The calculation, without hidden assumptions
Fraction arithmetic is easy to get wrong when the denominators differ, so this calculator keeps the intermediate numerator and denominator visible. Addition and subtraction show the cross-products, multiplication shows the product directly, and division shows the reciprocal step before simplifying.
How to use this calculator
Enter the numerator and denominator for each fraction. Negative numerators are supported; denominators cannot be zero.
Choose add, subtract, multiply or divide.
Read the unsimplified working, greatest common divisor, reduced fraction, decimal value and mixed-number form when applicable.
Where people use it
- •Homework and classroom checks
- •Measurement and recipe arithmetic
- •Construction dimensions expressed as fractions
Example: 3/4 + 5/8
Cross-multiplying gives (3×8 + 5×4)/(4×8) = 44/32. Dividing numerator and denominator by 4 gives 11/8, or 1 3/8.
What the result does not assume
- •Denominators must be non-zero integers. The calculator rejects invalid division by a zero-valued second fraction.
- •Very large integer inputs can exceed ordinary JavaScript safe-integer precision, so this tool is intended for practical fraction arithmetic rather than arbitrary-precision number theory.
Frequently asked questions
Do I need a common denominator first?+
Not manually. For addition and subtraction the calculator forms the equivalent common-denominator numerator using cross-products, then simplifies.
How do you divide fractions?+
Multiply the first fraction by the reciprocal of the second fraction, then simplify.
Does it show a mixed number?+
Yes when the absolute numerator is at least as large as the denominator.
Semantic next steps
Continue the calculation
These links move to a different input, formula or project stage rather than a keyword variation of this page.
Decimal ↔ Fraction Calculator — Exact Steps & Mixed Number
Convert a terminating decimal to an exact simplified fraction or convert a fraction back to decimal, with the place-value fraction, GCD reduction and mixed-number form shown.
OpenMixed Number ↔ Improper Fraction Calculator
Convert mixed numbers to improper fractions or improper fractions back to mixed form, with sign handling, simplification and the multiplication-plus-remainder steps shown.
OpenInch Fraction Calculator — Decimal, Millimeters & Tape-Measure Fractions
Round decimal inches or millimeters to the nearest 1/2 through 1/64 inch, show feet-and-inches form, error from the rounded mark and reverse fraction-to-decimal values.
OpenRecipe Scaling Calculator — Fractions, Servings & Ingredient List
Scale a pasted ingredient list from original to target servings, parse common decimals, fractions, mixed numbers and Unicode fractions, and return practical scaled quantities without pretending cooking time scales linearly.
OpenRatio Calculator
Simplify integer or decimal ratios, solve a missing proportion value, scale a ratio, and split a total into proportional shares with visible working.
OpenFraction Simplifier — Reduce to Lowest Terms
Reduce a fraction to lowest terms using the greatest common divisor, normalize the sign, and show decimal and mixed-number forms with the reduction step.
OpenPercentage Calculator
Solve percentage-of, what-percent, increase or decrease, percentage change, percentage difference and reverse percentage problems with the substituted working shown.
OpenFeet and Inches Calculator
Add, subtract, multiply, divide or convert feet and inches, including decimal and fractional inch inputs, with decimal feet and metric equivalents.
OpenFree publisher widget
Put this calculator on your website
Give readers the live calculator without rebuilding the math. Copy the responsive embed in one click, or customize width, height, border and corner radius before publishing. The branded MAXScanner attribution stays visible.
Calculator embed HTML
Paste this code into your page. Focus the code box to select it manually.
Keep the result connected to the real job
MAXScanner keeps the formula and assumptions beside the result so you can verify the number before using it in a drawing, estimate, specification, worksheet or document. Where a supplier, manufacturer, drawing or applicable standard owns a requirement, that source remains authoritative.