Fraction Calculator and Mixed Number Calculator: Decimal to Fraction
Add, subtract, multiply and divide fractions and mixed numbers with every step shown, simplify to lowest terms and convert between fractions and decimals.
Every convention this page applies is named in the result rather than assumed. Your numbers stay in this browser.
Choose the operation, then enter each fraction as a numerator over a denominator, with an optional whole part for mixed numbers. Every step is shown, including the lowest common denominator.
What to do
Add, subtract, multiply, divide or compare two fractions; simplify one; or convert a decimal into a fraction. Simplify and decimal conversion use only the fields they need.
How to type a fraction
Type it the way you write it: 3/4, 1 3/4 (a space between the whole number and the fraction), −2/3 or 5.
Whole part. For a mixed number such as 2 ¾, the 2. Leave it blank for a plain fraction. The sign of a mixed number goes here: −2 ¾ is whole −2, numerator 3, denominator 4.
Numerator. The top number. For a plain negative fraction put the sign here; for a mixed number put it on the whole part instead.
Denominator. The bottom number. It cannot be zero. Anything up to a million is accepted; the arithmetic stays exact.
About “Decimal to convert”
Type the decimal as you would write it: 0.375, 2.5, −0.125. It is read exactly as typed, so 0.1 becomes 1/10 rather than the long binary fraction a computer would otherwise hold. Up to 12 decimal places.
About “Largest denominator allowed”
The exact fraction is always shown. If its denominator is above this limit, the closest fraction that fits is shown too, with how far off it is: 0.333333 within 100 is 1/3. Useful for measurements and recipes, where 3/8 is wanted rather than 333333/1000000.
112+23=136
How it’s worked out
- Find the lowest common denominator of 2 and 3: 6.
- Rewrite over it: 3/2 = 9/6 and 2/3 = 4/6.
- Add the numerators: 9 + 4 = 13, so 13/6.
- That is already in lowest terms.
Use it as a fractions calculator and fraction solver: a mixed fraction calculator for whole numbers and fractions together, a simplifying and reducing fractions calculator (a fraction simplifier that brings any fraction to lowest terms), and an online calculator with fractions for adding fractions, subtracting fractions, multiplying fractions and dividing fractions. As a fraction calculator online it runs in your browser and shows every step, so a calculator with fractions also shows you the method.
Assumptions and formula
Each operand is read as an improper fraction in lowest terms, with a mixed number’s sign taken from its whole part. Addition, subtraction and comparison rewrite both fractions over the lowest common denominator; multiplication multiplies across; division multiplies by the reciprocal. The answer is reduced by the greatest common divisor and reported as a fraction, a mixed number and a decimal.
Inputs are limited to a million per part so every intermediate product is an exact integer. A decimal is read as typed and placed over a power of ten, so 0.1 is exactly 1/10; when you set a largest denominator, the closest fraction within it is found by continued fractions and reported with its error.
Worked example
For 1/2 + 1/3, the lowest common denominator of 2 and 3 is 6: 1/2 becomes 3/6 and 1/3 becomes 2/6, and 3 + 2 = 5 gives 5/6, already in lowest terms, which is 0.8333 as a decimal. For 3/4 ÷ 2/5, flip the divisor to 5/2 and multiply: 15/8, or 1 7/8.
Common fractions as decimals and percentages
Common fractions converted to decimals and percentages. Divide the top number by the bottom number for the decimal, then multiply by 100 for the percentage. Fractions such as 1/3 repeat for ever and are rounded here.
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/3 | 0.3333 | 33.33% |
| 2/3 | 0.6667 | 66.67% |
| 1/4 | 0.25 | 25% |
| 3/4 | 0.75 | 75% |
| 1/5 | 0.2 | 20% |
| 1/8 | 0.125 | 12.5% |
| 3/8 | 0.375 | 37.5% |
| 5/8 | 0.625 | 62.5% |
| 7/8 | 0.875 | 87.5% |
| 1/16 | 0.0625 | 6.25% |
To add or subtract fractions, give them a common denominator first: 1/4 + 1/3 becomes 3/12 + 4/12 = 7/12. To multiply, multiply the tops and the bottoms; to divide, flip the second fraction and multiply. The calculator simplifies the answer for you.
Eighths and sixteenths are worth knowing for measurements in inches: 5/8 inch is 0.625 inch, about 15.9 mm.
Frequently asked questions
How do I add fractions with different denominators?
Rewrite both over a common denominator, then add the numerators. For 1/2 + 1/3 the lowest common denominator is 6: 1/2 becomes 3/6 and 1/3 becomes 2/6, so the sum is 5/6. Any common denominator works — 2 × 3 = 6 here anyway — but the lowest one keeps the numbers small and avoids simplifying afterwards. The steps on this page show that rewrite explicitly. It also converts a decimal to a fraction and shows the decimal value of any fraction, with each step of the working shown.
How do I divide by a fraction?
Multiply by its reciprocal, meaning the fraction turned upside down. 3/4 ÷ 2/5 is 3/4 × 5/2 = 15/8, or 1 7/8. This works because dividing by 2/5 asks how many two-fifths fit, and there are five halves in each whole. Dividing by a fraction smaller than 1 gives a larger answer than you started with, which surprises people but is correct.
How do I turn a mixed number into an improper fraction?
Multiply the whole part by the denominator, add the numerator, and keep the denominator: 2 3/4 is (2 × 4 + 3)/4 = 11/4. For a negative mixed number the sign belongs to the whole, so −2 3/4 is −11/4, not −(2) + 3/4. This page asks for the whole part separately for exactly that reason.
How do I convert a decimal to a fraction?
Write the digits after the decimal point over a power of ten, then simplify. 0.375 is 375/1000, and dividing both by 125 gives 3/8. This page reads the decimal exactly as typed, so 0.1 is 1/10 — a computer that stores 0.1 as a binary number would otherwise offer a 55-digit denominator. If you want a fraction with a small denominator, set a limit and the closest fraction that fits is reported with its error.
What is the lowest common denominator, and why not just multiply the denominators?
The lowest common denominator is the smallest number both denominators divide into — the least common multiple. For 1/4 and 1/6 it is 12, whereas multiplying gives 24. Both are valid; the lowest one produces smaller numerators and an answer that is already in lowest terms more often. Teachers usually mark for it, so it is the one shown here.
How do I turn a decimal into a fraction, and a mixed number into an improper one?
A decimal to fraction calculator writes the decimal over a power of ten and simplifies: 0.375 is 375/1000, which reduces to 3/8. A fraction to decimal calculator goes the other way by dividing: 5/8 is 0.625. A mixed number calculator converts 2½ to 5/2 before adding or multiplying, then converts the answer back. Simplifying is the last step every time: a simplify fractions calculator divides top and bottom by their greatest common factor, so 18/24 becomes 3/4. This page shows each of those steps in the working.
How do multiplying and dividing fractions differ from adding them?
An adding fractions calculator has to find a common denominator first: 1/2 + 1/3 becomes 3/6 + 2/6 = 5/6. A multiplying fractions calculator skips that step entirely and multiplies straight across: 1/2 × 1/3 = 1/6. A dividing fractions calculator flips the second fraction and multiplies: 1/2 ÷ 1/3 = 1/2 × 3/1 = 3/2, or 1½. Subtraction follows the adding rule with a common denominator. This page shows each of those steps in the working so the method is visible, not just the answer.
How do I convert a fraction to a decimal?
Divide the numerator by the denominator: 3/8 is 3 ÷ 8 = 0.375. A mixed number keeps its whole part in front, so 2 3/8 is 2.375. When the denominator, in lowest terms, has a prime factor other than 2 or 5, the decimal never ends and repeats instead: 1/3 is 0.333… and 5/6 is 0.8333…. Every answer on this page is also given as a decimal.
How do I change a fraction into a percentage?
Divide the numerator by the denominator and multiply by 100: 3/8 is 0.375, which is 37.5%. When the denominator divides into 100 you can scale instead: 7/20 is 35/100, which is 35%. A fraction greater than 1 gives a percentage above 100, so 5/4 is 125%.
How do I turn a repeating decimal into a fraction?
Multiply by the power of ten that lines up the repeat, then subtract to cancel it. Call 0.272727… x: 100x = 27.2727…, so 100x − x = 27 and x = 27/99 = 3/11. When the repeat starts later, as in 0.1666…, shift both: 100x − 10x = 16.666… − 1.666… = 15, so x = 15/90 = 1/6. The decimal mode on this page reads decimals that end, such as 0.375. For a repeating one, type several digits, such as 0.16666667, and the closest fraction within the denominator limit, 1/6, is reported with its error.
How do I multiply negative fractions?
Multiply as usual, numerators together and denominators together, then set the sign: one negative fraction gives a negative answer, two give a positive one. −2/3 × 3/4 = −6/12 = −1/2, and −2/3 × −3/4 = 6/12 = 1/2. A minus sign on the top, on the bottom or in front of the fraction means the same thing, so −2/3, 2/−3 and −(2/3) are equal. Type a minus sign in front of a fraction here, such as −2/3, and the page applies the rule.
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