Fraction Calculator
This fraction calculator adds, subtracts, multiplies and divides two fractions and shows how it got there. Type fractions like 3/4, mixed numbers like 2 1/2, whole numbers or decimals. The answer comes back in lowest terms, as a mixed number and as a decimal, with the common denominator or the reciprocal written out so you can follow every step.
3/4, 2 1/2, 5 and 0.75 all work.How to use the fraction calculator
- Type the first fraction in the first box. It opens with
1/2. - Pick an operation: Add, Subtract, Multiply or Divide. Add is selected to start with.
- Type the second fraction. It opens with
1/3. - Read the answer as you type. The defaults give
1/2 + 1/3 = 5/6, which is about 0.8333 as a decimal.
Under the answer, the working shows the method for the operation you chose. For adding and subtracting it names the lowest common denominator (6 for halves and thirds), rewrites each fraction over it (3/6 and 2/6) and combines the numerators. For multiplying and dividing it shows the cancelling, or the flip to the reciprocal, and the products top and bottom. Every answer is reduced to lowest terms, then shown as a mixed number when it is bigger than 1.
Each box accepts four kinds of input, so you rarely need to convert anything first:
- Fractions:
3/4,15/8,-2/3 - Mixed numbers:
2 1/2, with a space between the whole number and the fraction - Whole numbers:
5 - Decimals:
0.75
If you only need one fraction tidied up rather than combined with another, the simplify fractions calculator reduces it and shows the greatest common factor it divided by.
The four fraction rules
Fractions have one rule per operation. Adding and subtracting need matching denominators; multiplying and dividing do not.
Adding and subtracting
The formula always works, but it uses b × d as the denominator, which is often bigger than it needs to be. Using the lowest common denominator keeps the numbers small: for 1/4 + 1/6 the formula gives 10/24, while the LCD of 12 gives 5/12 straight away. The least common denominator calculator finds the LCD for up to ten fractions at once, and how to add fractions walks through the method in full.
Multiplying
No common denominator is needed. The guide on how to multiply fractions covers cancelling, whole numbers, mixed numbers and word problems.
Dividing
Division turns into multiplication by the reciprocal. How to divide fractions explains why flipping works and how to divide by whole numbers and mixed numbers.
Worked examples
Example: 1/2 + 1/3 (the default)
The denominators are 2 and 3. Neither divides the other and they share no factor, so the LCD is their product, 6.
5/6 is already in lowest terms. As a decimal it is 0.8333…, which you can check: 0.5 + 0.3333… = 0.8333…
Example: 5/6 − 3/8
Multiples of 8 are 8, 16, 24. The first one 6 also divides is 24, so the LCD is 24.
11 is prime and does not divide 24, so 11/24 is final. That is ≈ 0.4583.
Example: 4/9 × 3/8
Cancel before multiplying. The 4 on top and the 8 underneath share a 4; the 3 on top and the 9 underneath share a 3.
Multiplying without cancelling gives 12/72, which reduces to the same 1/6 but needs a larger division at the end.
Example: 3/4 ÷ 9/10
Flip the second fraction and multiply.
The answer is a little under 1, which makes sense: 3/4 is a little smaller than 9/10, so 9/10 fits into it slightly less than once.
Fraction calculator with whole numbers and mixed numbers
A whole number is a fraction with a denominator of 1, so 5 is 5/1. The calculator reads it that way, which means you can type a whole number in either box and use any of the four operations.
| Problem | Rewritten | Answer |
|---|---|---|
| 3 + 2/5 | 15/5 + 2/5 | 17/5 = 3 2/5 |
| 5 − 3/4 | 20/4 − 3/4 | 17/4 = 4 1/4 |
| 6 × 2/3 | 6/1 × 2/3 = 12/3 | 4 |
| 2 ÷ 3/4 | 2/1 × 4/3 | 8/3 = 2 2/3 |
| 3/4 ÷ 2 | 3/4 × 1/2 | 3/8 |
Mixed numbers are typed with a space: 2 1/2. Internally each one becomes an improper fraction first, because that is the only form every operation can use. 2 1/2 becomes 5/2 (2 × 2 + 1 = 5), and 1 3/4 becomes 7/4.
If you want to see the conversion on its own, the mixed number calculator turns a mixed number into an improper fraction step by step, and the improper fraction calculator goes the other way.
3 1/3 × 1 1/2 is 5, not 3 × 1 = 3 plus 1/3 × 1/2 = 1/6. Converting to improper fractions avoids the trap.Decimals and negative fractions
A decimal you type is turned into the exact fraction it represents. 0.75 becomes 3/4, so 0.75 + 1/3 is worked as 9/12 + 4/12 = 13/12, which is 1 1/12 or about 1.0833.
That exactness has one consequence worth knowing. 0.333 is 333/1000, not one third, so 0.333 + 1/3 gives 1999/3000 rather than 2/3. When you mean a repeating decimal like 0.333…, type the fraction it stands for. The decimal to fraction calculator converts repeating decimals into exact fractions, and the fraction to decimal calculator shows which fractions repeat and which terminate.
Negative fractions take a minus sign in front: -3/4 or -1 1/2. The usual sign rules apply, so -3/4 + 1/2 = -1/4 and 2/3 − 5/6 = -1/6. A minus sign on a mixed number applies to the whole thing: -1 1/2 means −1.5, not −1 + 1/2.
Fraction results for common pairs
The same two fractions give four very different answers depending on the operation. This table puts them side by side, every result in lowest terms.
| a | b | a + b | a − b | a × b | a ÷ b |
|---|---|---|---|---|---|
| 1/2 | 1/3 | 5/6 | 1/6 | 1/6 | 1 1/2 |
| 2/3 | 1/4 | 11/12 | 5/12 | 1/6 | 2 2/3 |
| 3/4 | 1/6 | 11/12 | 7/12 | 1/8 | 4 1/2 |
| 5/8 | 1/2 | 1 1/8 | 1/8 | 5/16 | 1 1/4 |
| 2/5 | 3/10 | 7/10 | 1/10 | 3/25 | 1 1/3 |
| 3/4 | 2/3 | 1 5/12 | 1/12 | 1/2 | 1 1/8 |
Two patterns are worth noticing. Multiplying two fractions smaller than 1 always gives an answer smaller than both of them, and dividing by a fraction smaller than 1 always gives an answer bigger than the number you started with. If a result breaks those patterns, check the working.
Why adding needs a common denominator but multiplying does not
A denominator names the size of the pieces. Thirds are one size, quarters another. Adding counts pieces, and you can only count pieces of the same size together, the same way you cannot add 2 feet and 3 inches and call it 5 of anything. Rewriting both fractions over a common denominator cuts them into pieces of one size first.
The classic wrong answer shows why. Adding tops and bottoms, 1/2 + 1/3 would be 2/5. But 2/5 is 0.4, smaller than the 1/2 you started with, and adding a positive amount cannot make a number smaller. The correct 5/6 is about 0.83.
Multiplying asks a different question: how much is a part of a part? Half of a third is a sixth. The pieces get smaller in both directions at once, which is exactly what multiplying the denominators does, and no matching is required. Division is then the reverse of multiplication, so it inherits the same freedom.
The common denominator for adding is a common multiple of the denominators, and the least one is the LCM. The LCM calculator shows the prime-power table behind it, which is the same calculation in a different setting.
Other fraction tools on this site
This calculator handles the arithmetic. These cover the jobs around it:
- Reducing one fraction: the simplify fractions calculator linked earlier, or the guide to simplifying fractions by hand.
- Subtraction with the LCD laid out: the subtracting fractions calculator.
- Checking whether two fractions are equal: the guide to equivalent fractions.
- Finding the greatest common factor used to reduce an answer: the GCF calculator.
Common mistakes
- Adding the denominators.
1/2 + 1/3is 5/6, not 2/5. Only numerators are added, and only once the denominators match. - Finding a common denominator to multiply. It does no harm, but it is wasted work. Multiply straight across.
- Flipping the wrong fraction when dividing. Only the second fraction, the divisor, is flipped.
- Typing a mixed number without the space.
21/2is twenty-one halves;2 1/2is two and a half. - Treating 0.333 as one third. Type
1/3when you mean a third exactly. - Leaving an answer unsimplified. 10/24 is correct but unfinished; 5/12 is the answer most teachers expect.
- Cancelling across a plus sign. Cancelling only works across a multiplication. In
2/3 + 3/4the threes do not cancel.
Frequently asked questions
What is 1/2 + 1/3?
5/6. The lowest common denominator of 2 and 3 is 6, so 1/2 becomes 3/6 and 1/3 becomes 2/6. Adding the numerators gives 3/6 + 2/6 = 5/6, which is about 0.8333. The tempting answer 2/5 is wrong, because adding tops and bottoms gives 0.4, smaller than the 1/2 you started with.
What is 2/3 + 1/4?
11/12. The LCD of 3 and 4 is 12, so rewrite 2/3 = 8/12 and 1/4 = 3/12, then add the numerators: 8/12 + 3/12 = 11/12. That is about 0.9167. Since 11 is prime and does not divide 12, the fraction is already in lowest terms.
How do you use a fraction calculator with whole numbers?
Type the whole number on its own, such as 5. The calculator treats it as 5/1 and carries on with the operation you chose. So 5 − 3/4 becomes 20/4 − 3/4 = 17/4, shown as 4 1/4, and 6 × 2/3 becomes 12/3 = 4. Mixed numbers work too: type 2 1/2 with a space.
How do you add fractions with different denominators?
Rewrite both fractions over a common denominator, preferably the lowest one, then add the numerators and keep the denominator. For 5/6 + 1/4 the LCD is 12, giving 10/12 + 3/12 = 13/12, or 1 1/12. Simplify the result if the top and bottom share a factor.
What is 3/4 divided by 2?
3/8. Write 2 as 2/1, flip it to 1/2 and multiply: 3/4 × 1/2 = 3/8. A shortcut for dividing a fraction by a whole number is to multiply the denominator by it, so 3/4 divided by 2 is 3 over 4 × 2. As a decimal the answer is 0.375.
What is 1/2 times 1/3?
1/6. Multiply the numerators, 1 × 1 = 1, and the denominators, 2 × 3 = 6. Read it as “half of a third”: cut a third into two equal parts and each part is a sixth of the whole. No common denominator is needed to multiply fractions.
Can the fraction calculator handle negative fractions?
Yes. Put a minus sign in front, as in -3/4 or -1 1/2. The normal sign rules apply, so -3/4 + 1/2 = -1/4, and subtracting a larger fraction from a smaller one gives a negative answer: 2/3 − 5/6 = -1/6. A minus on a mixed number covers both the whole and the fraction part.
How do I turn the answer into a decimal?
The calculator shows the decimal under every answer, so there is nothing extra to do. To convert by hand, divide the numerator by the denominator: 5/6 = 5 ÷ 6 ≈ 0.8333. Fractions whose reduced denominator has only 2s and 5s as prime factors, such as 3/8 = 0.375, end; all others repeat.
Related calculators
Guides that use this calculator
Longer explanations of the method behind it, with worked examples.
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