Fraction Calculator With Steps
Add, subtract, multiply, or divide fractions and get a simplified exact answer with the working shown.
Quick Answer: How Does a Fraction Calculator Work?
A fraction calculator performs exact fraction arithmetic and simplifies the result. Addition and subtraction use a common denominator. Multiplication goes straight across. Division multiplies by the reciprocal. The final numerator and denominator are divided by their greatest common divisor, so the answer is in lowest terms.
The result is a fraction, not a rounded float. A decimal and a percent are shown beside it. Repeating decimals use parentheses, such as 0.(3) for 1/3.
How to Use the Fraction Calculator
- Enter the first fraction, including a whole number if it is mixed.
- Choose +, −, ×, or ÷.
- Enter the second fraction.
- Read the simplified answer and the working.
Use Simplify for one fraction, Convert for decimals and percents, and Compare when you need to know which fraction is larger. A whole-number field turns 2, 1, and 3 into the mixed number 2 1/3.
How Fraction Calculations Work
Adding Fractions
Fractions can be added only after they share a denominator. The least common denominator of 2 and 4 is 4. Then 1/2 = 2/4, and 2/4 + 3/4 = 5/4. The same idea is the formula a/b + c/d = (ad + bc) / bd, followed by simplifying. For the least common multiple of larger denominators, use the LCM calculator.
Subtracting Fractions
Subtraction uses the same common denominator, then subtracts numerators. 2/3 − 1/6 becomes 4/6 − 1/6 = 3/6 = 1/2. The sign stays with the numerator.
Multiplying Fractions
Multiply numerators and multiply denominators: a/b × c/d = ac / bd. Then reduce. 3/5 × 10/9 = 30/45 = 2/3.
Dividing Fractions
Keep the first fraction, change ÷ to ×, and flip the second fraction. 7/8 ÷ 1/4 = 7/8 × 4/1 = 7/2 = 3 1/2. For longer expressions, the scientific calculator handles powers and roots, while this page stays with exact fractions.
Simplifying Fractions
Divide the numerator and denominator by their greatest common divisor. GCD(42, 56) = 14, so 42/56 = 3/4. The GCF calculator finds that divisor for a longer list of integers. Each number here is limited to 15 digits so the page stays instant.
Worked Examples
| Problem | Answer | Working |
|---|---|---|
| 1/2 + 3/4 | 5/4 = 1 1/4 | LCD = 4. 1/2 = 2/4. 2/4 + 3/4 = 5/4. |
| 2/3 − 1/6 | 1/2 | LCD = 6. 2/3 = 4/6. 4/6 − 1/6 = 3/6 = 1/2. |
| 3/5 × 10/9 | 2/3 | 30/45. GCD(30, 45) = 15, so 30/45 = 2/3. |
| 7/8 ÷ 1/4 | 7/2 = 3 1/2 | 7/8 × 4/1 = 28/8 = 7/2. |
| 42/56 | 3/4 | GCD(42, 56) = 14. 42 ÷ 14 = 3 and 56 ÷ 14 = 4. |
| 2 1/3 | 7/3 | 2 × 3 + 1 = 7, so 2 1/3 = 7/3. |
| 0.125 | 1/8 | 0.125 = 125/1000. Divide by 125 to get 1/8. |
| 3/4 | 75% | 3 ÷ 4 = 0.75, and 0.75 × 100 = 75. |
| 3/4 vs 5/8 | 3/4 > 5/8 | 3 × 8 = 24 and 5 × 4 = 20. 24 is greater, so 3/4 is greater. |
Mixed Numbers and Improper Fractions
A mixed number is a whole number written next to a proper fraction. Convert it to an improper fraction before you calculate: whole × denominator + numerator, over the same denominator. 2 1/3 = 7/3.
The other direction splits an improper fraction into a whole number and a remainder. 7/4 = 1 3/4, and 5/4 = 1 1/4. A negative mixed number such as −2 1/3 means −(2 + 1/3), which is −7/3, not −2 + 1/3.
Fraction to Decimal and Percent
Divide the numerator by the denominator. 3/4 = 0.75 = 75%. 0.125 = 125/1000 = 1/8. Percent to fraction divides by 100 and reduces: 62.5% = 5/8. The percentage calculator is the better tool when the question is “what is 20% of 80?” rather than a fraction conversion.
Terminating decimals convert exactly. If you type 0.(3), that means the digit 3 repeats, and the exact value is 1/3. A rounded value such as 0.333 is not treated as 1/3.
Common Fraction Calculator Mistakes
- Adding denominators directly. 1/2 + 1/3 is not 2/5. Convert to sixths first: 3/6 + 2/6 = 5/6.
- Forgetting to simplify. 30/45 and 2/3 are the same value; lowest terms are easier to check.
- Dividing without the reciprocal. 7/8 ÷ 1/4 is 7/8 × 4/1, not 7/8 × 1/4.
- Sign mistakes. The negative sign belongs on the numerator, and −2 1/3 is entirely negative.
- Treating a rounded decimal as the exact fraction. 0.33 is 33/100. One third is 0.(3).
- Using a zero denominator. 5/0 is undefined, and dividing by 0/1 is undefined.
Who Uses a Fraction Calculator?
Students use it to check homework and see the working, not only the final fraction. The tools for students page collects other study calculators, and the basic calculator covers ordinary decimal arithmetic.
Recipes and measurements use the same operations: half of 3/4 cup is 3/8 cup, and 2 1/3 cups plus 1 1/2 cups is 3 5/6 cups. Woodworking and DIY cut lists add sixteenths and eighths. Ratios such as 3/4 and 5/8 can be compared without converting both to a rounded decimal first. More tools are listed in Calculator Tools.
Frequently Asked Questions
How do you add fractions with different denominators?
Find a common denominator, usually the least common denominator. Rewrite each fraction, add the numerators, and simplify. 1/2 + 3/4 uses LCD 4: 2/4 + 3/4 = 5/4, which is 1 1/4.
How do you subtract fractions?
Use the same common-denominator process, then subtract the numerators. 2/3 − 1/6 = 4/6 − 1/6 = 3/6 = 1/2.
How do you multiply fractions?
Multiply the numerators and multiply the denominators, then simplify. 3/5 × 10/9 = 30/45 = 2/3. You can cancel shared factors before multiplying.
How do you divide fractions?
Keep the first fraction, change division to multiplication, and flip the second fraction. 7/8 ÷ 1/4 = 7/8 × 4/1 = 7/2, or 3 1/2.
How do you simplify a fraction?
Divide the numerator and denominator by their greatest common divisor. GCD(42, 56) = 14, so 42/56 = 3/4.
What is a mixed number?
A mixed number is a whole number plus a proper fraction, such as 1 1/4. The same value as an improper fraction is 5/4.
How do you convert a mixed number to an improper fraction?
Multiply the whole number by the denominator, add the numerator, and keep the denominator. 2 1/3 = (2 × 3 + 1) / 3 = 7/3.
How do you convert a fraction to a decimal?
Divide the numerator by the denominator. 3/4 = 0.75. If the decimal repeats, this calculator shows the repeating block in parentheses, such as 0.(3) for 1/3, instead of a rounded float.
How do you convert a decimal to a fraction?
For a terminating decimal, write the digits over the matching power of 10 and reduce. 0.125 = 125/1000 = 1/8. Repeating notation such as 0.(3) converts to 1/3. A rounded decimal is not treated as a repeating value unless you enter the parentheses.
How do you convert a fraction to a percent?
Divide the fraction and multiply by 100. 3/4 = 0.75 = 75%. The other direction works too: 62.5% = 5/8.
Can the calculator handle mixed numbers?
Yes. Each fraction has a whole-number field. 2 in the whole field, 1 in the numerator, and 3 in the denominator means 2 1/3. A negative whole number, such as −2 1/3, applies to the entire mixed number.
Can I compare two fractions?
Yes. Compare mode uses cross-multiplication, so 3/4 and 5/8 are compared as 24 and 20. The result does not depend on a rounded decimal.
What happens when the denominator is zero?
The calculation stops. A denominator of zero is undefined, and division by zero is undefined.
Are fraction calculator results exact?
The fraction result uses integer arithmetic and is reduced by the GCD. Terminating decimals and written repeating decimals convert exactly. A long repeating expansion may be shown with an approximation mark; the fraction remains the exact value.
Does the calculator work on mobile?
Yes. The mode switch, fraction fields, and operator buttons are sized for touch, and the result sits with the calculator rather than below a long article.
Are my calculations uploaded?
No. The arithmetic runs in your browser. EverydayTools does not receive the fractions you enter.
Related Calculators
- GCF calculator for the greatest common divisor used when simplifying.
- LCM calculator for the least common denominator.
- Percentage calculator for percent of a number, increase, and decrease.
- Exponent calculator for powers, negative exponents, and fractional exponents.
- Scientific calculator for powers, roots, and longer expressions.
- Calculator for everyday decimal arithmetic.