OneTaskBy Tim King · Updated
Fraction Calculator
Add, Divide and Simplify With Steps
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How the Fraction Calculator works
This fraction calculator adds, subtracts, multiplies and divides two fractions and gives the answer in lowest terms, as a mixed number and as a decimal. Type fractions as 3/4, mixed numbers as 1 1/2, or whole numbers and decimals such as 2 or 0.25, so it also works as a division to fraction calculator: 3 divided by 4 gives 3/4. The working line shows the steps behind the result.
Fractions only add directly when they share a denominator, which is why adding 1/2 and 1/3 needs a common bottom number first. Multiplying is simpler: multiply the tops and multiply the bottoms. Dividing turns into multiplying by the reciprocal. Every answer is reduced by the greatest common factor of its numerator and denominator, and the arithmetic is exact, so long fractions never pick up rounding errors.
How the fraction calculator works
The formula for addition is a/b + c/d = (a×d + c×b) / (b×d), and subtraction is the same with a minus. Multiplication is (a×c) / (b×d) and division is (a×d) / (b×c). The result is divided top and bottom by their greatest common factor, then split into a whole part and a remainder for the mixed number.
First example. 1/2 + 1/3 = (1×3 + 1×2) / (2×3) = 5/6, which is 0.833333 as a decimal.
Second example. 2 1/2 ÷ 3/4 becomes 5/2 × 4/3 = 20/6, which simplifies to 10/3 or 3 1/3.
How many quarters are in 2 1/2? Divide 2 1/2 by 1/4: 5/2 × 4/1 = 20/2 = 10 quarters.
Common fractions as decimals and percentages
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/3 | 0.333333 | 33.3333% |
| 2/3 | 0.666667 | 66.6667% |
| 1/4 | 0.25 | 25% |
| 3/4 | 0.75 | 75% |
| 1/5 | 0.2 | 20% |
| 2/5 | 0.4 | 40% |
| 3/5 | 0.6 | 60% |
| 4/5 | 0.8 | 80% |
| 1/6 | 0.166667 | 16.6667% |
| 5/6 | 0.833333 | 83.3333% |
| 1/8 | 0.125 | 12.5% |
| 3/8 | 0.375 | 37.5% |
| 5/8 | 0.625 | 62.5% |
| 7/8 | 0.875 | 87.5% |
| 1/10 | 0.1 | 10% |
| 3/10 | 0.3 | 30% |
| 1/12 | 0.083333 | 8.3333% |
| 5/12 | 0.416667 | 41.6667% |
| 1/16 | 0.0625 | 6.25% |
| 3/16 | 0.1875 | 18.75% |
| 1/20 | 0.05 | 5% |
| 1/32 | 0.03125 | 3.125% |
| 1/100 | 0.01 | 1% |
Tips and pitfalls
- Do not add the bottoms. 1/2 + 1/3 is not 2/5; convert to a common denominator first.
- Flip only the second fraction. When dividing, take the reciprocal of the divisor, not the first fraction.
- Write mixed numbers with a space. 1 1/2 means one and a half; 11/2 means five and a half.
- Negative mixed numbers. -1 1/2 means -(1 + 1/2), which is -3/2, not -1 + 1/2.
Sources: Fraction.
Checked against: 1/2 + 1/3 = 5/6
FAQ
How do you add fractions with different denominators?
Multiply each fraction so they share a denominator, then add the numerators. For 1/4 + 1/6, use 12: 3/12 + 2/12 = 5/12. The calculator uses the product of the two denominators and then simplifies, which always lands on the same answer.
How do you divide fractions?
Keep the first fraction, change the division to multiplication and flip the second fraction. So 3/4 ÷ 1/2 becomes 3/4 × 2/1 = 6/4, which simplifies to 3/2 or 1 1/2. Dividing by a fraction smaller than one makes the answer bigger.
How do I simplify a fraction?
Divide the numerator and denominator by their greatest common factor. For 18/24 the GCF is 6, giving 3/4. The calculator does this automatically for every answer, and the GCF calculator shows the steps for any pair of numbers.
How do I turn a mixed number into an improper fraction?
Multiply the whole number by the denominator and add the numerator, keeping the same denominator. So 2 3/4 becomes (2 × 4 + 3)/4 = 11/4. The calculator accepts mixed numbers directly and converts them for you.
Can I enter decimals in the fraction calculator?
Yes. A decimal such as 0.375 is read exactly as 375/1000 and reduced to 3/8 before the sum is worked out. That makes the calculator a quick way to turn a decimal into a fraction: enter it and multiply by 1.
How do I turn a division into a fraction?
A division is already a fraction: 2 ÷ 3 is 2/3, with the number being divided on top. To reduce it, enter the top number as the first fraction, choose divide, and enter the bottom number as the second. 6 ÷ 8 comes back as 3/4, which is 0.75 as a decimal.
See also: all Arithmetic tools, Number Theory, Algebra and Geometry, Statistics, Trigonometry and Calculus.
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