Fraction Calculator
Add, subtract, multiply, and divide fractions with step-by-step work. Supports mixed numbers, simplification, decimal-to-fraction conversion, and fraction comparison.
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How It Works
To add fractions, find the LCD of all denominators. Convert each fraction to have the LCD as its denominator. Add the numerators and keep the denominator. Simplify the result using GCD.
1/4 + 1/6 → LCD=12 → 3/12 + 2/12 = 5/123/8 + 5/12 = 9/24 + 10/24 = 19/24Same process as addition: find the LCD, convert, then subtract the numerators. The denominator stays the same. Simplify the result.
a/b − c/d = (a×d − c×b) / (b×d) then simplify3/4 − 1/6 = 9/12 − 2/12 = 7/12Multiply numerators together, multiply denominators together. No common denominator needed. Simplify the result. Cross-cancel first to keep numbers small.
a/b × c/d = (a×c) / (b×d)2/3 × 3/4 = 6/12 = 1/2Flip the second fraction (take its reciprocal) and multiply. Division by a fraction is always multiplication by its reciprocal. Simplify the result.
a/b ÷ c/d = a/b × d/c = (a×d) / (b×c)3/4 ÷ 1/2 = 3/4 × 2/1 = 6/4 = 3/2Find the GCD of numerator and denominator. Divide both by the GCD. The result is the fraction in lowest terms. A fraction is fully simplified when GCD = 1.
a/b → (a÷GCD) / (b÷GCD)24/36 → GCD=12 → 2/3Convert mixed numbers to improper fractions first: multiply the whole number by denominator, add numerator. Then perform the operation normally. Convert back if needed.
w a/b = (w×b + a) / b2 3/4 = (2×4+3)/4 = 11/4Quick Reference
Common fraction calculations — verify instantly above.
Addition
1/2 + 1/3
5/6
Subtraction
3/4 − 1/6
7/12
Multiply
2/3 × 3/4
1/2
Division
3/4 ÷ 1/2
1 1/2
Simplify
24/36
2/3
Mixed
1 1/2 + 2 1/3
3 5/6
Decimal
0.75
3/4
Compare
2/3 vs 3/4
2/3 < 3/4
Tips & Shortcuts
Cross-cancel before multiplying to keep numbers small. In 4/9 × 3/8, cancel the 4 and 8 (÷4) and the 3 and 9 (÷3): 1/3 × 1/2 = 1/6.
To compare fractions quickly, cross-multiply: for 2/3 vs 3/4, compute 2×4=8 and 3×3=9. Since 8<9, then 2/3 < 3/4.
When dividing by a fraction, always remember: "Keep, Change, Flip" — keep the first fraction, change ÷ to ×, flip the second.
To find the LCD quickly, check if the larger denominator is a multiple of the smaller. If yes, use the larger. Example: LCD(4,8)=8.
A negative fraction: −3/4 is the same as (−3)/4 or 3/(−4). Always keep the negative sign on the numerator for clarity.
Mixed number to improper fraction: whole × denominator + numerator = new numerator. Example: 2 3/4 = (2×4+3)/4 = 11/4.
Common Mistakes
Adding denominators: 1/4 + 1/4 = 2/8
Keep the denominator the same when adding fractions with equal denominators: 1/4 + 1/4 = 2/4 = 1/2.
Not finding LCD before adding: 1/3 + 1/4 = 2/7
You must find the LCD first: LCD(3,4)=12. Then 4/12 + 3/12 = 7/12.
Forgetting to simplify the result
Always check if the answer simplifies. 6/12 is valid but 1/2 is the correct simplified form.
Dividing fractions by flipping the first instead of the second
Always flip the divisor (second fraction). For a/b ÷ c/d, the answer is a/b × d/c, not b/a × c/d.
Converting mixed numbers incorrectly: treating 2 3/4 as 23/4
Multiply whole by denominator then add numerator: 2 3/4 = (2×4+3)/4 = 11/4, not 23/4.
Cancelling across addition: (1+3)/(2+4) = 4/6
You can only cancel factors in multiplication or division, never across addition or subtraction.
Frequently Asked Questions
Find the Least Common Denominator (LCD). Convert each fraction so both have the LCD as denominator. Add the numerators and keep the denominator. Then simplify. Example: 1/4 + 1/6 → LCD=12 → 3/12 + 2/12 = 5/12.
Multiply numerators together and denominators together, then simplify. No common denominator needed. Example: 2/3 × 3/4 = 6/12 = 1/2.
Flip the second fraction (find its reciprocal) and multiply. Example: 3/4 ÷ 1/2 = 3/4 × 2/1 = 6/4 = 3/2 = 1 1/2.
Find the Greatest Common Divisor (GCD) of numerator and denominator, then divide both by it. Example: 12/16 — GCD is 4 — 12÷4=3, 16÷4=4 → 3/4.
A mixed number has a whole part and a fraction part, like 2 3/4. Enter it with a space: "2 3/4". The calculator converts it to an improper fraction (11/4) internally.
Write the decimal over 1, multiply numerator and denominator by 10^n (where n = decimal places), then simplify. Example: 0.75 × 100/100 = 75/100 = 3/4.
To divide fractions, multiply by the reciprocal of the divisor: (a/b) ÷ (c/d) = (a/b) × (d/c) = (ad)/(bc). Memory trick: Keep-Change-Flip (KCF) — keep the first fraction, change ÷ to ×, flip the second. Example: (3/4) ÷ (2/5) = (3/4) × (5/2) = 15/8 = 1⅞. Always simplify by dividing numerator and denominator by their GCF.
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