Fraction Calculator
Add, subtract, multiply or divide fractions and mixed numbers with full step-by-step working. Convert any fraction to a whole number, mixed number, decimal, or simplest form.
How to convert a fraction to a whole number
A fraction converts to a whole number only when the numerator divides exactly by the denominator with no remainder. To check: divide the numerator by the denominator. If the result is a whole number (remainder = 0), you have a whole number. If not, the result is a decimal or mixed number.
Use the Convert tab above — enter any numerator and denominator to instantly see whether it equals a whole number, and what all its other equivalent forms are.
How to add and subtract fractions
To add or subtract fractions, you must first find a common denominator. The easiest approach is to use the Least Common Multiple (LCM) of the two denominators. Once the denominators match, add or subtract the numerators and simplify.
For mixed numbers, first convert them to improper fractions, then apply the formula above.
How to multiply and divide fractions
Dividing by a fraction is the same as multiplying by its reciprocal — flip the second fraction and multiply. For mixed numbers, always convert to improper fractions first.
Mixed numbers and improper fractions
| Conversion | Method | Example |
|---|---|---|
| Mixed → Improper | (whole × denominator + numerator) / denominator | 2 3/4 = (2×4+3)/4 = 11/4 |
| Improper → Mixed | Divide numerator by denominator; remainder is new numerator | 11/4 = 2 remainder 3 = 2 3/4 |
| Fraction → Decimal | Divide numerator by denominator | 3/4 = 3÷4 = 0.75 |
| Fraction → Percent | Divide numerator by denominator × 100 | 3/4 = 0.75 × 100 = 75% |
| Fraction → Whole | Only possible if remainder = 0 | 8/4 = 2, but 7/4 = not a whole number |
Common questions
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A fraction equals a whole number only when its numerator is exactly divisible by its denominator. For example, 8/4 = 2 (a whole number) because 8 ÷ 4 = 2 with no remainder. If there is a remainder, the result is a mixed number, not a whole number. Enter any fraction in the Convert tab above to check instantly.
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Find a common denominator (the LCM of both denominators), convert each fraction to that denominator, then add the numerators. For example: 1/3 + 1/4 = 4/12 + 3/12 = 7/12. The calculator shows every step for your specific fractions.
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A mixed number is a combination of a whole number and a proper fraction, such as 2 3/4 (two and three quarters). It represents a value greater than 1. To convert a mixed number to an improper fraction: multiply the whole number by the denominator, add the numerator, and place the result over the original denominator. So 2 3/4 = (2×4 + 3)/4 = 11/4.
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Divide both the numerator and denominator by their Greatest Common Factor (GCF). For example, 12/18 — the GCF of 12 and 18 is 6, so 12/18 = 2/3. If the GCF is 1, the fraction is already in its simplest form.
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Divide the numerator by the denominator. The quotient is the whole number part, and the remainder becomes the new numerator over the original denominator. For example, 11/4: 11 ÷ 4 = 2 remainder 3, so 11/4 = 2 3/4.
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Multiply the numerators together and the denominators together, then simplify. For example: 2/3 × 3/4 = (2×3)/(3×4) = 6/12 = 1/2. If working with mixed numbers, first convert them to improper fractions.
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To divide by a fraction, multiply by its reciprocal (flip it upside down). For example: 2/3 ÷ 3/4 = 2/3 × 4/3 = 8/9. The phrase "keep, change, flip" is a common memory aid — keep the first fraction, change division to multiplication, flip the second fraction.
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A proper fraction has a numerator smaller than its denominator (e.g. 3/4), so its value is less than 1. An improper fraction has a numerator equal to or greater than its denominator (e.g. 7/4), so its value is 1 or more. Improper fractions can always be converted to mixed numbers.
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Simply divide the numerator by the denominator. For example, 3/4 = 3 ÷ 4 = 0.75. For mixed numbers like 2 3/4, convert to an improper fraction first (11/4), then divide: 11 ÷ 4 = 2.75.
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Yes. A negative fraction equals a negative whole number when its numerator is exactly divisible by its denominator. For example, -8/4 = -2, which is a whole number. The same rules apply — divide numerator by denominator and check for a zero remainder.