Fraction Calculator
Add, subtract, multiply and divide fractions and mixed numbers — exact simplified answers with the common denominator and every step shown.
Fraction Calculator: with the default inputs, result (simplified) is 11/12.
The top number.
The bottom number. Can't be zero.
- As a mixed number
- 11/12
- As a decimal
- 0.916667
Assumptions
- Arithmetic is exact (arbitrary-precision integers); only the decimal output is rounded.
- A non-zero whole number carries the sign of a mixed number; the fraction part is taken as positive.
| Fraction | Decimal | Percent | |
|---|---|---|---|
| 1/16 | 0.0625 | 6.25% | |
| 1/10 | 0.1 | 10% | |
| 1/8 | 0.125 | 12.5% | |
| 1/6 | 0.166667 | 16.6667% | |
| 1/5 | 0.2 | 20% | |
| 1/4 | 0.25 | 25% | |
| 1/3 | 0.333333 | 33.3333% | |
| 3/8 | 0.375 | 37.5% | |
| 2/5 | 0.4 | 40% | |
| 1/2 | 0.5 | 50% |
A fraction terminates as a decimal exactly when its denominator, in lowest terms, has no prime factors other than 2 and 5. That is why thirds, sixths and sevenths repeat and eighths do not.
How this is worked out
The formula
a/b + c/d = (a·d + c·b) / (b·d), then simplify (or use the LCD to keep numbers small) a/b − c/d = (a·d − c·b) / (b·d) a/b × c/d = (a·c) / (b·d) a/b ÷ c/d = a/b × d/c = (a·d) / (b·c) Mixed number W n/d = (W·d + n) / d
Open How it’s calculated above to see this worked through with your own numbers.
What you enter
- Numerator (first fraction)
- The top number.whole numbers only · defaults to 3
- Denominator (first fraction)
- The bottom number. Can't be zero.whole numbers only · defaults to 4
- Operation
- Choose one of 4 options.+ Add · − Subtract · × Multiply · ÷ Divide
- Numerator (second fraction)
- A number.whole numbers only · defaults to 1
- Denominator (second fraction)
- A number.whole numbers only · defaults to 6
- Whole number (first)(under More options)
- Optional. For 2¾ enter 2 here and 3/4 above. A negative whole number makes the whole mixed number negative.whole numbers only · defaults to 0
- Whole number (second)(under More options)
- Optional whole part of the second mixed number.whole numbers only · defaults to 0
What you get back
- Result (simplified)main answer
- As a mixed number
- As a decimal
What this assumes
- Arithmetic is exact (arbitrary-precision integers); only the decimal output is rounded.
- A non-zero whole number carries the sign of a mixed number; the fraction part is taken as positive.
About this calculator
A fraction is a division that hasn't been carried out yet: 3/4 means "3 divided by 4", or three pieces when the whole is cut into four. Keeping the division unfinished is the whole point — 1/3 is exact, while 0.333… never is. This calculator does the arithmetic exactly and shows the same steps a teacher would want to see.
How to use it
Type the two fractions, pick + − × ÷, and read the simplified answer. For mixed numbers such as 2¾, open More options and put the whole number in its own box; the calculator converts it to an improper fraction first (2¾ = 11/4) because that's the only form the rules below work on. A negative mixed number is entered with the minus sign on the whole number: −2¾ means −(2 + ¾).
Why the rules look the way they do
- Adding and subtracting only works when the pieces are the same size, so both fractions are rewritten over a common denominator. The least common denominator (the LCM of the two bottoms) keeps the numbers small; any common multiple would give the same simplified answer.
- Multiplying is "a fraction of a fraction": half of a third is a sixth, so you multiply tops and bottoms.
- Dividing asks "how many of the second fit in the first?" Multiplying by the reciprocal is the same question turned around, which is why you "flip and multiply".
Reading the result
The headline answer is in lowest terms — top and bottom divided by their greatest common divisor. The mixed-number form is useful for measurements (1 5/12 inches), and the decimal is there for calculators and spreadsheets. If the decimal looks like it repeats (0.8333…), that's a sign the fraction is the more honest answer.
Common mistakes
- Adding tops and bottoms straight across (3/4 + 1/6 is not 4/10).
- Forgetting to convert a mixed number before multiplying or dividing — 2½ × 2 is 5, not 4½.
- Cancelling before flipping in a division problem. Flip first, then cancel.
Frequently asked questions
▸How do I add fractions with different denominators?
Rewrite both over a common denominator, then add the numerators. For 3/4 + 1/6 the LCD is 12: 9/12 + 2/12 = 11/12.
▸How do I divide fractions?
Keep the first fraction, flip the second (swap its numerator and denominator), and multiply: 7/8 ÷ 1/4 = 7/8 × 4/1 = 28/8 = 7/2.
▸How do I simplify a fraction?
Divide the numerator and denominator by their greatest common divisor. 18/24 has GCD 6, so it simplifies to 3/4.
▸How do I turn a mixed number into an improper fraction?
Multiply the whole number by the denominator, add the numerator, and keep the denominator: 2¾ = (2 × 4 + 3)/4 = 11/4.
▸Why can't the denominator be zero?
A denominator of zero would mean dividing by zero, which has no value. The calculator shows an error instead of a made-up number.
Put this calculator on your own site
A working fractions, free for any site, with no ads and no sign-up. It resizes to fit wherever you paste it and updates itself as this page improves.
Paste this anywhere. It works on any site, carries no ads, never expires, and always shows the current version.
Fraction Calculator by CalculateItNow
The page's own title. The clearest description of what the link leads to.
The credit line sits outside the widget on purpose, so it is a real link on your page rather than one buried in a frame. Please keep it — it is what pays for CalculateItNow staying free and ad-free. The script only resizes the widget to fit its contents; drop it and the widget still works.
Browse every calculator widget·How to add it to WordPress, Squarespace or Wix
Related calculators
The questions people ask next to a fractions.
Find what percent one number is of another, take a percentage of a number, or calculate percentage increase and decrease — with the working shown.
Simplify a ratio, solve a proportion (A:B = C:?) or split a total in a given ratio — with the GCD, cross-multiplication and each part shown.
Greatest common divisor and least common multiple of 2–4 whole numbers, with Euclid's algorithm written out line by line and the prime factorizations.
Find the mean, median, mode, sum and range of up to 10 numbers, with the work shown and a deviation table that explains what the mean really is.
Round to any decimal place, to tens or thousands, or to N significant figures — half-up, banker's, floor, ceiling or truncate — with the rule explained.