Fraction Calculator - Persian Numerals
Perform arithmetic operations with fractions with Persian numeral system support.
A free online fraction calculator that adds, subtracts, multiplies, and divides fractions with automatic simplification. Enter fractions like 1/3 + 1/4 and the calculator finds the least common denominator, converts both fractions, adds them, and simplifies the result to lowest terms. Supports mixed numbers (2 1/3 + 1 1/2), decimal-to-fraction conversion (including repeating decimals like 0.333... = 1/3), and simplification of any fraction. Each operation shows the step-by-step work — the LCD, the converted fractions, and the final simplified result — making it ideal for students learning fraction arithmetic.
About This Numeral System
Persian numerals (۰ through ۹) are used in Iran, Afghanistan (for Dari), and in some Pakistani Urdu contexts. They share the same ancestor as Eastern Arabic numerals but have distinct glyph forms — most visibly, the Persian 4 (۴), 5 (۵), and 6 (۶) differ from their Arabic counterparts. If you work with Persian, Dari, or Urdu documents, this calculator renders results in the numeral forms you expect.
How This Calculator Works
Fraction Arithmetic: a/b + c/d = (a×d + b×c) / (b×d), then simplify by GCD
Fraction addition and subtraction require a common denominator, found by multiplying the denominators. The numerators are then combined and the result is simplified by dividing both numerator and denominator by their Greatest Common Divisor (GCD). Multiplication multiplies numerators and denominators directly. Division inverts the second fraction and multiplies.
Worked Examples
Input: 1/3 + 1/4
Result: LCD = 12. 4/12 + 3/12 = 7/12. Already in lowest terms.
Input: 2 1/3 × 1 1/2
Result: Convert: 7/3 × 3/2 = 21/6 = 7/2 = 3 1/2
Key Features
- Add, subtract, multiply, divide fractions
- Mixed number support
- Automatic simplification
- Decimal-to-fraction conversion
Frequently Asked Questions
How do I add fractions with different denominators?
Enter both fractions in the calculator (e.g., 1/3 + 1/4). The calculator automatically finds the least common denominator (LCD), converts both fractions, and adds them. For 1/3 + 1/4, the LCD is 12, so it becomes 4/12 + 3/12 = 7/12.
How do I convert a decimal to a fraction?
Enter a decimal number like 0.75 or 0.333... in the Decimal to Fraction mode. The calculator converts it to the simplest equivalent fraction — 0.75 becomes 3/4, and 0.333... becomes 1/3. For terminating decimals, the conversion is exact. For repeating decimals, the calculator recognises the repeating pattern and finds the matching rational number.
How do I convert a fraction to a decimal?
Enter a fraction like 3/8 and the calculator divides the numerator by the denominator to get the decimal equivalent: 3/8 = 0.375. The result shows both the exact decimal (for terminating fractions) and a rounded approximation for repeating decimals. For example, 1/3 displays as 0.333... with a note that it repeats.
Can the calculator simplify or reduce fractions automatically?
Yes! The calculator automatically simplifies all results to their lowest terms. For example, 6/8 is automatically reduced to 3/4 by dividing both numerator and denominator by their greatest common divisor (GCD). You can also use the "Simplify Fraction" mode to reduce any fraction directly — enter 12/16 and get 3/4.
How do I use the mixed fraction calculator?
Use the "Mixed Numbers" mode to perform operations with mixed numbers (e.g., 2 1/3 + 1 1/2). Enter the whole number and fraction parts separately. The calculator converts mixed numbers to improper fractions, performs the operation, and provides results in mixed number format. For example, 2 1/3 + 1 1/2 = 3 5/6.
Is this an online fraction calculator?
Yes. This is a free online fraction calculator that runs entirely in your browser with no download or sign-up required. It supports addition, subtraction, multiplication, division, simplification, mixed numbers, and decimal-to-fraction conversion. All calculations happen locally on your device.
How does fraction multiplication work?
To multiply fractions, multiply the numerators together and the denominators together. For example, 2/3 × 3/4 = (2×3)/(3×4) = 6/12, which simplifies to 1/2. The calculator performs this automatically.
How do I divide fractions?
To divide fractions, multiply the first fraction by the reciprocal of the second. For example, 1/2 ÷ 1/4 = 1/2 × 4/1 = 4/2 = 2. Simply enter both fractions and select the division operation, and the calculator handles the rest.
How do Persian numerals differ from Arabic numerals?
The most visible differences are in the digits 4, 5, and 6. Persian 4 (۴) looks like a small triangle, while Arabic 4 (٤) is more angular. Persian 5 (۵) looks like a small heart shape, while Arabic 5 (٥) is a circle. Persian 6 (۶) resembles a reversed 9, while Arabic 6 (٦) is a single dot above the line. If you are working with documents from Iran or Afghanistan, use the Persian mode. For documents from Egypt, Saudi Arabia, or the UAE, use the Arabic mode.
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