What Is a Fraction Calculator?
A fraction calculator is an online math tool that performs exact calculations with fractions. This calculator can add, subtract, multiply, and divide fractions and can also simplify the result, convert it to a mixed number, decimal, and percentage, and explain the calculation step by step.
How to Use the Fraction Calculator
- Enter the numerator and denominator for the first fraction.
- Enter a whole number if you are using a mixed number.
- Select addition, subtraction, multiplication, or division.
- Add more fraction rows if you need to calculate multiple fractions.
- Select Calculate to see the exact answer and the working steps.
How to Add Fractions
When two fractions have the same denominator, add their numerators and keep the denominator. When the denominators are different, first find a common denominator, convert the fractions, add the numerators, and simplify.
How to Subtract Fractions
To subtract fractions, use a common denominator, subtract the numerators, and reduce the result to its simplest form.
How to Multiply Fractions
Multiply the numerators together and multiply the denominators together. The resulting fraction is then reduced to simplest form.
How to Divide Fractions
To divide one fraction by another, multiply the first fraction by the reciprocal of the second fraction, then simplify.
Compare Fractions
Use Compare Fractions mode to determine whether one fraction is greater than, less than, or equal to another. The calculator uses a common denominator and shows the comparison steps.
Example: 3/4 = 6/8, so 3/4 > 5/8.
Fraction Conversion Tools
The calculator also includes dedicated modes for simplifying fractions, converting fractions to decimals or percentages, converting decimals and percentages to fractions, and changing between mixed numbers and improper fractions.
Mixed Numbers and Improper Fractions
A mixed number contains a whole number and a fraction, such as 2 3/4. To convert a mixed number to an improper fraction, multiply the whole number by the denominator, add the numerator, and place the result over the original denominator.
Example: 2 3/4 = (2 × 4 + 3)/4 = 11/4.
Fraction to Decimal and Percentage
A fraction can be converted to a decimal by dividing the numerator by the denominator. To convert a fraction to a percentage, multiply its decimal value by 100.
Example: 3/4 = 0.75 = 75%.
Proper, Improper, and Equivalent Fractions
A proper fraction has a numerator smaller than its denominator, such as 3/5. An improper fraction has a numerator equal to or greater than its denominator, such as 7/5. Equivalent fractions have the same value even though their numerators and denominators are different, such as 1/2 and 2/4.
Worked Examples
| Calculation | Result | Decimal |
|---|---|---|
| 1/2 + 1/3 | 5/6 | 0.833333... |
| 3/4 − 1/4 | 1/2 | 0.5 |
| 2/3 × 3/4 | 1/2 | 0.5 |
| 3/5 ÷ 1/2 | 6/5 = 1 1/5 | 1.2 |
| 3/4 compared with 5/8 | 3/4 > 5/8 | 0.75 > 0.625 |
| 3/4 → decimal → percentage | 0.75 → 75% | 0.75 |
Fraction Calculation Formulas
The main formulas used by the calculator are shown below. The calculator performs the arithmetic exactly and reduces the final fraction.
Frequently Asked Questions
How do you add fractions?
Find a common denominator, convert the fractions to equivalent fractions, add the numerators, and simplify the result.
How do you subtract fractions?
Use a common denominator, subtract the numerators, and reduce the resulting fraction to simplest form.
How do you multiply fractions?
Multiply the numerators together and the denominators together, then simplify the resulting fraction.
How do you divide fractions?
Multiply the first fraction by the reciprocal of the second fraction, then simplify.
Can this calculator handle mixed numbers?
Yes. Enter the whole number, numerator, and denominator. The calculator converts the mixed number to an exact improper fraction before calculating.
Can I calculate more than two fractions?
Yes. Use the Add Fraction button to add more rows and calculate a sequence of fractions using the selected operation.
Can I convert a fraction to a decimal or percentage?
Yes. The result section displays the decimal and percentage values alongside the simplified fraction.
What happens if a denominator is zero?
A denominator cannot be zero. The calculator will display an error instead of performing an invalid calculation.
What is the difference between a proper and improper fraction?
A proper fraction has a numerator smaller than its denominator. An improper fraction has a numerator equal to or larger than its denominator.
How do I compare two fractions?
Choose Compare Fractions mode. The calculator uses a common denominator and shows whether the first fraction is greater than, less than, or equal to the second.
Can I convert a decimal to a fraction?
Yes. Choose Decimal to Fraction mode, enter the decimal, and the calculator converts it to an exact simplified fraction.
Can I convert a percentage to a fraction?
Yes. Choose Percentage to Fraction mode, enter the percentage, and the calculator writes it over 100 and simplifies the result.
Can I simplify a fraction directly?
Yes. Choose Simplify a Fraction mode to find the greatest common factor and reduce the fraction to simplest form.
What is a mixed number?
A mixed number combines a whole number with a proper fraction, such as 2 3/4.
Related Calculators
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