Math

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.

fraction-calculator
Enter fractions as 3/4, mixed numbers as 1 2/3, or whole numbers as 5. Negatives: -1 2/3
Answer

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.

8 ÷ 4 = 2 ✓ whole number (no remainder) 7 ÷ 4 = 1.75 ✗ not a whole number (remainder 3) 12 ÷ 3 = 4 ✓ whole number (no remainder)

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.

a/b + c/d = (a×d + c×b) / (b×d) then simplify a/b − c/d = (a×d − c×b) / (b×d) then simplify

For mixed numbers, first convert them to improper fractions, then apply the formula above.

How to multiply and divide fractions

Multiply: a/b × c/d = (a×c) / (b×d) then simplify Divide: a/b ÷ c/d = (a×d) / (b×c) then simplify

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) / denominator2 3/4 = (2×4+3)/4 = 11/4
Improper → MixedDivide numerator by denominator; remainder is new numerator11/4 = 2 remainder 3 = 2 3/4
Fraction → DecimalDivide numerator by denominator3/4 = 3÷4 = 0.75
Fraction → PercentDivide numerator by denominator × 1003/4 = 0.75 × 100 = 75%
Fraction → WholeOnly possible if remainder = 08/4 = 2, but 7/4 = not a whole number

Common questions

  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.