Enter two fractions or mixed numbers, choose +, −, × or ÷, then select Calculate. Get a simplified exact answer, mixed-number and decimal forms, and visible working for every step.
Calculate fractions
Add, subtract, multiply or divide two fractions. Whole parts are optional.
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Answer
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Exact fraction
Mixed number
Decimal
Percent
How to calculate with fractions
Add like or unlike denominators
For like denominators, add only the numerators. For unlike denominators, use their LCD and multiply each fraction’s top and bottom by the same factor before adding.
Subtract mixed numbers
Convert the whole part and fraction to one improper fraction first: 2 1/3 = (2 × 3 + 1)/3 = 7/3. Find a common denominator, subtract and reduce.
Cross-cancel before multiplying
In a product, divide a numerator and a denominator by a shared factor before multiplying. This keeps numbers smaller without changing the value. Never cancel terms across + or −.
Divide with a reciprocal
Invert the second fraction, then multiply. The reciprocal of 2/3 is 3/2 because their product is 1. Zero has no reciprocal.
Simplify with GCF / GCD
Divide both parts by their greatest common factor, also called greatest common divisor. For 12/16, GCD(12, 16) = 4, giving 3/4.
Handle negative values
Keep the denominator positive and carry the sign on the numerator. A leading minus on a mixed number applies to its whole value: −2 1/3 = −7/3.
Recognize terminating and repeating decimals
Reduce first. Denominators containing only factors 2 and 5 terminate, such as 1/8 = 0.125. Other denominators repeat, such as 1/6 = 0.1(6). A rounded decimal is marked ≈.
Worked examples — try the exact problem
1. Like denominators
Keep the common denominator 5 and add 1 + 2. GCD(3, 5) = 1, so the result is already reduced.
2. Unlike denominators and an improper answer
LCD(3, 4) = 12. Multiply both parts of 2/3 by 4 and both parts of 3/4 by 3.
Add the numerators. GCD(17, 12) = 1; division gives 1 whole and remainder 5.
3. Negative values
Use the LCD 6 and keep the signs on the numerators.
Add −3 + 2 = −1. The result is already reduced.
4. Subtract mixed numbers
Multiply 2 × 3 and add 1 to convert to an improper fraction.
Use LCD 6 and subtract the numerators.
Divide both parts by GCD 3, then divide 3 by 2 for the mixed form.
5. Cross-cancel a product
Cancel 3 with 9 by dividing both by 3; cancel 8 with 4 by dividing both by 4.
Multiply the remaining numerators and denominators. GCD(2, 3) = 1.
6. Divide using a reciprocal
Invert the nonzero second fraction and change division to multiplication.
Multiply, reduce by GCD 3, then write the improper answer as a mixed number.
7. Zero numerator
The numerator product is 0. Divide both parts by GCD(0, 28) = 28 to get 0/1, or 0.
8. An explicitly repeating decimal
Let x = 0.(3). Multiplication by 10 shifts the same repeating tail one place; subtracting x cancels that tail.
Combine the left side to get 9x = 3.
Divide by 9, then reduce by GCD 3. A finite input of 0.3333 would be a different fraction.
Methodology and verification
Published by Starlight Tools (Starlight Robotics). Last calculation and content review: . This date records the page’s implementation review and automated checks, not an independent credentialed mathematical review.
All numerators, denominators, products and cross-products use BigInt integers. Addition and subtraction use the LCD found by LCM(a, b) = |a ÷ GCD(a, b) × b|. Division uses the reciprocal of a nonzero fraction. Every answer is reduced by GCD and its denominator is made positive. Percent conversion multiplies or divides the exact fraction by 100.
Inputs support 100 digits per integer field or 100 total digits in a decimal, including its repeating block. Intermediate products are not limited to 100 digits. Decimal rounding uses integer quotient and remainder, with ties away from zero; trailing zeros are removed and approximations use ≈. Repeating blocks or complete terminating expansions are displayed when found within 200 digits. Otherwise the exact fraction remains available with a labeled rounded decimal.
Fraction models draw every whole plus the remainder for magnitudes up to 12 with denominators up to 24. Larger results use an exact text description instead of a partial drawing. Negative results include a labeled number line.
100-digit numerator multiplication remains exact; 101-digit inputs are rejected.
0/7 = 0; denominators of 0 and division by 0/7 are rejected.
Practical fraction FAQ
Why are denominators not added?
The denominator names the size of each part. Adding 1/5 and 2/5 combines three fifths, so the result is 3/5, not 3/10. For unlike denominators, first rewrite both fractions using equal-sized parts.
What is the difference between LCD and LCM?
LCM means least common multiple of integers. The LCD, or least common denominator, is the LCM of the denominators you are using. For denominators 6 and 8, both the LCM and LCD are 24.
Are GCF and GCD the same?
Yes. Greatest common factor (GCF) and greatest common divisor (GCD) name the same positive integer. Dividing the numerator and denominator by it reduces a fraction to lowest terms.
When can I cross-cancel?
Cross-cancel common factors between any numerator and denominator in a product of fractions. For division, first replace division with multiplication by the reciprocal. Do not cancel across addition or subtraction.
Where does a negative sign belong?
For a simple fraction, a minus sign can go before the fraction, on its numerator or on its denominator. Two minus signs cancel. For mixed-number input here, put the sign on Whole only and keep the fractional parts unsigned; −2 1/3 means −(2 + 1/3). Final denominators are always positive.
Why do some decimals repeat?
After a fraction is reduced, its decimal terminates only if its denominator has no prime factors except 2 and 5. Otherwise long division repeats a remainder and the digits recur. Enter 0.(3) for exactly 1/3; the finite decimal 0.3333 is exactly 3333/10000.
Is zero a valid numerator?
Yes. Zero divided by any nonzero denominator is zero, so 0/7 = 0. A zero denominator is undefined, and division by a fraction whose numerator is zero is also undefined.
How does mixed-number subtraction work?
Convert each mixed number to an improper fraction, rewrite with a common denominator, subtract the numerators and reduce. For example, 2 1/3 − 5/6 = 14/6 − 5/6 = 9/6 = 1 1/2. This avoids separate borrowing steps.
How are answers rounded?
Exact fractions are never rounded. Decimal and percent displays use the selected 0–20 decimal places, round halfway cases away from zero and remove trailing zeros. The ≈ sign marks a rounded value; = marks an exact value. Parentheses enclose a repeating block. Full decimal expansions are shown only when they finish or reveal their repeat within 200 digits.
How do I add fractions with unlike denominators?
Find the LCD, multiply each numerator and denominator by the same integer to reach it, then add the numerators and reduce. For example, 2/3 + 3/4 = 8/12 + 9/12 = 17/12.
How do I divide fractions?
Keep the first fraction and multiply it by the reciprocal of the second, then reduce. For example, 5/6 ÷ 2/3 = 5/6 × 3/2 = 15/12 = 5/4. The second fraction must not be zero.
How do percent conversions work?
To convert a fraction to a percent, multiply its value by 100 and add %. To convert a percent to a fraction, divide the entered number by 100 and reduce. For example, 3/8 = 37.5%, and 12.5% = 1/8.
