How this tool works
The Fraction Calculator performs calculations using integer numerators and denominators wherever possible so that fraction results remain exact rather than relying only on rounded decimal values.
Fraction Input
The calculator supports:
Proper fraction: 3/4
Improper fraction: 7/4
Mixed number: 1 3/4
Negative fraction: -3/5
Negative mixed number: -2 1/3
Whole number: 5
Decimal: 0.75
Mixed numbers are converted into improper fractions before arithmetic is performed.
For example:
2 1/3 = (2 × 3 + 1) / 3 = 7/3
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Adding Fractions
For:
a/b + c/d
the calculator uses:
(a × d + c × b) / (b × d)
The result is then simplified.
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Subtracting Fractions
For:
a/b − c/d
the calculator uses:
(a × d − c × b) / (b × d)
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Multiplying Fractions
For:
a/b × c/d
the calculator uses:
(a × c) / (b × d)
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Dividing Fractions
Division is performed by multiplying the first fraction by the reciprocal of the second:
a/b ÷ c/d = a/b × d/c
The second fraction must not be zero.
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Simplifying Fractions
The calculator finds the greatest common divisor of the numerator and denominator:
Simplified Numerator =
Original Numerator ÷ GCD
Simplified Denominator =
Original Denominator ÷ GCD
For example:
84/126
GCD = 42
84 ÷ 42 = 2
126 ÷ 42 = 3
Simplified Fraction = 2/3
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Mixed and Improper Fraction Conversion
A mixed number is converted using:
Improper Numerator =
Whole Number × Denominator + Numerator
An improper fraction is converted into a mixed number using integer division:
Whole Number =
Numerator ÷ Denominator
Remainder =
Numerator mod Denominator
----------------
Decimal to Fraction
A terminating decimal is converted into an integer divided by a power of ten.
For example:
The resulting fraction is simplified using the greatest common divisor.
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Percentage to Fraction
A percentage is divided by 100 and then simplified:
Percentage as Fraction =
Percentage ÷ 100
For example:
37.5% = 37.5/100 = 375/1000 = 3/8
----------------
Fraction of a Number
The fraction is multiplied by the selected value:
Fraction of Number =
Fraction × Number
For example:
3/8 of 240 = 3/8 × 240 = 90
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Comparing Fractions
The calculator uses cross multiplication rather than comparing rounded decimal values.
For:
a/b and c/d
the calculator compares:
a × d
with:
c × b
If the cross products are equal, the fractions are equivalent.
All calculations are performed locally within the browser. Fraction results are simplified automatically, and decimal equivalents are formatted with practical precision.
Important assumptions
A fraction is entered as a numerator followed by / and a denominator.
Mixed numbers are entered as a whole number, a space, and a fraction, such as 2 1/3.
Denominators must not be zero.
Fraction arithmetic is performed using exact integer numerators and denominators where possible.
Mixed numbers are converted into improper fractions before calculations.
Results are automatically reduced to their lowest terms.
A negative sign applies to the entire fraction or mixed number.
In a mixed number, the fractional numerator is treated as non-negative.
Decimal-to-fraction conversion supports terminating decimal values.
Decimal conversion supports a maximum of 12 decimal places.
Scientific notation is not accepted as fraction input.
Percentage conversion treats the entered value as a percentage before dividing it by 100.
Division requires the second fraction to have a non-zero numerator.
Fraction comparison uses exact cross multiplication.
The missing-term calculation assumes that the entered fractions form an equivalent proportion.
Decimal equivalents may be rounded for display.
Very large values may be rejected when exact arithmetic would exceed JavaScript’s safe integer range.
Recent history is stored only in the current browser.
Limitations
The Fraction Calculator is provided for general mathematical, educational, and convenience purposes.
Decimal-to-fraction conversion is designed for terminating decimal values entered directly into the calculator. Repeating decimals such as:
0.333...
cannot be represented exactly unless the repeating pattern is identified separately.
The calculator does not interpret complex mathematical expressions such as:
(1/2 + 3/4) × 5/6
Each supported operation should be selected through its corresponding calculation mode.
Scientific notation, algebraic variables, irrational numbers, complex numbers, and symbolic expressions are not supported.
Simplified fraction arithmetic is subject to JavaScript’s safe integer range. Extremely large numerators or denominators may be rejected to protect result accuracy.
The decimal equivalent of a fraction may be rounded when the exact decimal representation is long or repeating.
The missing-term solver assumes that:
a/b = c/x
forms a valid proportion. It does not independently determine whether that relationship is appropriate for a real-world situation.
A mathematically correct fraction may still be unsuitable when:
Entered quantities use incompatible units;
Source data is rounded or inaccurate;
Measurement uncertainty is significant;
A fraction represents only part of a more complex formula; or
Domain-specific rules alter the calculation.
The calculator should not be used as the only basis for engineering, scientific, medical, financial, construction, regulatory, or safety-critical work. Important results should be verified independently.
Frequently asked questions
1: How do I add fractions with different denominators?+
Multiply each numerator by the other fraction’s denominator, add the resulting values, and multiply the denominators.nnFor example:nn1/3 + 1/4nn= (1 × 4 + 1 × 3) / (3 × 4)nn= (4 + 3) / 12nn= 7/12nnThe calculator automatically simplifies the final result where possible.
2: How do I simplify a fraction?+
Find the greatest common divisor of the numerator and denominator, then divide both by that number.nnFor example:nn24/36nnGreatest Common Divisor = 12nn24 ÷ 12 = 2n36 ÷ 12 = 3nnSimplified Fraction = 2/3
3: How do I convert a mixed number into an improper fraction?+
Multiply the whole number by the denominator, add the numerator, and keep the same denominator.nnFor example:nn2 3/5nnImproper Numerator = 2 × 5 + 3 = 13nnImproper Fraction = 13/5
4: How does the calculator convert a decimal into a fraction?+
The calculator removes the decimal point and places the resulting integer over a power of ten based on the number of decimal places.nnFor example:nn0.625 = 625/1000nnThe calculator then simplifies the fraction:nn625/1000 = 5/8
5: Are the entered fractions sent to PMNM?+
No. The Fraction Calculator performs its calculations locally within the browser.nnEntered fractions, decimals, percentages, and numerical values are not required to be transmitted to PMNM’s server. Recent calculation history is stored only in the current browser and can be cleared from the calculator.
Tool changelog
Initial release of the PMNM Fraction Calculator:nnIntroduced a comprehensive Fraction Calculator with Add Fractions, Subtract Fractions, Multiply Fractions, Divide Fractions, Simplify Fraction, Mixed and Improper Fraction Conversion, Decimal to Fraction, Percentage to Fraction, Fraction of a Number, Missing Fraction Term, and Compare Fractions modes.nnAdded support for proper fractions, improper fractions, whole numbers, mixed numbers, negative fractions, terminating decimals, exact cross multiplication, automatic fraction reduction, mixed-number results, decimal equivalents, example inputs, input validation, formula explanations, step-by-step calculations, copyable results, local browser history, responsive layouts, and browser-only processing.
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