Fraction Calculator
Add, subtract, multiply, and divide fractions, or convert a decimal to its fraction form.
What Is the Fraction Calculator?
A fraction calculator performs addition, subtraction, multiplication, division, and simplification on fractions exactly, keeping results as clean ratios rather than rounded decimals. Whatever operation you set, the answer comes back as a fraction, which is exactly the phrasing people search for when they type things like "2/3 x 4/5 as a fraction" or "what is 0.75 as a fraction." Fractions predate written history, with Egyptian scribes manipulating unit fractions thousands of years ago, and they remain the precise language for recipes, carpentry, music timing, and any measurement dividing naturally into parts. The tool handles the operations people find painful: finding common denominators for addition, flipping and multiplying for division, reducing by the greatest common divisor, and converting between mixed numbers and improper forms. Decimal approximations hide exact relationships; fractions preserve them.
Key Statistics
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Around 1650 BC
Egyptian papyri recorded sophisticated unit fraction arithmetic
Source: Rhind Mathematical Papyrus
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1
Any number times its reciprocal equals one, the property behind division by a fraction
Source: Field axioms
The Formula
a/b + c/d = (ad + bc) / bd. a/b x c/d = ac / bd. Always simplifies to lowest terms.
Worked Examples
What is 2/3 x 4/5 as a fraction? Multiply 2 times 4 and 3 times 5 to get 8/15. A woodworking project needs 3/8 inch plus 1/4 inch of material, so enter 3/8 + 1/4 = 3/8 + 2/8 = 5/8 inch. And 0.75 as a fraction is 3/4, while a recipe calling for 2/3 cup doubled becomes 2/3 x 2 = 4/3 = 1 1/3 cups.
Simplifying a messy fraction
- Start with 84 over 126
- Find the greatest common divisor of 84 and 126, which is 42
- Divide top and bottom by 42
The fraction reduces to 2/3.
Converting a decimal exactly
- Take the terminating decimal 0.375
- Write it as 375 over 1,000
- Reduce by the common factor of 125
0.375 equals exactly 3/8.
Multiplying as a fraction
- Take 2/3 times 4/5
- Multiply the numerators: 2 times 4 equals 8
- Multiply the denominators: 3 times 5 equals 15
2/3 x 4/5 is 8/15 as a fraction.
Real World Use Cases
Cooking and baking
Scale recipes by thirds and quarters where decimals introduce rounding drift.
Woodworking and construction
Tape measures read in sixteenths, and exact arithmetic prevents cumulative error.
Homework checking
Verify manual steps for common denominators and reduction independently.
Music practice
Note values are pure fractions of whole notes when arranging rhythms.
Expert Tips
- ✓ Multiplication needs no common denominator; multiply straight across and reduce afterwards.
- ✓ To divide, flip the second fraction and multiply.
- ✓ Estimate before calculating so an implausible answer reveals itself immediately.
- ✓ Mixed numbers convert to improper form before most operations; convert back at the end.
- ✓ Reduce last rather than first when multiplying several fractions, since cross cancellation is easier on small factors.
Frequently Asked Questions
What is 2/3 x 4/5 as a fraction? ▼
Multiply straight across: 2 times 4 is 8, and 3 times 5 is 15, so 2/3 x 4/5 equals 8/15. Multiplication needs no common denominator, and 8/15 is already in simplest form.
What is 0.75 as a fraction? ▼
0.75 as a fraction is 3/4. Write it as 75/100, then divide the top and bottom by their greatest common divisor of 25 to get 3/4.
How do I add fractions with different denominators? ▼
Find the least common denominator, convert each fraction to an equivalent fraction with that denominator, then add the numerators. For 1/2 plus 1/3, the common denominator is 6, giving 3/6 plus 2/6 equals 5/6.
How do I simplify a fraction? ▼
Divide the numerator and denominator by their greatest common divisor. For 8/12, the GCD is 4, so 8/12 simplifies to 2/3. This calculator simplifies automatically.
How do I multiply fractions? ▼
Multiply the numerators together and the denominators together, then simplify. For 2/3 times 4/5, multiply 2 times 4 and 3 times 5 to get 8/15, which is already simplest form.
How do I divide fractions? ▼
Keep the first fraction, change division to multiplication, and flip the second fraction. For 3/4 divided by 2/5, that becomes 3/4 times 5/2, which is 15/8 or 1 7/8.
What is an improper fraction and how do I convert it? ▼
An improper fraction has a numerator equal to or larger than the denominator, like 9/4. To convert it to a mixed number, divide the numerator by the denominator: 9 divided by 4 gives 2 with a remainder of 1, so 2 1/4.
How do I convert a fraction to a decimal or percent? ▼
Divide the numerator by the denominator to get a decimal, then multiply by 100 for the percent. The fraction 1/4 becomes 0.25 as a decimal and 25% as a percent.
What is 0.5 as a fraction? ▼
0.5 as a fraction is 1/2. Write 5/10, then divide both by 5 to get 1/2.
What is 1.25 as a fraction? ▼
1.25 as a fraction is 1 1/4, or 5/4 as an improper fraction. Write it as 125/100, divide top and bottom by 25 to get 5/4, then read it as 1 1/4.
Common Mistakes to Avoid
- ⚠ Entering a denominator of 0. Division by zero is undefined, and the calculator defaults to 1, silently changing your input. Double-check denominators before calculating.
- ⚠ Forgetting to convert mixed numbers before entering them. A recipe calling for ’1 1/2 cups’ must be entered as 3/2 (numerator 3, denominator 2), not as 1 and 1/2 across separate fields.’
- ⚠ Adding or subtracting fractions without checking the result can be simplified. The calculator simplifies automatically, but if you use the result in further manual steps, work with the simplified form to avoid unnecessarily large numbers.
- ⚠ Adding numerators and denominators separately. One half plus one third is five sixths, not two fifths.
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Last updated: · by CalculatorPro Tools