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Formula
a/b + c/d = (a × d + c × b) ÷ (b × d)
- a, c
- the numerators (top numbers)
- b, d
- the denominators (bottom numbers), which can't be 0
How each operation works
Adding and subtracting fractions
Fractions can only be added or subtracted once they share a denominator. The calculator rewrites both over the product of the two denominators, then adds or subtracts the numerators. For 1/4 + 1/6, that’s 6/24 + 4/24 = 10/24, which simplifies to 5/12.
Multiplying fractions
Multiply the numerators together and the denominators together: 2/3 × 3/5 = 6/15 = 2/5. No common denominator is needed.
Dividing fractions
Flip the second fraction and multiply. Dividing by 3/4 is the same as multiplying by 4/3, so 1/2 ÷ 3/4 = 1/2 × 4/3 = 4/6 = 2/3.
How to use the fraction calculator
- Enter the numerator and denominator of the first fraction.
- Choose add, subtract, multiply or divide.
- Enter the second fraction. To use a whole number, give it a denominator of 1, so 5 becomes 5/1.
- Read the simplified answer, then check the working underneath to follow each step.
Whole numbers and negative fractions
The fraction calculator takes whole numbers and negatives as well as ordinary fractions. Give a whole number a denominator of 1, so 3 × 2/5 is entered as 3/1 × 2/5 and returns 6/5, or 1 1/5. For a negative fraction, put the minus sign on the numerator: −3/4 + 5/6 is entered as −3 over 4 plus 5 over 6, and the answer is 1/12. A minus sign on the denominator gives the same value, and the answer always shows the sign in front.
Adding fractions by hand with the least common denominator
Multiplying the two denominators always works, but it can produce large numbers. On paper it’s usually quicker to use the least common denominator (LCD), the smallest number both denominators divide into.
To add 5/8 + 1/6:
- Find the LCD. Multiples of 8 are 8, 16, 24… and 24 is also a multiple of 6. So the LCD is 24.
- Rewrite each fraction over the LCD. 8 goes into 24 three times, so 5/8 = 15/24. 6 goes into 24 four times, so 1/6 = 4/24.
- Add the numerators. 15/24 + 4/24 = 19/24.
- Simplify if possible. 19 is prime and doesn’t divide 24, so 19/24 is already in lowest terms.
Subtracting mixed numbers
To work out 4 1/3 − 1 3/4, convert both to improper fractions first: 4 1/3 = 13/3 and 1 3/4 = 7/4. The LCD of 3 and 4 is 12, so the sum becomes 52/12 − 21/12 = 31/12. Dividing 31 by 12 gives 2 remainder 7, so the answer is 2 7/12. Converting first avoids the “borrowing” step that trips people up when the second fraction part (3/4) is larger than the first (1/3).
Simplifying to lowest terms
A fraction is in lowest terms when the numerator and denominator have no common factor other than 1. To get there, divide both by their greatest common divisor (GCD). For 18/24 the GCD is 6, so it simplifies to 3/4. The calculator does this automatically and shows the unsimplified result in the working, so you can see what was reduced.
Converting fractions to mixed numbers and decimals
When the numerator is larger than the denominator, the answer is shown in three forms:
- Improper fraction, such as 11/4, which is easiest to use in further calculations.
- Mixed number, such as 2 3/4, which is easier to picture and common in measurements and recipes.
- Decimal, such as 2.75, which is handy for comparing sizes or entering into other tools.
Some fractions, like 1/3, have decimals that repeat forever. The fraction is exact, while the decimal is rounded, so keep working with the fraction if you plan to do more calculations.
Inch fractions as decimals, percentages and millimeters
Tape measures, drill bits and wrench sizes in the U.S. use halves, quarters, eighths and sixteenths of an inch. Every fraction in this table has an exact decimal, and one inch is exactly 25.4 mm.
| Fraction of an inch | Decimal | Percent | Millimeters |
|---|---|---|---|
| 1/16 | 0.0625 | 6.25% | 1.5875 |
| 1/8 | 0.125 | 12.5% | 3.175 |
| 3/16 | 0.1875 | 18.75% | 4.7625 |
| 1/4 | 0.25 | 25% | 6.35 |
| 5/16 | 0.3125 | 31.25% | 7.9375 |
| 3/8 | 0.375 | 37.5% | 9.525 |
| 7/16 | 0.4375 | 43.75% | 11.1125 |
| 1/2 | 0.5 | 50% | 12.7 |
| 9/16 | 0.5625 | 56.25% | 14.2875 |
| 5/8 | 0.625 | 62.5% | 15.875 |
| 11/16 | 0.6875 | 68.75% | 17.4625 |
| 3/4 | 0.75 | 75% | 19.05 |
| 13/16 | 0.8125 | 81.25% | 20.6375 |
| 7/8 | 0.875 | 87.5% | 22.225 |
| 15/16 | 0.9375 | 93.75% | 23.8125 |
For thirds, sixths and other fractions whose decimals repeat, see the full table in the guide to fractions, decimals and percentages.
Real-life uses
Scaling recipes
Recipes are written in fractions, and scaling them means multiplying. Making one and a half batches of a recipe that calls for 2/3 cup of milk is 3/2 × 2/3 = 1 cup. Halving a recipe that uses 3/4 teaspoon of salt gives 3/4 × 1/2 = 3/8 teaspoon. If you’re scaling every ingredient by the same amount, the ratio calculator can do it from the serving counts.
Measuring and building
Woodworkers and DIYers add and subtract inch fractions constantly. A 3/8 in board on top of a 5/16 in shim is 6/16 + 5/16 = 11/16 in thick. Two 5/8 in seam allowances on a sewing pattern add up to 10/8, or 1 1/4 in, of extra fabric.
Time
Fractions of an hour convert to minutes by multiplying by 60. Three quarters of an hour is 3/4 × 60 = 45 minutes. For adding up longer spans of time, the hours calculator handles the clock arithmetic for you.
Sharing and splitting
If three roommates each pay a third of the rent and one of them covers half of another’s share for a month, that person pays 1/3 + 1/6 = 1/2 of the rent. Fractions keep these splits exact, where decimals like 0.333 would leave a few cents unaccounted for.
Tips and shortcuts
- Cancel before you multiply. In 4/9 × 3/8, the 4 and 8 share a factor of 4, and the 3 and 9 share a factor of 3. Cancelling first leaves 1/3 × 1/2 = 1/6, with no large numbers to simplify afterward.
- Compare by cross-multiplying. To see whether 5/7 or 7/10 is larger, compare 5 × 10 = 50 with 7 × 7 = 49. The fraction on the side with the larger product is bigger, so 5/7 wins.
- Check with decimals. If the decimal of your answer looks wildly off from a rough estimate, recheck the operation you chose.
Common mistakes
- Adding the denominators. 1/2 + 1/3 is not 2/5. With a common denominator it’s 3/6 + 2/6 = 5/6.
- Flipping the wrong fraction when dividing. Only the second fraction, the divisor, is inverted. 1/2 ÷ 3/4 becomes 1/2 × 4/3, not 2/1 × 3/4.
- Forgetting to convert mixed numbers. Multiplying 2 1/2 × 2 1/2 by multiplying the whole parts and fraction parts separately gives 4 1/4, but the correct answer is 5/2 × 5/2 = 25/4 = 6 1/4.
- Leaving answers unsimplified. 6/8 is correct but not finished. Teachers and recipe readers usually expect 3/4.
Glossary
- Numerator: the top number, counting how many parts you have.
- Denominator: the bottom number, saying how many equal parts make a whole.
- Proper and improper fractions: a proper fraction is less than 1, such as 3/5. An improper fraction has a numerator at least as large as its denominator, such as 7/4.
- Mixed number: a whole number plus a proper fraction, such as 1 3/4.
- Equivalent fractions: fractions with the same value, such as 2/4 and 1/2.
- Reciprocal: a fraction flipped upside down. The reciprocal of 3/4 is 4/3.
- Ratio: a comparison of two quantities rather than a part of one whole. The ratio calculator simplifies and solves them, and the percentage calculator turns a share into a percentage.
Worked examples
Adding fractions with different denominators
Add 3/4 and 5/6.
Inputs: First numerator = 3; First denominator = 4; Operation = + Add; Second numerator = 5; Second denominator = 6
(3 × 6 + 5 × 4) / (4 × 6) = 38/24 Simplified: 19/12
Answer: 3/4 + 5/6 = 19/12 (1 7/12) ≈ 1.5833333333
Dividing fractions
Divide 2/3 by 4/9.
Inputs: First numerator = 2; First denominator = 3; Operation = ÷ Divide; Second numerator = 4; Second denominator = 9
2/3 × 9/4 = 18/12 Simplified: 3/2
Answer: 2/3 ÷ 4/9 = 3/2 (1 1/2) ≈ 1.5
Taking a fraction of a recipe amount
You are making 2/3 of a recipe that calls for 3/4 cup of sugar.
Inputs: First numerator = 2; First denominator = 3; Operation = × Multiply; Second numerator = 3; Second denominator = 4
(2 × 3) / (3 × 4) = 6/12 Simplified: 1/2
Answer: 2/3 × 3/4 = 1/2 ≈ 0.5
Subtracting mixed numbers
A 3 1/2 ft board has 1 1/4 ft cut off. Entered as improper fractions: 7/2 − 5/4.
Inputs: First numerator = 7; First denominator = 2; Operation = − Subtract; Second numerator = 5; Second denominator = 4
(7 × 4 − 5 × 2) / (2 × 4) = 18/8 Simplified: 9/4
Answer: 7/2 − 5/4 = 9/4 (2 1/4) ≈ 2.25
Assumptions and limitations
- Numerators and denominators must be whole numbers between −1,000,000,000,000 and 1,000,000,000,000. Decimals aren't accepted.
- Arithmetic is exact, and every answer is reduced to lowest terms.
- Mixed numbers can't be typed in directly. Convert them to improper fractions first, so 2 1/3 becomes 7/3.
- Negative numerators and denominators are allowed. A minus sign in the denominator is moved to the numerator in the answer.
- A mixed number is shown only when the answer is larger than 1 or smaller than −1 and isn't a whole number.
- The decimal form is rounded to up to 10 decimal places.
- A denominator of 0 isn't allowed, and you can't divide by a fraction equal to 0.
Frequently asked questions
How do I enter a mixed number like 2 1/3?
Multiply the whole number by the denominator and add the numerator, keeping the same denominator. 2 1/3 becomes (2 × 3 + 1)/3 = 7/3. Enter 7 as the numerator and 3 as the denominator.
How do I enter a whole number?
Give it a denominator of 1. To multiply 5 by 3/4, enter 5/1 × 3/4, and the calculator returns 15/4, or 3 3/4.
How do you calculate fractions with different denominators?
To add or subtract, rewrite both fractions over a common denominator, then combine the numerators. For 2/3 + 1/4 the least common denominator is 12, so the sum is 8/12 + 3/12 = 11/12. The calculator uses the product of the two denominators instead, which gives the same simplified answer. Multiplying and dividing don't need a common denominator.
How is a negative mixed number shown?
The minus sign applies to the whole mixed number. −7/2 is shown as −3 1/2, which means −(3 + 1/2), or −3.5.
How do I turn a decimal into a fraction?
Write the decimal over the matching power of 10, then simplify. 0.375 has three decimal places, so it's 375/1000. The greatest common divisor of 375 and 1,000 is 125, which reduces it to 3/8.
Can you do fractions on a regular calculator?
Many scientific calculators have a fraction key, often labeled a b/c or n/d. A basic calculator only works in decimals, so dividing the numerator by the denominator gives the decimal value but loses the exact fraction. This calculator keeps the answer as an exact fraction and shows the decimal alongside it.
Can the calculator simplify a single fraction?
Yes. Multiply it by 1/1. For example, 18/24 × 1/1 returns 3/4, its lowest terms.