Fraction Calculator
Enter two fractions, choose add, subtract, multiply or divide, and get the answer in lowest terms as a fraction, a mixed number and a decimal. Every step is written out: the common denominator, the multiplication, and the greatest common divisor that reduces the result. Free, no sign-up.
Two fractions
First fraction
Operation
Second fraction
1/2 + 1/3 = 5/6
Common denominator: LCM(2, 3) = 6
1/2 = (1 × 3)/6 = 3/6
1/3 = (1 × 2)/6 = 2/6
3/6 + 2/6 = 5/6
5/6 is already in lowest terms (GCD = 1)
5/6
Improper fraction
5/6
Mixed number
0.833333
Decimal
How to Use the Fraction Calculator
- 1. Enter the first fraction. Type a whole-number numerator and denominator. The tool opens on 1/2 + 1/3.
- 2. Choose the operation. Add, subtract, multiply or divide, and enter the second fraction.
- 3. Read the result. The headline gives the answer in lowest terms, followed by the working, then the improper fraction, the mixed number and the decimal.
- 4. Convert mixed numbers first. There is no box for a whole part, so write 2 1/4 as 9/4 before entering it (see below).
How Each Operation Works
| Operation | Rule | Example |
|---|---|---|
| Add | Rewrite both over the least common denominator, then add the numerators | 1/2 + 1/3 = 3/6 + 2/6 = 5/6 |
| Subtract | Same common denominator, then subtract the numerators | 3/4 − 5/6 = 9/12 − 10/12 = −1/12 |
| Multiply | Multiply numerators, multiply denominators | 2/3 × 9/10 = 18/30 = 3/5 |
| Divide | Invert the second fraction and multiply | 3/4 ÷ 5/8 = 3/4 × 8/5 = 24/20 = 6/5 |
Addition and subtraction need a common denominator because you can only combine pieces of the same size. The calculator uses the least common multiple of the two denominators, which keeps the numbers small; the LCM of 4 and 6 is 12, not 24. The most common mistake is adding the denominators as well (1/2 + 1/3 is not 2/5).
Every result is then reduced by its greatest common divisor (GCD). For 24/20 the GCD is 4, so the answer is 6/5, which is also the mixed number 1 1/5 and the decimal 1.2. The decimal is rounded to six places, so 5/6 appears as 0.833333.
Mixed Numbers and Negative Fractions
To enter a mixed number, convert it to an improper fraction: multiply the whole part by the denominator, add the numerator, and keep the denominator. So 2 1/4 is (2 × 4 + 1)/4 = 9/4, and 1 3/5 is 8/5. The answer comes back as an improper fraction and as a mixed number, so you can convert in both directions.
For a negative fraction, put the minus sign on the numerator (−2/3). Multiplying 5/4 by −2/3 gives −10/12, which reduces to −5/6. Dividing by a fraction whose numerator is zero is refused, because it means dividing by zero; a zero denominator is never accepted.
| Calculation | Simplified | Mixed number | Decimal |
|---|---|---|---|
| 1/2 + 1/3 | 5/6 | 5/6 | 0.833333 |
| 7/8 + 5/8 | 3/2 | 1 1/2 | 1.5 |
| 3/4 − 5/6 | −1/12 | −1/12 | −0.083333 |
| 2/3 × 9/10 | 3/5 | 3/5 | 0.6 |
| 3/4 ÷ 5/8 | 6/5 | 1 1/5 | 1.2 |
| 7/3 + 1/7 | 52/21 | 2 10/21 | 2.47619 |
Which Tool Do You Need?
| You want to… | Use |
|---|---|
| Do arithmetic with two fractions | This calculator |
| Turn a decimal such as 0.375 into a fraction, or a single fraction into a decimal | Decimal to Fraction Converter |
| Simplify a ratio or solve a proportion | Ratio Calculator |
| Find the greatest common factor or least common multiple of whole numbers | GCF & LCM Calculator |
| Practise with printable fraction problems | Fraction Worksheet Generator |
Frequently Asked Questions
- How do I add fractions with different denominators?
- Find the least common multiple of the denominators, rewrite each fraction over it, and add the numerators. For 1/2 + 1/3 the LCM of 2 and 3 is 6, so you add 3/6 + 2/6 to get 5/6. The calculator shows each of these steps.
- How do I multiply and divide fractions?
- To multiply, multiply the numerators and the denominators: 2/3 × 9/10 = 18/30 = 3/5. To divide, invert the second fraction and multiply: 3/4 ÷ 5/8 = 3/4 × 8/5 = 24/20 = 6/5.
- How do I simplify a fraction?
- Divide the numerator and the denominator by their greatest common divisor. 18/30 has a GCD of 6, so it reduces to 3/5. The calculator always reduces its answer and shows the GCD it used, or says the fraction is already in lowest terms.
- Can I enter mixed numbers?
- Not directly. Convert each mixed number to an improper fraction first: multiply the whole part by the denominator and add the numerator, so 2 1/4 becomes 9/4. Results come back both as an improper fraction and as a mixed number.
- How do I subtract fractions and get a negative result?
- Subtract as you would for a positive answer. 3/4 − 5/6 uses the common denominator 12, so 9/12 − 10/12 = −1/12. A negative answer simply means the second fraction is larger.
- Why can't I divide by a fraction with zero on top?
- Dividing by 0/5 is dividing by zero, because that fraction equals 0. The calculator refuses it rather than showing a meaningless answer.