Fraction Calculator — Add, Subtract, Multiply and Divide with Steps

What is a Fraction Calculator?

A Fraction Calculator (भिन्न कैलकुलेटर) adds, subtracts, multiplies and divides fractions and mixed numbers and gives the answer in its simplest form. Fractions appear everywhere — maths homework, recipes, measurements in inches, sharing costs, probability and construction — and working with them by hand involves several steps where it is easy to slip: finding a common denominator, converting mixed numbers, flipping the second fraction for division and simplifying at the end.

This free calculator does all of that with exact arithmetic. It never converts your fractions to rounded decimals behind the scenes, so 1/3 stays exactly 1/3. Every answer comes with the working — the least common denominator, the reciprocal, the greatest common divisor — so students can follow the method, check homework and learn, while everyone else gets a quick, reliable result. Two extra modes simplify any fraction and convert decimals to fractions.

Key Features

• All four operations — +, −, × and ÷.
• Mixed numbers such as 2 1/3, including negative values.
• Step-by-step working for every calculation.
• Simplest form using the greatest common divisor.
• Mixed number, decimal and percentage versions of every answer.
• Simplify mode for reducing any fraction to lowest terms.
• Decimal → fraction for terminating decimals such as 0.375 or 2.5.
• Exact results with large whole numbers (up to 15 digits per box).

How to Use It — Step by Step

1. Choose a mode: Fraction arithmetic, Simplify a fraction or Decimal → fraction.
2. Enter the first fraction: numerator on top, denominator below. For a mixed number, also fill in the “whole” box.
3. Pick the operation: +, −, × or ÷.
4. Enter the second fraction in the same way.
5. Read the answer — simplest fraction, mixed number, decimal and percentage — and the steps underneath.

Adding and Subtracting Fractions

Fractions can only be added or subtracted when they have the same denominator. The neatest choice is the least common denominator (LCD), which is the least common multiple of the denominators.

Example: 3/4 + 5/6

1. LCD of 4 and 6 = 12.
2. 3/4 = 9/12 (multiply top and bottom by 3); 5/6 = 10/12 (multiply by 2).
3. 9/12 + 10/12 = 19/12.
4. 19 and 12 share no common factor, so 19/12 is already simplest; as a mixed number it is 1 7/12 (≈ 1.5833).

Subtraction works the same way: 5/6 − 3/4 = 10/12 − 9/12 = 1/12.

Multiplying and Dividing Fractions

Multiplication needs no common denominator — multiply straight across: 2/3 × 9/10 = 18/30, which simplifies (GCD 6) to 3/5.

Division means multiplying by the reciprocal of the second fraction (“keep, change, flip”): 3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8 = 1 7/8. Dividing by a fraction less than 1 makes the result bigger, which often surprises people at first.

Working with Mixed Numbers

To calculate with a mixed number, first change it to an improper fraction: multiply the whole number by the denominator and add the numerator.

Example: 2 1/3 × 1 1/2 → 7/3 × 3/2 = 21/6 = 7/2 = 3 1/2.

For negative mixed numbers, the minus sign applies to the whole value: −2 1/3 = −7/3, not −2 + 1/3. In the calculator, put the minus sign on the whole number.

Simplifying Fractions

A fraction is in simplest form when the numerator and denominator have no common factor other than 1. To simplify, divide both by their greatest common divisor (GCD). The calculator finds the GCD using Euclid's algorithm, which repeatedly replaces the larger number with the remainder of dividing it by the smaller one until the remainder is zero.

Example: 84/126. Euclid: 126 ÷ 84 leaves 42; 84 ÷ 42 leaves 0, so the GCD is 42. 84 ÷ 42 = 2 and 126 ÷ 42 = 3, giving 2/3.

Decimals to Fractions

Any terminating decimal can be written as a fraction over a power of 10 and then simplified:

• 0.375 = 375/1000 = 3/8 (GCD 125).
• 2.5 = 25/10 = 5/2 = 2 1/2.
• 0.04 = 4/100 = 1/25.

Equivalent Fractions

Fractions that look different can have the same value. Multiplying or dividing the numerator and denominator by the same non-zero number gives an equivalent fraction: 1/2 = 2/4 = 3/6 = 50/100. This is exactly what happens when you rewrite fractions with a common denominator before adding them, and in reverse when you simplify. Two fractions a/b and c/d are equivalent when a × d = b × c — a quick cross-multiplication check. For example, 6/8 and 9/12 are equivalent because 6 × 12 = 72 and 8 × 9 = 72.

Comparing and Ordering Fractions

To see which of two fractions is larger, either convert both to the same denominator or cross-multiply. Is 5/8 bigger than 3/5? Cross-multiply: 5 × 5 = 25 and 8 × 3 = 24. Since 25 > 24, 5/8 is larger. To order several fractions, convert them all to decimals (shown in the result boxes) or to the LCD. Remember that with the same numerator, a larger denominator means a smaller fraction: 1/8 is less than 1/6 because the whole is cut into more pieces.

Fractions of an Inch

Tape measures and rulers in inches are marked in halves, quarters, eighths and sixteenths, so adding lengths often means adding fractions. For example 5 3/8 in + 2 7/16 in: convert to sixteenths — 86/16 + 39/16 = 125/16 = 7 13/16 in. The table below shows common inch fractions in decimal inches and millimetres (1 inch = 25.4 mm exactly).

For converting whole measurements between inches, centimetres and other units, use our Unit Converter.

Everyday Uses

• Homework — checking answers and learning the method from the steps.
• Cooking — scaling recipes, such as 3/4 cup × 1 1/2.
• Measurements — adding lengths in inches like 5 3/8 + 2 7/16.
• Woodwork and construction — cutting lists and spacing.
• Money and shares — dividing amounts in fractional shares.
• Probability — combining fractional probabilities.

Tips for Students and Parents

• Try first, then check. Solve the problem on paper, then compare each line with the calculator's steps to find exactly where a mistake happened.
• Learn the LCD shortcut. If one denominator divides the other (4 and 8), the larger one is the LCD. If they share no factors (3 and 5), the LCD is their product.
• Cancel before multiplying. In 4/9 × 3/8, cancel 4 with 8 and 3 with 9 first to get 1/3 × 1/2 = 1/6 — smaller numbers, fewer errors.
• Estimate. 3/4 + 5/6 should be a bit more than 1.5, so 19/12 ≈ 1.58 makes sense.

Common Mistakes to Avoid

• Adding denominators — 1/2 + 1/3 is 5/6, not 2/5.
• Forgetting to flip the second fraction when dividing.
• Misreading mixed numbers — 2 1/3 means 2 + 1/3, not 2 × 1/3.
• Leaving answers unsimplified — 18/30 should become 3/5.
• Zero denominators — a denominator can never be 0.

Tips and Troubleshooting

• “Use whole numbers…” — each box takes whole numbers only; convert decimals with the decimal mode first.
• “A denominator cannot be 0” — check the bottom boxes.
• “Cannot divide by zero” — the second fraction is 0 in a division.
• Empty whole box — that is fine; it simply means a plain fraction.

Quick Glossary

• Numerator / denominator: the top and bottom numbers of a fraction.
• Proper fraction: numerator smaller than the denominator, such as 3/4.
• Improper fraction: numerator equal to or larger than the denominator, such as 19/12.
• LCD: least common denominator.
• GCD (HCF): greatest common divisor, also called the highest common factor.
• Reciprocal: a fraction flipped upside down; the reciprocal of 2/5 is 5/2.

Why Use This Fraction Calculator?

It gives exact answers, handles mixed and negative numbers, explains every step and offers simplifying and decimal conversion in the same place. It is free, quick and private — ideal for students, parents, teachers and anyone working with measurements.

Fraction Calculator — Key Facts

Frequently Asked Questions

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