Calculation details
Planning estimate only, not financial, tax, or legal advice. Verify assumptions and current rules before making decisions.
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What does this calculator estimate?
A fractions calculator performs addition, subtraction, multiplication, and division on two fractions and returns the simplified result plus its decimal form. Enter the numerators, denominators, and operation to calculate.
- Add: (n1×d2 + n2×d1) ÷ (d1×d2)
- Results are simplified to lowest terms
- Denominators cannot be zero
How fraction arithmetic works
Fractions are exact ratios of integers. Adding and subtracting require a common denominator (the product of both denominators here); multiplication multiplies straight across; division multiplies by the reciprocal. Simplifying divides by the GCD so the result is in lowest terms.
Limitations to watch for
This tool handles two fractions at a time with one operation. The common denominator used is the simple product, so unlike fractions with large denominators can produce intermediate values that must be simplified. Negative results and improper fractions (numerator > denominator) are shown as-is rather than as mixed numbers.
How to use it in practice
Use fractions when you need exact values (recipe scaling, construction measurements, probability) rather than rounded decimals. Check that the simplified result is in lowest terms — it always is here. Convert the decimal output when you need a quick magnitude check.
['Enter the numerators and denominators of both fractions.', 'Choose the operation (add, subtract, multiply, divide).', 'The tool simplifies and shows the decimal equivalent.']
How this calculator works
Formula
Add: (n1×d2 + n2×d1) ÷ (d1×d2). Subtract: (n1×d2 − n2×d1) ÷ (d1×d2). Multiply: (n1×n2) ÷ (d1×d2). Divide: (n1×d2) ÷ (d1×n2). The result is simplified by dividing numerator and denominator by their greatest common divisor.
Worked example
1/2 + 1/3 = (1×3 + 1×2) ÷ (2×3) = 5/6 ≈ 0.8333.
Assumptions to verify
- Neither denominator is zero.
- Inputs are integers (whole-number numerators and denominators).
- Results are reduced to lowest terms.
Frequently asked questions
How do I add fractions?
Multiply the first numerator by the second denominator and vice versa, add, then divide by the product of the denominators: (n1×d2 + n2×d1) ÷ (d1×d2).
How do I divide fractions?
Multiply the first fraction by the reciprocal of the second: (n1×d2) ÷ (d1×n2).
What is simplifying a fraction?
Dividing the numerator and denominator by their greatest common factor so the fraction is in lowest terms (e.g., 4/6 → 2/3).
Why can't a denominator be zero?
Division by zero is undefined in mathematics — a fraction with a zero denominator has no value.
What is an improper fraction?
A fraction where the numerator is larger than the denominator (e.g., 7/4). This tool shows it as-is rather than converting to a mixed number.
How do I convert a fraction to a decimal?
Divide the numerator by the denominator. The tool shows this alongside the simplified fraction.
What is a common denominator?
A shared multiple of both denominators that lets you add or subtract fractions directly. This tool uses the product of the two denominators.
Cite this tool
BoringToolsKit. “Fractions Calculator.” boringtoolskit.com/fractions-calculator/ (reviewed 2026-08-25). Free to reference in articles, syllabi, and answer posts with a link.
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