Fractions & Math Manipulation Tools
Fractions, ratios, long division, PEMDAS, prime factorisation and radical simplification — computed with exact rational arithmetic and displayed step by step. No floats, no rounding surprises, no uploads.
Most popular
- fractions-mathFractions● ready
Enter two fractions and an operator to get the exact answer as a fraction, mixed number and decimal — with every step shown and the quantities drawn as bars.
- fractions-mathSimplify Fraction● ready
Enter a fraction to reduce it to lowest terms, with Euclid's algorithm laid out one division at a time and the GCF shown.
- fractions-mathMixed ↔ Improper● ready
Enter a mixed number like 2 3/4 or an improper fraction like 11/4 — the converter detects which it is and shows the other with the steps.
- fractions-mathLCD● ready
Enter two or more denominators to get their least common multiple, with each number factored into primes and the highest powers explained.
- fractions-mathPEMDAS● ready
Enter an expression with + − × ÷ ^ and parentheses to get the value with every operation applied — and displayed — in the correct order.
Fraction Arithmetic
- fractions-mathFractions● ready
Enter two fractions and an operator to get the exact answer as a fraction, mixed number and decimal — with every step shown and the quantities drawn as bars.
- fractions-mathMixed ↔ Improper● ready
Enter a mixed number like 2 3/4 or an improper fraction like 11/4 — the converter detects which it is and shows the other with the steps.
- fractions-mathSimplify Fraction● ready
Enter a fraction to reduce it to lowest terms, with Euclid's algorithm laid out one division at a time and the GCF shown.
- fractions-mathEquivalent Fractions● ready
Enter a base fraction and how many to generate to get a list of equivalent fractions, each with its own fraction bar so the value stays visually the same.
- fractions-mathFraction ↔ Percent● ready
Turn a fraction into its exact percentage (including repeating decimals) or a percentage back into a reduced fraction, with the steps shown.
Common Denominators & Comparison
- fractions-mathCommon Denominator● ready
Enter two or more fractions to get each one rewritten over the least common denominator, with the multiplier used for each shown step by step.
- fractions-mathLCD● ready
Enter two or more denominators to get their least common multiple, with each number factored into primes and the highest powers explained.
- fractions-mathCompare Fractions● ready
Enter two fractions to find out whether one is less than, greater than or equal to the other, with the cross-products shown and both plotted on a number line.
- fractions-mathSimplify Ratio● ready
Enter a ratio like 24:36 to reduce it to lowest terms, with the greatest common factor and each term's share of the total shown.
- fractions-mathProportion● ready
Fill three of the four terms in a/b = c/d and leave the unknown blank to solve it exactly, with the cross-multiplication shown.
Arithmetic & Number Theory
- fractions-mathLong Division● ready
Enter a dividend and divisor to get the quotient, remainder and every digit-by-digit step of the long division.
- fractions-mathLong Multiplication● ready
Enter two whole numbers to get the product with the partial products laid out column by column, exactly as you would write it by hand.
- fractions-mathPEMDAS● ready
Enter an expression with + − × ÷ ^ and parentheses to get the value with every operation applied — and displayed — in the correct order.
- fractions-mathPrime Factors● ready
Enter a whole number to get its prime factors in exponent form, with each division-by-the-smallest-prime step laid out as a ladder.
- fractions-mathSimplify √● ready
Enter a whole number to pull the largest perfect-square factor out of the radical, giving a simplified √ form plus a decimal approximation.
- fractions-mathPoints vs Change● ready
Enter a starting and ending percentage to see both the point difference and the relative change, side by side with an explanation of the difference.
All tools
- fractions-mathFractions● ready
Enter two fractions and an operator to get the exact answer as a fraction, mixed number and decimal — with every step shown and the quantities drawn as bars.
- fractions-mathMixed ↔ Improper● ready
Enter a mixed number like 2 3/4 or an improper fraction like 11/4 — the converter detects which it is and shows the other with the steps.
- fractions-mathFraction ↔ Percent● ready
Turn a fraction into its exact percentage (including repeating decimals) or a percentage back into a reduced fraction, with the steps shown.
- fractions-mathSimplify Fraction● ready
Enter a fraction to reduce it to lowest terms, with Euclid's algorithm laid out one division at a time and the GCF shown.
- fractions-mathEquivalent Fractions● ready
Enter a base fraction and how many to generate to get a list of equivalent fractions, each with its own fraction bar so the value stays visually the same.
- fractions-mathCommon Denominator● ready
Enter two or more fractions to get each one rewritten over the least common denominator, with the multiplier used for each shown step by step.
- fractions-mathLCD● ready
Enter two or more denominators to get their least common multiple, with each number factored into primes and the highest powers explained.
- fractions-mathCompare Fractions● ready
Enter two fractions to find out whether one is less than, greater than or equal to the other, with the cross-products shown and both plotted on a number line.
- fractions-mathSimplify Ratio● ready
Enter a ratio like 24:36 to reduce it to lowest terms, with the greatest common factor and each term's share of the total shown.
- fractions-mathProportion● ready
Fill three of the four terms in a/b = c/d and leave the unknown blank to solve it exactly, with the cross-multiplication shown.
- fractions-mathLong Division● ready
Enter a dividend and divisor to get the quotient, remainder and every digit-by-digit step of the long division.
- fractions-mathLong Multiplication● ready
Enter two whole numbers to get the product with the partial products laid out column by column, exactly as you would write it by hand.
- fractions-mathPoints vs Change● ready
Enter a starting and ending percentage to see both the point difference and the relative change, side by side with an explanation of the difference.
- fractions-mathPEMDAS● ready
Enter an expression with + − × ÷ ^ and parentheses to get the value with every operation applied — and displayed — in the correct order.
- fractions-mathPrime Factors● ready
Enter a whole number to get its prime factors in exponent form, with each division-by-the-smallest-prime step laid out as a ladder.
- fractions-mathSimplify √● ready
Enter a whole number to pull the largest perfect-square factor out of the radical, giving a simplified √ form plus a decimal approximation.
About Fractions & Math Manipulation Tools
Most fraction calculators give you a decimal that is subtly wrong and no way to check it. These tools keep everything as exact fractions: the common denominator is found properly, the greatest common factor is derived with Euclid's algorithm, and long division is laid out digit by digit the way it is written on paper. When a decimal is genuinely useful — a percentage, a radical's approximate value — it is offered alongside the exact answer and clearly labelled as an approximation. Repeating decimals are detected rather than truncated, ratios are reduced to lowest whole-number terms, and a proportion can be solved for whichever of its four terms you leave blank. The result of every tool is a worked solution: the substituted formula and the intermediate values, so the answer can be verified and not merely trusted. Everything runs locally in the browser and works offline.
Related categories
- Math & Statistics Tools
Scientific calculator, prime numbers, matrices, statistics, and more.
- Units & Numbers Tools
Convert units and work with numbers — length, weight, temperature, and more.
- Geometry & Measurement Calculators
Area, perimeter, volume and coordinate geometry calculators with live diagrams.
Frequently asked questions
Are the fraction results exact, or rounded?
Exact. The arithmetic runs on arbitrary-precision integers, so 1/3 + 1/6 is reported as 1/2 rather than 0.49999999999999994. A decimal appears only where it helps, and repeating decimals are shown as such instead of being cut off.
Why do these tools show work instead of just the answer?
Because the point is usually to learn or check the method, not to have the number. Each tool prints the formula with your values substituted — the common denominator and multiplier for each fraction, the Euclidean divisions for a GCF, the partial products of a long multiplication — so the result can be reproduced by hand.
Does this duplicate tools that already exist elsewhere on the site?
No. Fraction↔decimal conversion and scientific notation live in Units & Numbers, and GCD/LCM live in Math & Statistics. Those tools are cross-linked from here instead of being rebuilt, so a fraction question reaches whichever page fits it rather than two that compete.
Can it handle negative and improper fractions?
Yes. Negative numerators and denominators are normalised so the sign sits with the numerator, improper fractions are accepted everywhere and can be converted to mixed numbers, and zero denominators are rejected with a clear message instead of producing infinity.