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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)

✅

📐 Step-by-Step Working

🔢 Simplify / Reduce a Fraction
Enter the Fraction to Simplify
Numerator

→
?

Options


Simplified Result

✅

📐 Step-by-Step Working

⚖️ Compare Two Fractions
Enter Both Fractions
Fraction 1

vs
Fraction 2

⚖️

📐 Step-by-Step Comparison

⚡ The 30-Second Version

Add or subtract: you can only add or subtract fractions that share a denominator. Find the least common denominator, convert both fractions, then add or subtract the numerators.

Multiply: multiply straight across — numerator × numerator, denominator × denominator — then simplify. No common denominator needed.

Divide: dividing by a fraction is the same as multiplying by its reciprocal — Keep, Change, Flip.

Simplify: a fraction is in simplest form when the numerator and denominator share no common factor other than 1.

The #1 trap: adding straight across gives the wrong answer — 1/2 + 1/3 is 5/6, not 2/5.

💡 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.

Quick start in 5 steps:

1
Open the Fraction Arithmetic tab and pick +, −, ×, or ÷.
2
Type each fraction’s numerator and denominator into the stacked boxes.
3
Click Calculate & Show Steps — the simplified answer appears with every intermediate step, so you can copy the working into your homework.
4
Use the Simplify Fraction tab to reduce any fraction (18/24 → 3/4) or convert it to a mixed number, decimal, and percentage.
5
Use the Compare Fractions tab to settle “which is bigger” — for example, 3/4 vs 5/6 — with a visual bar chart.

➕ How to Add Fractions — Step by Step

To add fractions with different denominators, find the least common denominator (LCD), convert both fractions to equivalent fractions, then add the numerators.

Worked example: 1/2 + 1/3

1
Find the LCD of 2 and 3. Multiples of 2: 2, 4, 6… Multiples of 3: 3, 6… → LCD = 6.
2
Convert: 1/2 = 3/6 (multiply top and bottom by 3); 1/3 = 2/6 (multiply top and bottom by 2).
3
Add the numerators: 3/6 + 2/6 = 5/6. The denominator stays 6.
4
Simplify: 5 and 6 share no common factor, so 5/6 is already in lowest terms. 1/2 + 1/3 = 5/6

Shortcut: if the two denominators share no common factors, the LCD is simply their product (2 × 3 = 6).

➖ How to Subtract Fractions

Subtraction works exactly like addition: get a common denominator first, then subtract the numerators.

Worked example: 3/4 − 1/6

1
Find the LCD of 4 and 6. Multiples of 4: 4, 8, 12… Multiples of 6: 6, 12… → LCD = 12.
2
Convert: 3/4 = 9/12 (× 3); 1/6 = 2/12 (× 2).
3
Subtract the numerators: 9/12 − 2/12 = 7/12.
4
Simplify: GCF(7, 12) = 1, so 7/12 is final. 3/4 − 1/6 = 7/12

If the answer is an improper fraction (numerator ≥ denominator), convert it to a mixed number — for example, 5/4 = 1 1/4.

✖️ How to Multiply Fractions

Multiplication is the simplest operation: multiply numerator × numerator and denominator × denominator. No common denominator is needed.

Worked example: 2/3 × 3/4

1
Multiply across: (2 × 3)/(3 × 4) = 6/12.
2
Simplify: GCF(6, 12) = 6 → 6/12 = 1/2. 2/3 × 3/4 = 1/2

Shortcut — cross-cancel first: cancel the 2 with the 4 (both ÷ 2) and the 3 with the 3 (both ÷ 3) before multiplying: 1/1 × 1/2 = 1/2. Same answer, much smaller numbers.

➗ How to Divide Fractions

To divide fractions, use Keep–Change–Flip: keep the first fraction, change ÷ to ×, flip the second fraction (use its reciprocal).

Worked example: 3/4 ÷ 1/2

1
Keep–Change–Flip: 3/4 ÷ 1/2 becomes 3/4 × 2/1.
2
Multiply: (3 × 2)/(4 × 1) = 6/4.
3
Simplify: GCF(6, 4) = 2 → 6/4 = 3/2 = 1 1/2. 3/4 ÷ 1/2 = 1 1/2

Sanity check: dividing by 1/2 should double the number — and 3/4 doubled is 6/4 = 1 1/2. ✓

🔀 Adding and Subtracting Mixed Numbers

Convert each mixed number to an improper fraction first: multiply the whole number by the denominator and add the numerator. Example: 2 3/4 = (2 × 4 + 3)/4 = 11/4.

Worked example: 2 1/2 + 1 3/4

1
Convert: 2 1/2 = 5/2; 1 3/4 = 7/4.
2
Common denominator: 5/2 = 10/4.
3
Add: 10/4 + 7/4 = 17/4.
4
Convert back: 17 ÷ 4 = 4 remainder 1 → 4 1/4. 2 1/2 + 1 3/4 = 4 1/4

Subtraction works the same way: 3 1/4 − 1 2/3 = 13/4 − 5/3 = 39/12 − 20/12 = 19/12 = 1 7/12.

🔽 How to Simplify Fractions

Divide the numerator and denominator by their greatest common factor (GCF) — the largest number that divides evenly into both.

Worked example: simplify 18/24

1
Find GCF(18, 24): factors of 18 → 1, 2, 3, 6, 9, 18; factors of 24 → 1, 2, 3, 4, 6, 8, 12, 24. Largest shared factor: 6.
2
Divide: 18 ÷ 6 = 3; 24 ÷ 6 = 4. 18/24 = 3/4

Euclid’s shortcut for big numbers: GCF(a, b) = GCF(b, a mod b). Example: GCF(48, 18) → 48 mod 18 = 12 → GCF(18, 12) → 18 mod 12 = 6 → GCF(12, 6) → 12 mod 6 = 0 → the GCF is 6.

A fraction is fully simplified when the GCF of its numerator and denominator is 1.

🔄 Fractions, Decimals & Percentages

Convert a fraction to a decimal by dividing the numerator by the denominator, then multiply by 100 for the percentage. To go from a decimal back to a fraction, write the decimal over the matching power of 10 and simplify: 0.75 = 75/100 = 3/4.


Fraction Decimal Percentage
1/2 0.5 50%
1/3 0.333… 33.3%
2/3 0.667… 66.7%
1/4 0.25 25%
3/4 0.75 75%
1/5 0.2 20%
1/8 0.125 12.5%
1/10 0.1 10%

Watch out for repeating decimals: 1/3 = 0.333… never terminates, so 0.33 is only an approximation. The calculator’s Simplify tab shows the exact decimal equivalent.

📐 Fraction Formulas Cheat Sheet


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
Frac → Decimal: a/b = a ÷ b
Decimal → Frac: 0.75 = 75/100 → simplify by GCF

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.

⚠️ Common Fraction Mistakes to Avoid

1
Adding straight across. 1/2 + 1/3 is 5/6, not 2/5. Denominators name the size of the pieces — you can only add pieces of the same size, so find a common denominator first.
2
Using a common denominator for multiplication or division. × and ÷ work straight across (or via reciprocals) — a common denominator is only ever needed for + and −.
3
Forgetting to flip the second fraction when dividing. 3/4 ÷ 1/2 means 3/4 × 2/1, not 3/4 × 1/2 — Keep, Change, Flip, in that order.
4
Leaving the answer unsimplified. 6/12 is correct but incomplete — always reduce to lowest terms (1/2) by dividing by the GCF.
5
Confusing the LCD with the GCF. The LCD (from the LCM) is for adding and subtracting; the GCF is for simplifying. Different jobs, different numbers.

🧠 Quick Mental-Math Shortcuts

1
Cross-cancel before multiplying. In 2/3 × 3/4, cancel the 3s and the 2/4 first: 1/1 × 1/2 = 1/2.
2
Benchmark against 1/2. Is 5/11 bigger than 1/2? 5/11 ≈ 0.45, so no — no LCD needed.
3
Dividing by a fraction grows the number. ÷ 1/2 doubles it; ÷ 1/4 quadruples it. So 1/2 ÷ 1/4 = 2.
4
To halve a fraction, double the denominator. Half of 3/4 is 3/8. To double it, double the numerator instead.
5
Same denominators? Just work the tops. 5/8 + 1/8 = 6/8 = 3/4.

➖ Fractions with Negative Numbers

Sign rules: a negative sign in the numerator or the denominator makes the whole fraction negative; negatives in both cancel out: (−3)/4 = 3/(−4) = −3/4, while (−3)/(−4) = 3/4.

Worked example: −1/2 + 1/3

1
Common denominator: LCD of 2 and 3 is 6 → −1/2 = −3/6; 1/3 = 2/6.
2
Add: −3/6 + 2/6 = −1/6. −1/2 + 1/3 = −1/6

By convention, always move a negative denominator to the numerator: write −3/4, not 3/−4.

⚖️ Comparing Fractions: Which Is Bigger?

Convert both fractions to a common denominator and compare the numerators — the bigger numerator wins. Comparing the decimals works too.

Worked example: 3/4 vs 5/6

1
Common denominator: LCD of 4 and 6 is 12 → 3/4 = 9/12; 5/6 = 10/12.
2
Compare: 10 > 9, so 5/6 > 3/4 (as decimals: 0.833… > 0.75).

Quick check with 1/2 as a benchmark: 3/5 = 0.6 > 1/2, while 5/11 ≈ 0.45 < 1/2.

🍕 Fractions in Real Life

1
Cooking & baking: halving a recipe that calls for 3/4 cup of flour? 3/4 × 1/2 = 3/8 cup. Doubling 2/3 cup of sugar? 2/3 × 2 = 4/3 = 1 1/3 cups.
2
Pizza night: you eat 3/8 of a pizza and your friend eats 1/4. Together that’s 3/8 + 2/8 = 5/8 of the pizza.
3
DIY & carpentry: a 1/2-inch board plus a 3/8-inch shim stacks to 4/8 + 3/8 = 7/8 inch. Tape measures read in fractions for a reason.
4
Homework & tests: 17 out of 20 on a quiz is 17/20 = 0.85 = 85%.

📚 Reference This Page

CalcifyAll. “Fraction Calculator — Add, Subtract, Multiply & Divide Fractions.” https://calcifyall.com/fraction-calculator/ Last updated: October 2, 2026.

Frequently Asked Questions

Find the least common denominator (LCD) of both denominators, convert each fraction to an equivalent fraction with that denominator, then add the numerators and keep the denominator. Finally, simplify. Example: 1/4 + 1/3 → LCD is 12 → 3/12 + 4/12 = 7/12.

1/2 + 1/3 = 5/6. The least common denominator of 2 and 3 is 6: convert to 3/6 + 2/6, then add the numerators to get 5/6.

Because denominators name the size of the pieces, not a quantity you can add. Halves and thirds are different-sized pieces, so adding the denominators mixes piece sizes. You must first convert both fractions to the same denominator (sixths): 3/6 + 2/6 = 5/6.

Use the same method as addition: find a common denominator, convert both fractions, subtract the numerators, and simplify. Example: 3/4 − 1/6 → LCD is 12 → 9/12 − 2/12 = 7/12.

Multiply numerator by numerator and denominator by denominator, then simplify. No common denominator is needed. Example: 2/3 × 3/4 = 6/12 = 1/2. Tip: cross-cancel common factors before multiplying to keep the numbers small.

Use Keep–Change–Flip: keep the first fraction, change ÷ to ×, and flip the second fraction (use its reciprocal). Then multiply. Example: 3/4 ÷ 1/2 = 3/4 × 2/1 = 6/4 = 3/2 = 1 1/2.

Divide the numerator and denominator by their greatest common factor (GCF). Example: to simplify 18/24, find GCF(18, 24) = 6, then 18 ÷ 6 = 3 and 24 ÷ 6 = 4, giving 3/4.

Divide the numerator by the denominator. Example: 3/4 = 3 ÷ 4 = 0.75. Some fractions produce repeating decimals, such as 1/3 = 0.333…

Write the decimal over the matching power of 10, then simplify. Example: 0.75 = 75/100; dividing top and bottom by 25 gives 3/4.

Convert each mixed number to an improper fraction, add them with a common denominator, then convert back. Example: 2 1/2 + 1 3/4 = 5/2 + 7/4 = 10/4 + 7/4 = 17/4 = 4 1/4.

A proper fraction has a numerator smaller than its denominator (3/4) and is less than 1. An improper fraction has a numerator greater than or equal to its denominator (5/4) and is 1 or more. A mixed number pairs a whole number with a proper fraction (1 1/4).

The least common denominator (LCD) is the smallest number that both denominators divide into evenly — it is the least common multiple (LCM) of the denominators. List multiples: for 4 and 6, the multiples of 4 are 4, 8, 12… and of 6 are 6, 12…; the first shared multiple is 12, so the LCD is 12.