Fraction Calculator
3/8 + 5/16 = 11/16: rewrite 3/8 as 6/16, then add the tops. Enter up to five fractions or mixed numbers below; the answer and every step update as you type.
Answer in simplest form
11/16
- Decimal
- 0.6875
- Percent
- 68.75%
3/8 + 5/16
How it’s calculated
- Add — common denominator 166/16 + 5/16 = 11/16
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How to calculate with fractions
| Operation | Rule | Example |
|---|---|---|
| Add | Common denominator, add the tops | 3/8 + 5/16 = 6/16 + 5/16 = 11/16 |
| Subtract | Common denominator, subtract the tops | 3/4 − 1/6 = 9/12 − 2/12 = 7/12 |
| Multiply | Tops × tops, bottoms × bottoms | 2/3 × 3/4 = 6/12 = 1/2 |
| Divide | Flip the second, then multiply | 3/4 ÷ 3/8 = 3/4 × 8/3 = 2 |
| Simplify | Divide top and bottom by their GCF | 210/385 = 6/11 |
The calculator applies these rules exactly — with whole numbers, not rounded decimals — so 1/3 + 1/3 + 1/3 is exactly 1, and the answer is always in simplest form. Open How it’s calculated to see the common denominator and every reduction.
Adding and subtracting: the least common denominator
Fractions can only be added when their bottoms match. The smallest bottom that works for both is the least common denominator — the least common multiple of the two denominators.
- Find the LCD. For 7/12 and 5/18, the multiples of 18 are 18, 36, 54…; 36 is the first that 12 divides, so the LCD is 36.
- Rewrite each fraction. 7/12 = 21/36 (× 3), 5/18 = 10/36 (× 2).
- Add or subtract the tops. 21/36 + 10/36 = 31/36.
- Simplify if the top and bottom share a factor.
These are the steps used in OpenStax Prealgebra (§4.5), the free college textbook from Rice University.
Mixed numbers and improper fractions
A mixed number has a whole part and a fraction: 2 1/3. An improper fraction has a top at least as large as its bottom: 7/3. They are the same number:
- Mixed → improper: whole × bottom + top, over the bottom. 2 1/3 = (2 × 3 + 1)/3 = 7/3.
- Improper → mixed: divide; the quotient is the whole part, the remainder the new top. 7/3 = 2 remainder 1 = 2 1/3.
Enter the whole number in the first box of each fraction, and the calculator converts it for you. Answers are shown both ways.
Order of operations with several fractions
With more than two fractions, multiplication and division come before addition and subtraction:
1/2 + 1/3 × 3/4 = 1/2 + 1/4 = 3/4 — not (1/2 + 1/3) × 3/4 = 5/8.
You can enter up to five fractions with any mix of + − × ÷; the steps show which part was worked out first.
Fractions of an inch
Tape measures and rulers in the U.S. are marked in halves, quarters, eighths and sixteenths of an inch. Adding two measurements is ordinary fraction addition: a 3/8-inch board on a 5/16-inch spacer stands 11/16 inch tall.
| Fraction of an inch | Decimal inch | Millimeters |
|---|---|---|
| 1/16 | 0.0625 | 1.5875 |
| 1/8 | 0.125 | 3.175 |
| 3/16 | 0.1875 | 4.7625 |
| 1/4 | 0.25 | 6.35 |
| 5/16 | 0.3125 | 7.9375 |
| 3/8 | 0.375 | 9.525 |
| 7/16 | 0.4375 | 11.1125 |
| 1/2 | 0.5 | 12.7 |
| 5/8 | 0.625 | 15.875 |
| 11/16 | 0.6875 | 17.4625 |
| 3/4 | 0.75 | 19.05 |
| 7/8 | 0.875 | 22.225 |
Millimeters are exact because an inch is exactly 25.4 mm. For lumber in fractions of an inch, the board foot calculator works with nominal and actual sizes.
Fractions in recipes
Scaling a recipe is multiplication by a fraction. To make half of a recipe that calls for 3/4 cup of sugar: 3/4 × 1/2 = 3/8 cup, which is 6 tablespoons. To make one and a half batches of 2/3 cup of milk: 2/3 × 1 1/2 = 2/3 × 3/2 = 1 cup.
Common fractions as decimals and percents
| Fraction | Decimal | Percent |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/3 | 0.(3) | 33.(3)% |
| 2/3 | 0.(6) | 66.(6)% |
| 1/4 | 0.25 | 25% |
| 3/4 | 0.75 | 75% |
| 1/5 | 0.2 | 20% |
| 1/6 | 0.1(6) | 16.(6)% |
| 1/8 | 0.125 | 12.5% |
| 1/12 | 0.08(3) | 8.(3)% |
Digits in parentheses repeat forever. For percentages of amounts, use the percentage calculator; to go straight from a fraction to a decimal or back, the fraction to decimal and decimal to fraction calculators are on the way.