Math & General

Fraction Calculator

Add, subtract, multiply and divide fractions in one click. Simplify, convert to mixed numbers or decimals, find LCM/GCD, and compare fractions — with full step-by-step working shown.

7 Calculation Types
Step-by-Step Working
Mixed Number Support
100% Free
Updated April 2026
Before You Calculate

What Are Fractions — and Why Does Getting Them Right Actually Matter?

April 2026  ·  4 min read  ·  Keeroot Solutions

A fraction is the fundamental mathematical way of expressing a part of a whole. Every fraction has two parts: the numerator (top number — how many parts you have) and the denominator (bottom number — how many equal parts the whole is divided into). So 3/4 means: the whole is cut into 4 equal parts, and you have 3 of them. Simple enough — until you need to add 3/4 and 2/5, or divide 7/8 by 3/11, and suddenly the rules matter.

Fractions are not just a school topic. They appear constantly in real life: a recipe calls for 3/4 cup of butter and you want to make 1.5 times the quantity (answer: 1 1/8 cups). A contractor buys 5 metres of timber but needs lengths of 3/8 metre each — how many pieces? (answer: 13, with 1/8 metre left over). A financial ratio shows earnings of 7/12 of target — is that above or below last quarter's 5/9? The mental arithmetic gets genuinely difficult, and small fraction errors compound into real mistakes.

Why Fraction Arithmetic Trips People Up

The rules for fractions are different for different operations — and that inconsistency is where errors happen. For addition and subtraction, you must first find a common denominator before you can add numerators. You cannot add 1/3 + 1/4 by adding numerators and denominators — 2/7 is wrong (the correct answer is 7/12). For multiplication, there is no need for a common denominator — you simply multiply numerator by numerator and denominator by denominator. For division, you flip the second fraction (take its reciprocal) and multiply — a rule that confuses many students because it seems counterintuitive. And after every operation, the result should be simplified to its lowest terms using the Greatest Common Divisor (GCD).

This calculator handles all seven types: addition, subtraction, multiplication, division, simplification, fraction-to-decimal and decimal-to-fraction conversion, and comparison. For every operation, it shows the full step-by-step working — not just the answer — so you can understand the method, not just copy the result. Also see our Percentage Calculator and Discount Calculator for related calculations.

Which Mode Should You Use?

Add / Subtract / Multiply / Divide — Standard two-fraction arithmetic. Supports mixed numbers (like 1 3/4) directly. Simplify — Reduce any fraction to its lowest terms. Convert — Switch between fraction and decimal form. Compare — Determine which of two fractions is greater using cross-multiplication. Each mode shows exactly how the result was reached so you can verify or learn from the working.

Result Analysis
—
—

Fraction Calculator — All Types

Select a calculation type, enter your fractions, and get the answer with complete step-by-step working

➕
Add
a/b + c/d
➖
Subtract
a/b − c/d
✖️
Multiply
a/b × c/d
➗
Divide
a/b ÷ c/d
✨
Simplify
Reduce a/b
🔄
Convert
Fraction ↔ Decimal
⚖️
Compare
Which is bigger?
➕ Addition: a/b + c/d = ?
Enter any fraction
and it will be reduced
to its simplest form.
→ decimal, %, mixed number
✨ RESULT
—
—
Formula applied
Result Summary
More Useful Results
Visual Breakdown
Step-by-Step Working
    Share This Result
    Where Fractions Actually Appear
    Real-World Applications — Why This Isn't Just School Maths
    🍳
    Cooking & Recipes

    Recipes scale fractions constantly. A recipe serving 4 calls for 2/3 cup of oil — scaled to 6 servings: 2/3 × 6/4 = 12/12 = 1 cup. Getting this wrong means over-seasoned or under-risen food. Doubling, halving, and scaling recipes is pure fraction arithmetic.

    2/3 × 3/2 = 1
    🔨
    Construction & DIY

    Timber, pipes, and tiles are measured in fractions of metres or feet. A shelf 3/4 metre wide needs to fit in a 2 1/2 metre wall with 3 equal gaps — that's fraction division and subtraction. Measurement errors in fractions lead to unusable cuts and wasted material.

    5/2 ÷ 4 = 5/8 m each
    💰
    Finance & Ratios

    Financial ratios, interest calculations, and portfolio allocations all use fractions. A P/E ratio of 22.5 is 45/2. A fund with 3/8 in equities and 1/4 in bonds has 5/8 total in growth assets. Comparing returns across funds involves comparing and adding fractions.

    3/8 + 1/4 = 5/8
    📐
    Engineering & Science

    Gear ratios, electrical resistance (in parallel: 1/R = 1/R1 + 1/R2), chemical concentrations, and unit conversions in physics all involve fraction arithmetic. Precision matters — a 1% error in a gear ratio compounds over thousands of rotations.

    1/R = 1/4 + 1/6 = 5/12
    🎵
    Music & Rhythm

    Musical time signatures are pure fractions. A 3/4 time signature has 3 quarter-note beats per bar. Mixing a dotted half note (3/4) with two quarter notes (2/4) fills exactly one 5/4 bar. Music composition involves constant fraction addition and comparison.

    3/4 + 1/2 = 5/4
    🧪
    Pharmacy & Medicine

    Drug dosages are precise fractions of body weight (mg/kg). A dose of 1/4 mg/kg for a 68 kg patient is 17 mg. Diluting a solution to 3/8 concentration from a 3/4 stock requires fraction division. Errors here have direct patient safety implications.

    (3/4) ÷ 2 = 3/8
    Avoid These Errors

    5 Common Fraction Mistakes (and the Correct Method)

    1
    Adding numerators and denominators separately. The most frequent fraction error: 1/3 + 1/4 ≠ 2/7. This is wrong because it treats the denominators as independent units rather than divisors of a whole. The correct method finds a common denominator first: convert to 4/12 + 3/12 = 7/12. The rule: for addition and subtraction, ONLY numerators can be added — after converting to a common denominator.
    2
    Forgetting to flip when dividing. Dividing fractions requires multiplying by the reciprocal of the second fraction — not dividing directly. 2/3 ÷ 4/5 ≠ (2÷4)/(3÷5). The correct method: 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6. The "KCF" rule: Keep the first fraction, Change the operation to multiplication, Flip the second fraction.
    3
    Not simplifying the final answer. 6/12 is a valid fraction, but 1/2 is its simplified form. Leaving answers unsimplified can fail academic questions, create confusion in practical contexts, and make further calculations unnecessarily messy. Always divide both numerator and denominator by their GCD. A fraction is fully simplified when GCD(numerator, denominator) = 1.
    4
    Converting mixed numbers incorrectly. To convert 2 3/4 to an improper fraction: multiply the whole number by the denominator (2 × 4 = 8), then add the numerator (8 + 3 = 11), keeping the same denominator. Result: 11/4. A common error is 2 3/4 = 23/4 (treating the whole number as a two-digit number) or 2 3/4 = 11/8 (multiplying denominator by 2 instead of adding). Formula: whole × denominator + numerator, over same denominator.
    5
    Multiplying denominators when the LCM would be smaller. 1/6 + 1/4 — multiplying denominators gives 24 as the common denominator (4/24 + 6/24 = 10/24 = 5/12). But LCM(6,4) = 12, giving a simpler path: 2/12 + 3/12 = 5/12 directly. Both approaches give the same simplified answer, but using LCM keeps numbers manageable. For large denominators like 1/36 + 1/48, the difference between LCM (144) and product (1728) is significant. For addition and subtraction, always use LCM rather than multiplying denominators.
    🔢
    Built & Maintained By
    Keeroot Solutions
    Digital Product Studio · Coimbatore, India · keeroot.com · Last updated: April 2026
    This Fraction Calculator is built and maintained by Keeroot Solutions. It supports all seven fraction operations — addition, subtraction, multiplication, division, simplification, conversion, and comparison — with complete step-by-step working for every result. The GCD algorithm uses the Euclidean method, the LCM uses the GCD-based formula, and all arithmetic uses exact integer rationals (no floating-point approximation) to ensure precision. All calculations run locally in your browser — no data is transmitted or stored.
    ✅ Exact integer arithmetic 📐 7 operation modes 🔒 No data stored 📅 Updated April 2026
    Percentage Calculator Discount Calculator GST Calculator About KeeHelper

    Fraction Formulas — Complete Reference

    All fraction operation rules with worked examples

    OperationFormulaExampleResult
    Additiona/b + c/d = (ad + bc) / bd1/3 + 1/47/12
    Subtractiona/b − c/d = (ad − bc) / bd3/4 − 1/35/12
    Multiplicationa/b × c/d = (a×c) / (b×d)2/3 × 3/46/12 = 1/2
    Divisiona/b ÷ c/d = (a×d) / (b×c)2/3 ÷ 4/510/12 = 5/6
    Simplify (GCD)(a÷GCD) / (b÷GCD)12/18, GCD=62/3
    To Decimala ÷ b3/40.75
    To Mixed Number⌊a/b⌋ remainder (a mod b)/b7/32 1/3
    LCM Tip for addition/subtraction: Instead of multiplying denominators (which can get large), find the Least Common Multiple (LCM) of the denominators first. For 1/6 + 1/4: LCM(6,4) = 12, so convert to 2/12 + 3/12 = 5/12. Same answer as (1×4 + 1×6)/(6×4) = 10/24 = 5/12 — just simpler numbers.

    How to Use This Calculator

    Step-by-step guide to getting the most out of all 7 fraction tools

    For Add / Subtract / Multiply / Divide: Select the operation, enter the numerator and denominator for each fraction, and click Calculate. The result is automatically simplified using the GCD. You can also switch to Mixed Number mode to input numbers like 1 3/4 directly.

    For Simplify: Enter any fraction (e.g., 24/36) and the calculator finds the GCD and reduces it step by step.

    For Convert: Switch between Fraction → Decimal and Decimal → Fraction. Decimal-to-fraction conversion shows the exact fraction (e.g., 0.125 = 1/8) using the GCD method.

    For Compare: Enter two fractions to find which is greater, lesser, or if they are equal. Results show cross-multiplication working.

    Frequently Asked Questions

    Common questions about fractions and how to solve them

    How do you add fractions with different denominators?
    Find the LCM of the denominators, convert both fractions to equivalent fractions with that LCM as the denominator, then add the numerators. Example: 1/3 + 1/4. LCM(3,4) = 12. Convert: 4/12 + 3/12 = 7/12. Simplify if needed (already in simplest form).
    How do you divide fractions?
    To divide by a fraction, multiply by its reciprocal (flip the second fraction). Example: 2/3 ÷ 4/5 = 2/3 × 5/4 = (2×5)/(3×4) = 10/12 = 5/6. The acronym KCF helps: Keep the first fraction, Change division to multiplication, Flip the second fraction.
    How do I simplify a fraction to its lowest terms?
    Find the Greatest Common Divisor (GCD) of the numerator and denominator, then divide both by it. Example: 24/36 — GCD(24,36) = 12. 24÷12 = 2, 36÷12 = 3. So 24/36 = 2/3. A fraction is in lowest terms when GCD(numerator, denominator) = 1.
    How do I convert a mixed number to an improper fraction?
    Multiply the whole number by the denominator, then add the numerator. Keep the same denominator. Example: 2 3/4 = (2×4 + 3)/4 = (8+3)/4 = 11/4. To reverse: divide numerator by denominator: 11÷4 = 2 remainder 3, so 11/4 = 2 3/4.
    What is the difference between GCD and LCM?
    GCD (Greatest Common Divisor) is the largest number that divides both numbers. Used to simplify fractions. LCM (Least Common Multiple) is the smallest number that both numbers divide into. Used to find a common denominator for addition/subtraction. For 12 and 18: GCD = 6, LCM = 36. GCD × LCM = product of the two numbers (12×18 = 216 = 6×36 ✓).
    How do you convert a repeating decimal to a fraction?
    For 0.333...: let x = 0.333..., then 10x = 3.333..., subtract: 9x = 3, so x = 3/9 = 1/3. This calculator handles terminating decimals (e.g., 0.75 = 3/4) by multiplying by the appropriate power of 10 and simplifying with GCD.
    Is this calculator private? Is any data stored?
    Yes, completely private. All calculations run entirely in your browser using JavaScript — no data is ever sent to a server. Your inputs disappear when you close or refresh the tab.