Fraction Calculator
Add, subtract, multiply, divide and simplify fractions — with every step shown, plus mixed numbers and decimals.
Calculate
Tip: type a decimal like 0.75 in the numerator with denominator 1 — it converts automatically. You can also type formulas or saved numbers in any box.
- 1/2 + 1/4
- Common denominator 2 × 4 = 8
- = 4/8 + 2/8
- = 6/8
- Simplify: divide top and bottom by 2 → 3/4
Practice mode
What is 1/2 + 1/3?
How to Use the Fraction Calculator
Enter each fraction as a whole number plus numerator and denominator — for plain fractions like 1/2, leave the whole number at 0. Mixed numbers work directly: for 2 1/3, type whole = 2, numerator = 1, denominator = 3. Got a decimal instead? Type it in the numerator with denominator 1 (for example, 0.75 over 1) and the calculator converts it to a fraction automatically. Pick +, −, ×, ÷, or Simplify for a single fraction, and every answer appears as a simplified fraction, a mixed number, and a decimal — with each step worked out below.
Adding Fractions Explained
You can only add fractions that share a denominator — the bottom numbers must match. If they don't, convert first:
For 1/2 + 1/4: the common denominator is 2 × 4 = 8. Convert: 1/2 becomes 4/8, and 1/4 becomes 2/8. Add the tops: 4 + 2 = 6, giving 6/8, which simplifies to 3/4. The calculator shows exactly this chain, so you can follow along or check homework line by line.
Subtraction works the same way with a minus. Multiplication is simpler — multiply straight across (tops × tops, bottoms × bottoms) — and division flips the second fraction, then multiplies: a/b ÷ c/d = a/b × d/c.
Simplifying Fractions: Worked Example
Simplify 8/12
Step 1: Find the greatest common divisor (GCD) of 8 and 12. Divisors of 8: 1, 2, 4, 8. Divisors of 12: 1, 2, 3, 4, 6, 12. The biggest shared one is 4.
Step 2: Divide top and bottom by 4: 8 ÷ 4 = 2, 12 ÷ 4 = 3.
Result: 8/12 = 2/3, which can't be reduced further.
The GCD is found with Euclid's algorithm — repeatedly replace the larger number with the remainder of dividing by the smaller, until the remainder is zero. It's fast even for huge numbers, and it's the same method the calculator uses internally on every answer.
Working With Mixed Numbers
A mixed number like 2 1/3 is shorthand for 2 + 1/3. To do arithmetic, convert it to an improper fraction first: multiply the whole number by the denominator and add the numerator → (2 × 3 + 1)/3 = 7/3. After calculating, convert back by dividing: 7 ÷ 3 = 2 remainder 1, so 7/3 = 2 1/3 again. The calculator handles both directions for you and always shows the mixed form alongside the plain fraction.
Watch the sign on negative mixed numbers: −2 1/3 means −(2 + 1/3) = −7/3, not −2 + 1/3. This trips up even confident students, so the calculator normalizes the sign onto the numerator automatically.
Common Fraction Mistakes
- Adding denominators: 1/2 + 1/2 is 2/2 = 1, not 2/4. Denominators never get added.
- Forgetting to simplify: 6/8 and 3/4 are the same value, but most teachers want 3/4. Always reduce.
- Flipping the wrong fraction: in a/b ÷ c/d, only the second fraction flips.
- Dividing by zero: a fraction with 0 on the bottom is undefined — the calculator will tell you, not crash.
- Decimal drift: 1/3 = 0.333… never ends. Keep fractions as fractions until the final step to avoid rounding error — the calculator shows both so you can choose.
Stuck on a concept? Try the practice mode above: it generates random problems, checks your answer, and reveals the correct one when you miss — a quick way to build fluency before a quiz.
My saved numbers reuse them in any calculator
Save a number once — like your rent or hourly rate — then just type its name instead of the number, in any calculator here. You can also type formulas like 5000 * 1.1 right into any box.
Saved only in this browser — nothing is sent to us.
Frequently Asked Questions
How do you add fractions?
Give both fractions a common denominator, add the numerators, then simplify. For 1/2 + 1/4: convert to 2/4 + 1/4 = 3/4. The calculator shows each of these steps.
How do you simplify a fraction?
Divide the top and bottom by their greatest common divisor (GCD). For 8/12, the GCD is 4: 8÷4=2, 12÷4=3, so 8/12 simplifies to 2/3.
What is 1/2 + 1/4?
1/2 + 1/4 = 3/4. Working: 1/2 becomes 2/4, then 2/4 + 1/4 = 3/4 (already in lowest terms).
How do I convert a fraction to a decimal?
Divide the numerator by the denominator: 3/4 = 3 ÷ 4 = 0.75. Every answer on this page shows the decimal alongside the fraction.
What is a mixed number?
A mixed number combines a whole number with a fraction, like 2 1/3. It equals the improper fraction (2×3+1)/3 = 7/3. To convert back, divide: 7 ÷ 3 = 2 remainder 1, so 2 1/3.