Fraction Calculator — Add, Subtract, Multiply & Divide Fractions | CalcifyAll
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Fraction Calculator

Add, subtract, multiply, and divide fractions with full step-by-step working shown. Simplify any fraction, convert to decimals, and compare fractions instantly.

➕ Add Fractions ➖ Subtract Fractions ✖️ Multiply Fractions ➗ Divide Fractions 🔢 Simplify Fractions ⚖️ Compare Fractions 📊 Decimal Converter
Fraction Calculator
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Add Fractions
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Simplify & Reduce
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LCM & GCF
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Mixed Numbers
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Step-by-Step Working
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100% Free
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Compare Fractions
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Decimal Conversion
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Fraction Calculator
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Add Fractions
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Simplify & Reduce
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LCM & GCF
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Mixed Numbers
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Step-by-Step Working
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100% Free
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Compare Fractions
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Decimal Conversion
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➗ Fraction Arithmetic Calculator
Select Operation
Choose an operation, then enter your fractions below
Enter Your Fractions
Fraction 1
+
Fraction 2
=
?
Result (Simplified)
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📐 Step-by-Step Working
🔢 Simplify / Reduce a Fraction
Enter the Fraction to Simplify
Numerator
→
?
Options
Simplified Result
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📐 Step-by-Step Working
⚖️ Compare Two Fractions
Enter Both Fractions
Fraction 1
vs
Fraction 2
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📐 Step-by-Step Comparison
📐 Fraction Formulas Reference
Addition: a/b + c/d = (a×d + c×b) / (b×d) → simplify by GCF Subtraction: a/b − c/d = (a×d − c×b) / (b×d) → simplify by GCF Multiplication: a/b × c/d = (a×c) / (b×d) → simplify by GCF Division: a/b ÷ c/d = (a×d) / (b×c) → multiply by reciprocal Simplify: a/b → (a÷GCF) / (b÷GCF) GCF (GCD): Euclid's algorithm — GCF(a,b) = GCF(b, a mod b) LCM: LCM(a,b) = (a × b) / GCF(a,b) Mixed Number: improper a/b = (a÷b) and (a mod b)/b

The key to all fraction arithmetic is finding the Greatest Common Factor (GCF) to simplify results, and the Least Common Multiple (LCM) to find a common denominator when adding or subtracting. This calculator shows every step so you understand the process, not just the answer.

💡 How to Use the Fraction Calculator

Fraction Arithmetic: Select your operation (+, −, ×, ÷), enter the numerator and denominator for each fraction, and click Calculate. The result is automatically simplified to its lowest terms. Both proper fractions (e.g. 3/4) and improper fractions (e.g. 7/4) are supported.

Simplify / Reduce: Enter any fraction and this calculator finds the Greatest Common Factor (GCF) to reduce it to its simplest form. It also converts to a mixed number, decimal equivalent, and percentage.

Compare Fractions: Enter two fractions to see which is larger, smaller, or whether they are equal. The calculator converts both to a common denominator for a fair comparison, shows the decimal values side-by-side, and visualises the difference as a bar chart.

💎 6 Key Rules for Working with Fractions
1
Always simplify your answer. A fraction is in its simplest (lowest) form when the numerator and denominator share no common factors other than 1. Divide both by their Greatest Common Factor (GCF) to reduce. For example, 8/12 simplifies to 2/3 because GCF(8,12) = 4.
2
To add or subtract fractions, find a common denominator first. You can only add or subtract fractions with the same denominator. Find the Least Common Multiple (LCM) of both denominators, convert each fraction, then add/subtract the numerators. The denominator stays the same.
3
Multiplying fractions is the simplest operation. Just multiply numerator by numerator and denominator by denominator. No common denominator needed. Always simplify the result — you can even cross-cancel before multiplying to keep numbers smaller.
4
Dividing fractions means multiplying by the reciprocal. Flip the second fraction (swap numerator and denominator) and then multiply. For example, 2/3 ÷ 4/5 becomes 2/3 × 5/4 = 10/12 = 5/6. “Keep, Change, Flip” is a helpful mnemonic.
5
Convert mixed numbers to improper fractions before calculating. A mixed number like 2½ must become 5/2 before you can use it in arithmetic. Multiply the whole number by the denominator and add the numerator: (2×2)+1 = 5. Then convert back at the end if needed.
6
A negative denominator should always be moved to the numerator. By convention, fractions are written with a positive denominator. If your result has a negative denominator (e.g. 3/−4), move the negative sign to the numerator: −3/4. This makes fractions easier to compare and simplify.
Frequently Asked Questions
To add fractions with different denominators, you must first find a common denominator — typically the Least Common Multiple (LCM) of both denominators. Then convert each fraction to an equivalent fraction with that denominator (multiply numerator and denominator by the same factor). Once both fractions share a denominator, simply add the numerators and keep the denominator. Finally, simplify the result by dividing numerator and denominator by their GCF. Example: 1/4 + 1/6 → LCM(4,6) = 12 → 3/12 + 2/12 = 5/12.
The Greatest Common Factor (GCF) — also called the Greatest Common Divisor (GCD) — is the largest number that divides evenly into both the numerator and denominator of a fraction. To simplify a fraction, divide both the numerator and the denominator by their GCF. For example, to simplify 18/24: GCF(18,24) = 6, so 18÷6 = 3 and 24÷6 = 4, giving 3/4. The most efficient way to find GCF is Euclid’s Algorithm: GCF(a, b) = GCF(b, a mod b), repeating until the remainder is 0.
An improper fraction has a numerator larger than or equal to its denominator (e.g. 7/4, 9/3). To convert to a mixed number: divide the numerator by the denominator. The quotient becomes the whole number, and the remainder becomes the new numerator over the original denominator. Example: 7/4 → 7 ÷ 4 = 1 remainder 3 → 1 and 3/4. To go the other way (mixed to improper): multiply the whole number by the denominator, then add the numerator. Example: 2 and 3/4 → (2×4)+3 = 11, so 11/4.
To divide fractions, use the “Keep, Change, Flip” method: (1) Keep the first fraction the same; (2) Change the division sign to multiplication; (3) Flip the second fraction (write its reciprocal — swap numerator and denominator). Then multiply the two fractions normally: multiply numerators together and denominators together, and simplify the result. Example: 2/3 ÷ 4/5 → Keep 2/3, Change ÷ to ×, Flip 4/5 to 5/4 → 2/3 × 5/4 = 10/12 = 5/6.
The reciprocal of a fraction is obtained by flipping it — swapping the numerator and denominator. The reciprocal of 3/4 is 4/3. The reciprocal of 2 (which is 2/1) is 1/2. When you multiply a fraction by its reciprocal, the result is always 1: 3/4 × 4/3 = 12/12 = 1. Reciprocals are essential for fraction division: dividing by a fraction is the same as multiplying by its reciprocal.
The most reliable method is to convert both fractions to a common denominator, then compare the numerators — the fraction with the larger numerator is greater. Alternatively, convert both fractions to decimals by dividing numerator by denominator, then compare the decimals directly. For example, to compare 3/5 and 5/8: convert to decimals: 3/5 = 0.6, 5/8 = 0.625. Since 0.625 > 0.6, we know 5/8 > 3/5. Cross-multiplication also works: multiply 3×8 = 24 and 5×5 = 25; since 25 > 24, the fraction on the right (5/8) is larger.
Yes — unlike addition and subtraction, multiplication does not require a common denominator. Simply multiply the numerators together to get the new numerator, and multiply the denominators together to get the new denominator. Then simplify. For example: 2/3 × 3/4 = (2×3)/(3×4) = 6/12 = 1/2. A useful shortcut is to cross-cancel before multiplying — if a numerator and a different fraction’s denominator share a common factor, divide both by it first. This keeps numbers smaller and makes simplification easier.
The Least Common Multiple (LCM) of two numbers is the smallest number that is a multiple of both. For fractions, the LCM of the denominators gives you the Least Common Denominator (LCD) — the smallest possible common denominator. Using the LCD rather than just multiplying the denominators keeps numbers smaller and reduces simplification work. Example: to add 1/4 + 1/6, LCM(4,6) = 12 (not 24). This gives 3/12 + 2/12 = 5/12, which is already in simplest form. LCM is calculated as: LCM(a,b) = (a × b) ÷ GCF(a,b).