Mixed Number Calculator

Convert between mixed numbers and improper fractions, perform arithmetic operations with step-by-step solutions.

Choose Operation

Result

Result
17/5

Step-by-Step Solution

(whole x denom + num) / denom

Understanding Mixed Numbers

A mixed number is a combination of a whole number and a proper fraction, such as 3 2/5. Mixed numbers are commonly used in everyday life for measurements, cooking, and general arithmetic. They provide a more intuitive way to express quantities that are between two whole numbers.

Key Operations

Mixed to Improper

Multiply the whole number by the denominator, add the numerator, and keep the same denominator.

3 2/5 = (3x5+2)/5 = 17/5

Improper to Mixed

Divide the numerator by the denominator. The quotient is the whole part; the remainder is the new numerator.

17/5 = 3 remainder 2 = 3 2/5

Arithmetic with Mixed Numbers

Convert to improper fractions first, find common denominators for add/subtract, then simplify.

2 1/3 + 1 2/4 = 7/3 + 6/4

How to Add and Subtract Mixed Numbers

  1. Convert each mixed number to an improper fraction.
  2. Find the least common denominator (LCD).
  3. Rewrite each fraction with the LCD.
  4. Add or subtract the numerators, keeping the LCD.
  5. Simplify the result and convert back to a mixed number if needed.

How to Multiply and Divide Mixed Numbers

  1. Convert each mixed number to an improper fraction.
  2. For multiplication: multiply numerators together and denominators together.
  3. For division: multiply by the reciprocal of the second fraction.
  4. Simplify the result and convert back to a mixed number if needed.

Simplifying Fractions

To simplify a fraction, find the greatest common divisor (GCD) of the numerator and denominator, then divide both by it. A fraction is in simplest form when the GCD of its numerator and denominator is 1. This calculator automatically simplifies all results to their lowest terms.