Use this free fraction calculator to add, subtract, multiply or divide two fractions. The answer comes back fully simplified, as a mixed number, and as a decimal — the three forms teachers, cooks and builders all ask for.
What Is the Fraction Calculator?
A fraction calculator performs arithmetic on fractions, which are numbers written as a numerator over a denominator, and simplifies the result by dividing the top and bottom by their greatest common divisor (GCD). As well as adding, subtracting, multiplying and dividing, it converts the answer to a mixed number and a decimal, so you can read the result in whichever form you need for homework, cooking, measuring or building work at home or on site.
How to Use This Calculator
- Enter the first fraction’s numerator and denominator.
- Choose the operation.
- Enter the second fraction.
- Click Calculate Fractions.
- Read the simplified fraction, mixed number and decimal.
Formula
Add/Subtract: a/b ± c/d = (a×d ± c×b) ÷ (b×d). Multiply: a/b × c/d = (a×c) ÷ (b×d). Divide: a/b ÷ c/d = (a×d) ÷ (b×c). Then simplify by the GCD.
Worked Example
3/4 + 2/3 = (3×3 + 2×4) ÷ (4×3) = 17/12. Simplified: 17/12 (already simplest). As a mixed number: 1 5/12. As a decimal: 1.416667.
How It Works, In Plain Words
The four boxes are two fractions: a numerator and denominator for the first, the same for the second, with the operation in between. Adding and subtracting follow the Formula’s cross-multiply pattern: each numerator is multiplied by the other fraction’s denominator and the results are combined over the product of the denominators — in the worked example, (3×3 + 2×4) ÷ (4×3) = 17/12. Multiplying is simpler, straight across the top and straight across the bottom, and dividing flips the second fraction first, exactly as the divide FAQ below describes. Whatever the operation, the raw answer is then simplified: the tool finds the greatest common divisor of top and bottom — the GCD the What Is section names — and divides both by it. In the example, 17 and 12 share no common divisor, so 17/12 is already simplest, as the Worked Example notes. Finally the answer is translated twice: into a mixed number by pulling out the whole part (17/12 becomes 1 5/12), and into a decimal (1.416667).
Real-World Uses
First scenario: homework checking, the first benefit in the list below. A student who worked 3/4 + 2/3 by hand can compare all three forms — 17/12, 1 5/12 and 1.416667 — against their own working, and if their answer differs, the Formula section shows the common-denominator route the tool took. Second scenario: the kitchen and workshop measures the Benefits list mentions — halves, thirds and quarters. Adding two fractional amounts is only half the job; the form you need next differs, a mixed number for a measuring jug or tape, the decimal for anything digital, and the tool prints all three at once. Third scenario: any answer bigger than one. The Benefits list promises the tool handles improper fractions automatically, and the worked example shows why that matters: 17/12 arrives already converted to 1 5/12, the form most people actually measure in, with no second conversion step.
Benefits
- Homework answers checked with the working form shown.
- Cooking and workshop measurements (halves, thirds, quarters) without errors.
- Results in all three forms — fraction, mixed number, decimal.
- Handles improper fractions automatically.
Features of Our Tool
- Instant results as you click Calculate — no page reload
- Shows the full breakdown, not just one number
- Free forever, no sign-up or download
- Works on phones, tablets and computers
- Your numbers stay in your browser — nothing is stored
Common Mistakes to Avoid
- Adding denominators together (3/4 + 2/3 is NOT 5/7 — you must use a common denominator).
- Forgetting to simplify the final answer.
- Entering a zero denominator, which is undefined.
More Common Mistakes to Avoid
Three more are easy to make. First, flipping the wrong fraction when dividing: the FAQ below is explicit that the second fraction flips, never the first — flip the first and the answer is the reciprocal of the truth. Second, mixing methods between operations: multiplying goes straight across, but adding needs the common denominator first, and using the straight-across shortcut on an addition is exactly how the 5/7 error in the list above happens. Third, reading the decimal line as the exact answer: 1.416667 is 17/12 rounded for display, so for measuring and marking, work from the fraction or the mixed number, 1 5/12, and treat the decimal as the quick check.
Frequently Asked Questions
How do you add fractions?
Use a common denominator: a/b + c/d = (a x d + c x b) / (b x d), then simplify. Example: 3/4 + 2/3 = 17/12.
How do you divide fractions?
Flip the second fraction and multiply: a/b divided by c/d = a/b x d/c.
What is 3/4 + 2/3?
17/12, which is 1 5/12 as a mixed number and about 1.4167 as a decimal.
How do you simplify a fraction?
Divide the numerator and denominator by their greatest common divisor (GCD). For example 8/12 simplifies to 2/3 (GCD 4).
What is a mixed number?
A whole number plus a proper fraction, e.g. 17/12 = 1 5/12.
Can I enter a mixed number like 1 5/12?
Not directly — the tool has numerator and denominator boxes only, one pair per fraction. Convert the mixed number to an improper fraction first: the FAQ above shows 17/12 = 1 5/12, so a 1 5/12 entry means 17 in the numerator box and 12 in the denominator box. The answer still comes back in all three forms, mixed number included.
Why does the tool show 1.416667 but the FAQ says 1.4167?
They are the same number at different lengths. The tool prints the decimal to six places — 1.416667 — while the FAQ above rounds it to four and says “about 1.4167”. Neither is the exact answer; the exact answer is the fraction itself, 17/12, and the decimals are rounded readings of it.