Fraction Calculator
Add, subtract, multiply or divide fractions and mixed numbers, with step-by-step working. Answers are simplified and shown as a mixed number and a decimal.
Type a number, press a/b, type denominator. Operate (+−×÷) and press = to simplify.
Or use the standard form below
What is a fraction calculator?
This fraction calculator adds, subtracts, multiplies and divides fractions and mixed numbers, and shows the working: the common denominator, how each fraction is converted, the combined result and how it simplifies. Every answer is given three ways — as a simplified fraction, as a mixed number and as a decimal.
There are two ways to use it. The keypad at the top works like a handheld fraction calculator: type a number, press a/b, type the denominator, choose an operation and press =; S↔D switches the answer between fraction and decimal. The form underneath is better for homework: it takes mixed numbers (enter 2, 1 and 3 for 2 1/3) and prints the step-by-step working under the answer.
The working follows the methods taught in school — a least common denominator for adding and subtracting, multiplying straight across, and "flip and multiply" for dividing — so you can compare it line by line with your own and find exactly where an answer went wrong.
Formula
Adding and subtracting
Rewrite both fractions over a common denominator, then add or subtract the numerators and keep the denominator:
a/b ± c/d = (a × L/b ± c × L/d) / L, where L is the least common denominator — the least common multiple of b and d.
If the denominators already match, just combine the numerators: 2/9 + 5/9 = 7/9. Never add the denominators: 1/2 + 1/3 is 5/6, not 2/5.
Multiplying
a/b × c/d = (a × c) / (b × d) — multiply the numerators, multiply the denominators. No common denominator is needed.
Dividing
a/b ÷ c/d = a/b × d/c = (a × d) / (b × c) — keep the first fraction, flip the second (take its reciprocal) and multiply. Dividing by a fraction whose numerator is 0 is undefined.
Simplifying
Divide the numerator and the denominator by their greatest common factor (GCF). For 18/30 the GCF is 6, so 18/30 = 3/5. A fraction is in lowest terms when the GCF of its numerator and denominator is 1. Our GCF and LCM calculator finds both numbers if you want to check a step.
Mixed numbers
To turn a mixed number into an improper fraction, multiply the whole number by the denominator and add the numerator: 2 1/3 = (2 × 3 + 1)/3 = 7/3. To go back, divide: 49 ÷ 12 = 4 remainder 1, so 49/12 = 4 1/12. The minus sign of a negative mixed number applies to the whole thing: −2 1/3 = −(2 + 1/3) = −7/3.
Worked example
Adding with different denominators: 3/4 + 1/6
- The least common denominator of 4 and 6 is 12.
- Convert each fraction: 3/4 = 9/12 and 1/6 = 2/12.
- Add the numerators: 9/12 + 2/12 = 11/12.
- 11 and 12 share no common factor, so the answer 11/12 is already in lowest terms (≈ 0.916667).
Subtracting: 5/12 − 3/8
The least common denominator of 12 and 8 is 24, so 5/12 − 3/8 = 10/24 − 9/24 = 1/24. Multiplying the denominators (12 × 8 = 96) also works — 40/96 − 36/96 = 4/96 = 1/24 — but leaves bigger numbers to simplify.
Adding mixed numbers: 2 1/3 + 1 3/4
- Convert to improper fractions: 2 1/3 = 7/3 and 1 3/4 = 7/4.
- The least common denominator of 3 and 4 is 12: 7/3 = 28/12 and 7/4 = 21/12.
- Add: 28/12 + 21/12 = 49/12.
- 49 ÷ 12 = 4 remainder 1, so the answer is 4 1/12.
Multiplying: 2/3 × 9/10
Multiply across: (2 × 9)/(3 × 10) = 18/30, which simplifies by 6 to 3/5. A faster way is to cancel before multiplying: 9 and 3 share a factor of 3, and 2 and 10 share a factor of 2, leaving (1 × 3)/(1 × 5) = 3/5.
Dividing: 3/4 ÷ 5/8
Flip 5/8 to 8/5 and multiply: (3 × 8)/(4 × 5) = 24/20 = 6/5, or 1 1/5. Check by multiplying back: 6/5 × 5/8 = 30/40 = 3/4.
Multiplying mixed numbers: 2 1/2 × 1 1/3
Convert first — 5/2 × 4/3 — then multiply: 20/6 = 10/3 = 3 1/3. Multiplying the whole numbers and fractions separately (2 × 1 and 1/2 × 1/3) gives the wrong answer, 2 1/6.
How to use this calculator
- In the form, enter the first fraction's numerator and denominator. For a mixed number such as 2 1/3, also enter 2 as the whole number; leave the whole number blank for an ordinary fraction.
- Choose add, subtract, multiply or divide.
- Enter the second fraction the same way.
- Read the simplified fraction, the mixed number and the decimal. The step-by-step line shows the working in the order you would write it.
- For a negative fraction, put the minus sign on the numerator (−3 over 4). For a negative mixed number, put it on the whole number (−2 with 1 over 3).
Using the keypad instead: type the numerator, press a/b, type the denominator, press an operator, enter the second fraction and press =. S↔D switches between fraction and decimal, ⌫ deletes and AC clears. On a keyboard, F works as a/b and Enter as =.
Mistakes the working helps you catch
- Adding the denominators: 1/2 + 1/3 is 5/6, not 2/5.
- Flipping the wrong fraction when dividing — only the second fraction, the divisor, is flipped.
- Stopping before the fraction is fully simplified, or dividing top and bottom by a number that does not go into both.
- Losing the sign of a negative mixed number: −2 1/3 is −7/3, not −5/3.
Related reading: adding fractions with different denominators and converting between fractions and decimals. To turn an answer into a percentage, use the percentage calculator.
Sources
- Common Core State Standards for Mathematics — Grade 5, Number and Operations: Fractions (adding and subtracting fractions with unlike denominators, multiplying fractions)
- Common Core State Standards for Mathematics — Grade 6, The Number System (dividing fractions by fractions)
Frequently asked questions
How do I add fractions with different denominators?
Find the least common denominator (the least common multiple of the two denominators), convert both fractions to it, then add the numerators. For 3/4 + 1/6 the LCD is 12, so 9/12 + 2/12 = 11/12. The calculator shows each of these steps.
How do I divide fractions?
Keep the first fraction, flip the second and multiply: 3/4 ÷ 5/8 = 3/4 × 8/5 = 24/20 = 6/5. A common way to remember it is "keep, change, flip". You cannot divide by a fraction equal to zero.
How do I enter a mixed number like 2 1/3?
In the form, type 2 in the whole-number box, 1 as the numerator and 3 as the denominator. The calculator converts it to 7/3 before calculating and shows that conversion as the first step. Leave the whole-number box empty for an ordinary fraction.
How do I simplify a fraction?
Divide the numerator and denominator by their greatest common factor. 18/30 has a GCF of 6, so it simplifies to 3/5. Every result here is already simplified, and the steps show which number it was divided by.
Can I use negative fractions?
Yes. Enter the minus sign on the numerator (−3 over 4 for −3/4), or on the whole number for a negative mixed number (−2 with 1 over 3 for −2 1/3, which equals −7/3). A negative denominator also works; the answer always shows the sign on the numerator.
Should I give my answer as an improper fraction or a mixed number?
They are equal — 49/12 and 4 1/12 are the same number — so it depends on what is asked. Improper fractions are easier to keep calculating with; mixed numbers are easier to read and are often expected as a final answer in earlier grades. The calculator gives both.
How do I turn a fraction into a decimal or a percentage?
Divide the numerator by the denominator: 11/12 = 0.916667 (the 6 repeats). Multiply by 100 for a percentage: about 91.67%. Fractions whose denominators have prime factors other than 2 and 5, such as 1/3 or 1/12, give repeating decimals, so the decimal shown is rounded.
What happens if a denominator is zero?
A fraction with a zero denominator is undefined, so the calculator shows no result until both denominators are non-zero. The same applies when dividing by a fraction whose numerator is zero.