How to work with fractions
- Add / subtract: use a common denominator.
a/b + c/d = (ad + bc) / bd - Multiply: multiply straight across.
a/b × c/d = ac / bd - Divide: flip the second fraction and multiply.
a/b ÷ c/d = ad / bc - Simplify: divide the top and bottom by their greatest common divisor.
A mixed number like 2 ¾ is converted to an improper fraction first: 2 × 4 + 3 = 11, so 2 ¾ = 11/4.
Worked examples
Adding: 3/4 + 2/3. The denominators differ, so rewrite both over a common denominator of 12: 9/12 + 8/12 = 17/12, which is the mixed number 1 5/12.
Subtracting: 5/6 − 1/4. Over a common denominator of 12: 10/12 − 3/12 = 7/12.
Multiplying: 2/3 × 3/5 = 6/15. Both 6 and 15 divide by 3, so the answer simplifies to 2/5.
Dividing: 3/4 ÷ 1/2. Flip the second fraction and multiply: 3/4 × 2/1 = 6/4 = 3/2, or 1 1/2.
Fractions as decimals
Handy for measurements, recipes and drill-bit sizes:
| Fraction | Decimal | Fraction | Decimal |
|---|---|---|---|
| 1/16 | 0.0625 | 1/2 | 0.5 |
| 1/8 | 0.125 | 5/8 | 0.625 |
| 1/6 | 0.1667 | 2/3 | 0.6667 |
| 1/5 | 0.2 | 3/4 | 0.75 |
| 1/4 | 0.25 | 4/5 | 0.8 |
| 1/3 | 0.3333 | 5/6 | 0.8333 |
| 3/8 | 0.375 | 7/8 | 0.875 |
Frequently asked questions
How do I simplify a fraction?
Divide the top and bottom by their greatest common divisor (GCD) — the largest number that goes into both. For 18/24 the GCD is 6, so it simplifies to 3/4. The calculator always shows the simplified result.
What's the difference between an improper fraction and a mixed number?
An improper fraction has a top number larger than the bottom, like 17/12. A mixed number writes the same value as a whole number plus a fraction: 1 5/12. They're equal; mixed numbers are easier to picture, improper fractions are easier to calculate with.
How do I convert a fraction to a decimal or percent?
Divide the top by the bottom: 3 ÷ 8 = 0.375. Multiply by 100 for a percentage: 37.5%. The results panel shows both.
How do I enter a negative fraction?
Put the minus sign on the numerator (for example −3 over 4), or on the whole number for a mixed number (−2 and 1/2 means −2.5).
Why can't the denominator be zero?
The denominator says how many equal parts something is divided into, and dividing into zero parts has no meaning. For the same reason, you can't divide by a fraction whose numerator is zero.