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Operations, simplify, mixed numbers, decimals

Fraction Calculator

This calculator adds, subtracts, multiplies, and divides fractions; reduces to lowest terms with the greatest common factor shown; converts decimals and mixed numbers; and includes a Big Number tab for very large whole-number numerators and denominators. The Operations tab shows least common multiple steps when you add or subtract.

By Jeff Beem

Updated

Fraction operations

Add, subtract, multiply, or divide two fractions. Result is simplified. Common denominator logic is shown for + and −.

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Result
Fraction3/4

= 0.75

Steps

  • Common denominator (least common multiple of 2 and 4) = 4
  • Scale: 1/2 = 2/4, 1/4 = 1/4
  • Result before simplify: 3/4
  • Simplified: 3/4

Part-to-whole

First

Second

Result

Addition & subtraction rules

Addition: a/b + c/d = (ad + bc)/bd, common denominator to combine units.

Subtraction: a/b − c/d = (ad − bc)/bd, difference between two parts of a whole.

Simplification: Divide numerator and denominator by their greatest common divisor to reach lowest terms.

How to use this calculator

Pick a tab at the top: Operations for two-fraction +, −, ×, ÷ (Steps and pie charts on +/−); Mixed Numbers for whole + fraction inputs; Simplifier to reduce one fraction with the GCF line shown; Decimal ↔ Fraction for terminating decimal conversion; or Big Number for integer digit strings of any size. Enter values in the left column; the dark result card updates live. Zero denominators and division by a zero numerator show an error. Operations defaults to 1/2 + 1/4 → 3/4; Simplifier to 6/8 → 3/4; Decimal ↔ Fraction to 0.375 → 3/8.

Reading results on each tab

Five tabs share one result panel. On Operations, the Steps list and part-to-whole pie charts sit under the dark result card; Operations also shows a decimal equivalent under the fraction when the answer is not a whole number. Simplifier shows the greatest common divisor used and before/after pies. Mixed Numbers and Big Number show a simplified result only — no Steps list or pie charts.

Worked examples at the defaults

Example: Operations → 1/2 + 1/4

Default inputs: 1/2 and 1/4 with + selected. Result: 3/4, decimal 0.75 under the fraction. Steps: common denominator (LCM of 2 and 4) = 4; scale to 2/4 + 1/4; simplified 3/4. Pie charts preview both inputs and the result (display capped at 24 slice markers).

Simplifier → 6/8

Default 6/8 reduces to 3/4. The result panel shows greatest common divisor 2 for improper numerator 6 and denominator 8. Optional whole part (e.g. 2 with 6/8) converts to an improper fraction before reduction.

Decimal ↔ Fraction → 0.375

Default decimal 0.375 converts to 3/8 (375/1000 reduced). Switch to Fraction → Decimal and enter 3/8 to read 0.375. Non-terminating decimals are only as exact as the digits you type.

Mixed Numbers & Big Number

Mixed Numbers default 0 1/2 + 0 1/4 → 3/4 (simple fraction because the whole part is 0). Big Number default 1/2 + 1/4 → 3/4 as an integer fraction string; integer digits only, no Steps or pie charts.

Fraction Calculator: Add, Subtract, Simplify & Convert

This calculator runs five fraction tools in one page: two-fraction arithmetic with LCM steps, mixed numbers, simplify with GCF shown, decimal conversion, and big-number fractions. All math runs locally in your browser.

What this calculator does

This fraction calculator combines five tools: Operations (+, −, ×, ÷ on two fractions; Steps and pie charts on this tab only; decimal equivalent under the fraction when the result is not a whole number), Mixed Numbers (whole + fraction inputs converted to improper fractions internally; result in mixed form when the value is at least 1, otherwise a simple fraction like 3/4), Simplifier (lowest terms with greatest common divisor shown), Decimal ↔ Fraction (terminating decimal ↔ reduced fraction), and Big Number (integer digit strings only, arbitrary size). Denominator zero is invalid; division also fails when the divisor fraction’s numerator is zero.

How the math works

Addition and subtraction need a common denominator. One form is
ab±cd=ad±bcbd\frac{a}{b} \pm \frac{c}{d} = \frac{ad \pm bc}{bd}
The Operations tab’s Steps list scales to the least common multiple of the denominators so intermediate numbers stay smaller. Multiplication:
ab×cd=acbd\frac{a}{b} \times \frac{c}{d} = \frac{ac}{bd}
Division multiplies by the reciprocal:
ab÷cd=adbc\frac{a}{b} \div \frac{c}{d} = \frac{ad}{bc}
Results reduce by the greatest common divisor.
Default Operations check: 1/2 + 1/4 → LCM of 2 and 4 is 4 → 2/4 + 1/4 = 3/4 (decimal 0.75). Simplifier: 6/8 → GCD 2 → 3/4. Decimal: 0.375 → 375/1000 → 3/8. On Mixed Numbers with +, 4 2/3 + 1 1/2 → wholes 5, fractions scaled to LCD 6 → total 6 1/6. With ÷ selected, 3 1/2 ÷ 1 1/4 → 7/2 × 4/5 = 14/5 = 2 4/5 in the result panel.

Limits of the model

Decimal→fraction builds from the digits you type; fraction→decimal uses floating-point division, so repeating decimals show rounding. Big Number rejects non-integer digit strings. Pie charts cap at 24 slice markers for readability. The Addition & subtraction rules panel on Operations summarizes formulas; it does not replace the Steps list for your entered values.

Fraction Calculator FAQ

Which tabs does this fraction calculator include?

Five tabs share one result panel: Operations (two fractions + operator; Steps and pie charts), Mixed Numbers (whole + fraction per value), Simplifier (reduce one fraction; greatest common divisor shown), Decimal ↔ Fraction, and Big Number (integer digit strings only). Steps and pie charts appear on Operations and Simplifier only.

How do I add fractions with different denominators on this page?

Open Operations, enter both fractions, and choose +. The Steps panel lists the least common multiple (LCM) and scaled numerators before simplification. Default 1/2 + 1/4 → LCM 4 → 2/4 + 1/4 = 3/4 with decimal 0.75 under the result.

Why does the calculator reject a zero denominator?

A fraction is numerator ÷ denominator; division by zero is undefined. If either denominator is zero, or you divide by a fraction whose numerator is zero, the result panel shows an error instead of a fraction.

How does the Simplifier tab work at its default?

Default input is 6/8. The result panel shows simplified 3/4 and the line “Greatest common divisor of 6 and 8 = 2.” Optional whole part (e.g. 2 with 6/8) converts to an improper fraction before reduction.

How do I convert a decimal to a fraction here?

On Decimal ↔ Fraction, leave mode on Decimal → Fraction and enter a terminating decimal. Default 0.375 → 3/8 (375/1000 reduced). Switch to Fraction → Decimal and enter numerator/denominator to read a floating-point decimal (exact only for terminating rationals).

How do Mixed Numbers and Big Number differ from Operations?

Mixed Numbers defaults 0 1/2 + 0 1/4 → 3/4 (simple fraction when the whole part is 0). No Steps or pies. Big Number defaults 1/2 + 1/4 → 3/4 using BigInt math on digit strings; no mixed display, Steps, or pies.

How do I divide mixed numbers in this widget?

On Mixed Numbers, select ÷ and enter each value as whole, numerator, denominator. Example: 3 whole 1/2 ÷ 1 whole 1/4 converts to 7/2 ÷ 5/4 = 14/5, displayed as 2 4/5. The widget uses invert-and-multiply internally, then simplifies.

What are the limits of decimal and pie display?

Fraction → decimal uses JavaScript floating-point division. Very long decimal strings follow normal parse limits. Part-to-whole pie charts cap at 24 slice markers (ratio shading, not one marker per unit when the denominator is larger). Big Number accepts integer digit strings only.

Mathematical Reference Note

Calculation Logic: This tool uses standard mathematical algorithms. While we strive for accuracy, errors in logic or user input can result in incorrect data.

Verification: Results should be cross-checked if used for important academic, professional, or personal calculations.

Standard Terms: This tool is provided free of charge and as-is. CalcRegistry provides no warranty regarding the accuracy or fitness of these results for your specific needs.

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