply, and divide fractions. Supports mixed numbers and automatically simplifies results to lowest terms.

**Category:** Math
**Keywords:** fractions, fraction calculator, add fractions, subtract fractions, multiply fractions, divide fractions, mixed numbers, math
**URL:** https://complete.tools/fractions-calculator

## How it calculates

The calculations for fractions are based on standard arithmetic operations. For two fractions a/b and c/d, addition is calculated as follows: (a/b) + (c/d) = (ad + bc) / (bd). For subtraction: (a/b) - (c/d) = (ad - bc) / (bd). Multiplication is expressed as: (a/b) × (c/d) = (ac) / (bd). Division is represented by: (a/b) ÷ (c/d) = (a/b) × (d/c) = (ad) / (bc). Here, 'a' and 'c' are the numerators, while 'b' and 'd' are the denominators of the respective fractions. The calculator automatically simplifies the resulting fractions by finding the greatest common divisor (GCD) of the numerator and denominator and dividing both by this number. This ensures that the final output is expressed in its simplest form.

## Who should use this

1. Home cooks adjusting ingredient measurements in recipes that require fraction manipulation. 2. Teachers preparing lesson plans that involve understanding fractions in mathematics. 3. Surveyors calculating land areas using fractional dimensions. 4. Health professionals determining dosages based on fractional measurements in prescriptions. 5. Architects designing plans that involve fractional scaling of dimensions.

## Worked examples

Example 1: A recipe calls for 3/4 cup of sugar, and you want to double it. Using the multiplication formula: (3/4) × 2/1 = (3×2)/(4×1) = 6/4, which simplifies to 3/2 or 1 1/2 cups of sugar. Example 2: A construction project requires 2/3 of a yard of cement, and you need to subtract the 1/4 yard already used. Using the subtraction formula: (2/3) - (1/4) = (8/12) - (3/12) = 5/12 yards remaining. Example 3: To compare the lengths of two pieces of wood, one measuring 5/6 meters and the other 1/2 meters, you can add them together. Using addition: (5/6) + (1/2) = (5/6) + (3/6) = 8/6, which simplifies to 4/3 or 1 1/3 meters total length.

## Limitations

The calculator may encounter precision limits when handling very small or very large fractions, as floating-point arithmetic can introduce rounding errors. Additionally, when dealing with mixed numbers, the tool assumes proper input formats, which may lead to inaccurate results if the input is incorrect. Edge cases, such as dividing by zero, will not produce a valid output and may result in an error. The tool also assumes that all inputs are in fractional form, which may limit its usability for users not familiar with proper fraction notation. Lastly, it does not handle complex fractions or algebraic fractions, which involve variables in the numerator or denominator.

## FAQs

**Q:** How does the calculator simplify fractions?


**A:** The calculator simplifies fractions by calculating the greatest common divisor (GCD) of the numerator and denominator and dividing both by this number to express the fraction in its lowest terms.


**Q:** Can I use this tool for mixed numbers?


**A:** Yes, the tool supports mixed numbers. Users can input them in the format of whole number + fraction, and the calculator will convert them to improper fractions for calculation.


**Q:** What happens if I enter an improper fraction?


**A:** The calculator accepts improper fractions and will simplify the result if needed. It will also provide the option to convert the result into a mixed number if applicable.


**Q:** Is there a limit to the size of fractions I can enter?


**A:** While the calculator can handle a wide range of fractions, extremely large numerators or denominators may lead to performance issues or precision errors due to the limitations of floating-point arithmetic.

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