How to use it· 4 steps
- Type the first number: a fraction such as 3/4, a mixed number such as 1 3/4 (whole number, space, fraction), a whole number or a decimal.
- Choose +, −, × or ÷ and type the second number. A minus sign in front makes it negative: −2/3.
- Read the simplified fraction, the mixed number and the decimal, then follow the numbered working beneath them.
- Switch to Simplify to reduce a single fraction, or to Decimal → fraction to convert 0.375 or a repeating decimal such as 0.(3).
Step by step
How to use the fraction calculator
- 1Type the first number: a fraction such as 3/4, a mixed number such as 1 3/4 (whole number, space, fraction), a whole number or a decimal.
- 2Choose +, −, × or ÷ and type the second number. A minus sign in front makes it negative: −2/3.
- 3Read the simplified fraction, the mixed number and the decimal, then follow the numbered working beneath them.
- 4Switch to Simplify to reduce a single fraction, or to Decimal → fraction to convert 0.375 or a repeating decimal such as 0.(3).
How each operation works
Adding and subtracting need a common denominator, and the smallest one is the least common multiple of the two denominators. Take 1 3/4 + 2/5. The mixed number becomes an improper fraction first: (1 × 4 + 3)/4 = 7/4. The LCM of 4 and 5 is 20, so 7/4 becomes 35/20 and 2/5 becomes 8/20. Add the numerators — 35 + 8 = 43 — keep the denominator, and the answer is 43/20, or 2 3/20, or 2.15.
Cross-multiplication is the shortcut that skips finding the LCM: a/b + c/d = (a × d + b × c)/(b × d). It always works, but it uses the product of the denominators rather than the smallest shared one, so the result usually needs more simplifying — 1/6 + 1/4 comes out as 10/24 that way, against 5/12 directly through the LCM of 12. The working shows both, so you can check one against the other.
Multiplying needs no common denominator at all: multiply the tops, multiply the bottoms, then simplify. 7/4 × 2/5 = 14/20 = 7/10. Dividing is multiplying by the reciprocal of the second fraction — keep, change, flip — so 7/4 ÷ 2/5 = 7/4 × 5/2 = 35/8 = 4 3/8. Dividing by zero, or by a fraction equal to zero, is reported rather than answered.
Simplifying with the greatest common divisor
A fraction is in lowest terms when its numerator and denominator share no factor other than 1. Dividing both by their greatest common divisor gets there in one step, and Euclid's algorithm finds the GCD quickly even for large numbers: for 84/126, 126 = 1 × 84 + 42 and 84 = 2 × 42 + 0, so the GCD is 42 and the fraction is 2/3. Every fraction has exactly one lowest-terms form, which is why two correct methods always meet at the same answer.
Turning an improper fraction into a mixed number is a division with remainder: 43 ÷ 20 is 2 remainder 3, so 43/20 = 2 3/20. Improper fractions are usually preferred in algebra, because they multiply and divide cleanly; mixed numbers read better in measurements and recipes. Both are shown.
Negative mixed numbers trip people up. −1 3/4 means −(1 + 3/4) = −7/4, not −1 + 3/4 = −1/4. The minus sign belongs to the whole number, and this calculator reads it that way.
Decimals to fractions, repeating decimals included
A terminating decimal becomes a fraction by counting its decimal places: 0.375 has three, so it is 375/1000, which simplifies by the GCD of 125 to 3/8. Any decimal that ends converts this way, and the result is exact.
Repeating decimals use a neat trick, and the calculator shows it. Write the repeating digits in brackets — 0.(3) for 0.333…, 0.1(6) for 0.1666… — the bracket standing in for the bar drawn over the digits by hand. For x = 0.1(6), multiply by 100 and by 10 so the repeating tails line up: 100x − 10x = 16.666… − 1.666… = 15, so 90x = 15 and x = 15/90 = 1/6. In the same way 0.(142857) is 1/7, and 0.(9) is exactly 1.
The reverse also holds: a fraction in lowest terms has a terminating decimal only when its denominator has no prime factors other than 2 and 5. Anything else repeats, and the decimal line marks the repeating block — 1/7 shows as 0.(142857). For a long measured value such as 3.14159, the exact fraction 314159/100000 is not very useful, so the converter also offers the closest fraction with a denominator up to 1,000 — here 355/113, the classic approximation of π.
Exact arithmetic, and what that means here
Most calculators turn fractions into decimals and lose digits on the way — 1/3 becomes 0.333333 and three of them make 0.999999. This one keeps every number as a whole-number numerator and denominator of any length, so 1/3 stays 1/3 and an answer like 123456789/987654321 + 1/3 = 150891632/329218107 is exact to the last digit. Only the decimal line is rounded, to ten places, and it says when it has been.
There are limits worth stating. A calculation takes two numbers; for a longer chain, copy the result into the first box and carry on. It handles numbers, not algebra, so (x + 1)/2 is beyond it. Each number is capped at 40 digits, which is far past anything a worksheet needs. And it reads a slash as a fraction bar, so 1/2/3 is not accepted — split it into two steps.
As with everything on this site, the arithmetic runs in your browser and nothing you type is sent or stored.
Answers
Frequently asked questions
How do I type a mixed number?
Whole number, a space, then the fraction: 2 1/2. For a negative mixed number put the minus sign first — −2 1/2 — which means −5/2.
How do you add fractions with different denominators?
Rewrite both over a common denominator — the LCM of the two is the smallest — then add the numerators. 1/4 + 1/6: the LCM is 12, so 3/12 + 2/12 = 5/12.
How do you divide fractions?
Multiply by the reciprocal of the second fraction: keep the first, change ÷ to ×, flip the second. 3/4 ÷ 1/2 = 3/4 × 2/1 = 6/4 = 3/2.
What does 0.(3) mean?
The digits in brackets repeat forever, so 0.(3) is 0.333… and 0.1(6) is 0.1666… — the same as drawing a bar over the repeating digits.
Can it simplify a fraction on its own?
Yes — choose Simplify, type the fraction, and it divides top and bottom by their greatest common divisor, showing the GCD it used.
Is the answer exact?
The fraction is always exact. The decimal is exact when it terminates, marked with brackets when it repeats, and otherwise rounded to ten decimal places, which the result says.