01 — Adding Fractions
Accessible text: a over b plus c over d equals a d plus b c, all over b d. Use the least common denominator in the written steps. Example: 1/2 + 1/3 = 5/6. Edge case: 0/5 + 1/2 = 1/2. Adding fractions calculator
Fraction desk / 01
Fraction Calculator
Add, subtract, multiply, and divide fractions. Get simplified answers and see each step of the calculation.
Exact answer
Simplified fraction:
Mixed number:
Decimal approximation:
How the Answer Was Calculated
Adding Fractions Calculator
Like denominators add numerators. Unlike denominators use the least common denominator. Formula: a/b + c/d = (ad + bc)/bd. Example: 1/4 + 1/6 = 5/12.
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Exact result:
Simplified result: · Mixed number: · Decimal:
Subtracting Fractions Calculator
a/b − c/d = (ad − bc)/bd. Example: 3/4 − 1/6 = 7/12. Negative results keep their sign. Subtraction is not commutative; swap recomputes the opposite difference.
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Exact result:
Simplified: · Mixed: · Decimal:
Multiplying Fractions Calculator
a/b × c/d = ac/bd. Example: 2/3 × 3/5 = 6/15 = 2/5 after cancelling a factor of 3.
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Exact: · Mixed: · Decimal:
Dividing Fractions Calculator
a/b ÷ c/d = a/b × d/c. Example: 3/4 ÷ 2/5 = 15/8 = 1 7/8. Dividing by 0/5 is rejected.
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Exact: · Mixed:
Simplify Fractions
Divide numerator and denominator by their GCD. Example: 24/36, GCD 12, result 2/3. Integer fields accept at most 100 digits.
Original fraction:
Greatest common divisor:
Simplified fraction:
Decimal:
Mixed Numbers and Improper Fractions
2 1/3 = 7/3. 11/4 = 2 3/4. A negative mixed number such as −2 1/3 means −(2 + 1/3), not −2 + 1/3.
Mixed number to improper fraction
Result: · Mixed form:
Convert Decimals and Fractions
0.375 is read as 375/1000 and simplifies to 3/8. Finite decimals are parsed as digit strings, not as binary floating-point. At most 24 digits after the decimal point. Repeating decimals are not inferred from a typed expansion such as 0.333.
Decimal to fraction
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Fraction: · Decimal:
Compare Two Fractions
Compare cross-products of normalized fractions with positive denominators. 3/4 vs 2/3: 3×3=9 and 2×4=8, so 3/4 is greater.
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See the Fraction
Common Fraction Questions
Fraction Formulas Explained
02 — Subtracting Fractions
Keep the sign of the difference. Example: 3/4 − 1/6 = 7/12. Edge case: 1/3 − 2/3 = −1/3. Subtracting fractions calculator
03 — Multiplying Fractions
Multiply across, then simplify. Example: 2/3 × 3/5 = 2/5. Edge case: 0/3 × 5/7 = 0. Multiplying fractions calculator
04 — Dividing Fractions
Multiply by the reciprocal. Example: 3/4 ÷ 2/5 = 15/8. Edge case: a zero divisor is invalid. Dividing fractions calculator
05 — Simplifying Fractions
Example: 24/36 = 2/3. Edge case: 7/13 is already simplest. Simplify fractions
06 — Mixed Number Conversion
Example: 2 1/3 = 7/3. Negative mixed numbers mean the opposite of the positive mixed value. Mixed number calculator
07 — Decimal Conversion
Parse the decimal string exactly. Repeating decimals need infinitely many digits. Decimal to fraction calculator
08 — Comparing Fractions
Example: 3/4 > 2/3 because 9 > 8. Do not compare rounded decimals. Compare fractions calculator
Common Fraction Mistakes
1. Adding denominators directly
Incorrect: 1/2 + 1/3 = 2/5. Why: numerators and denominators cannot be added as two independent pairs. Correct: rewrite with LCD 6 to get 3/6 + 2/6 = 5/6. Example: 1/2 + 1/3 = 5/6. Add fractions
2. Forgetting a common denominator
Incorrect: adding unlike fractions by touching only numerators. Why: the pieces are different sizes. Correct: find the LCD. Example: 1/4 + 1/6 needs twelfths. Add fractions
3. Multiplying incorrectly
Incorrect: 2/3 × 3/5 = 5/8 by adding. Why: products use multiplication across. Correct: 6/15 = 2/5. Multiply fractions
4. Dividing without the reciprocal
Incorrect: 3/4 ÷ 2/5 = 3/4 × 2/5. Why: division multiplies by d/c, not by the divisor itself. Correct: 3/4 × 5/2 = 15/8. Divide fractions
5. Forgetting to simplify
Incorrect: leaving 6/15 as the final answer when 2/5 is required. Why: equivalent fractions should be reduced. Correct: divide by GCD 3. Simplify
6. Mishandling negative fractions
Incorrect: turning 1/3 − 2/3 into a positive 1/3. Why: the difference can be negative. Correct: −1/3. Also 4/−8 = −1/2. Subtract
7. Confusing mixed and improper fractions
Incorrect: reading 2 1/3 as 21/3. Why: the whole and the fraction combine as 2×3+1. Correct: 7/3. Mixed numbers
8. Comparing rounded decimals
Incorrect: deciding 1/3 vs 3/10 from 0.33 vs 0.30. Why: rounding can hide order. Correct: cross-multiply 10 vs 9. Compare
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Detroit MI 48221