What Is a Mixed Number?
A mixed number is a number that combines a whole number with a proper fraction, such as 3 ½ or 5 ¾. Mixed numbers are used in everyday life for measurements (2 ½ cups of flour), construction (3 ¼ inch screws), and many other practical contexts where quantities fall between whole numbers. This calculator performs all four basic arithmetic operations — addition, subtraction, multiplication, and division — on mixed numbers and fractions, providing simplified results with step-by-step solutions.
Working with mixed numbers requires converting between mixed number form and improper fraction form. An improper fraction has a numerator larger than its denominator (like 7/2), while a mixed number separates the whole and fractional parts (3 ½). This calculator handles both conversions automatically, showing each step so you can follow and learn the process.
How to Use This Calculator
Enter the first mixed number by typing the whole number part and the fraction (numerator and denominator). Select the operation (+, −, ×, ÷). Enter the second mixed number. Results appear instantly in three formats: as a simplified mixed number, as an improper fraction, and as a decimal. You can enter pure fractions by leaving the whole number as 0, or whole numbers by leaving the numerator as 0.
How Mixed Number Operations Work
Addition and Subtraction
To add or subtract mixed numbers: (1) Convert each mixed number to an improper fraction. (2) Find the least common denominator (LCD). (3) Convert fractions to equivalent fractions with the LCD. (4) Add or subtract the numerators. (5) Simplify and convert back to a mixed number.
Example: 2 ¾ + 1 ⅓. Convert: 11/4 + 4/3. LCD = 12. Convert: 33/12 + 16/12 = 49/12. Simplify: 4 1/12.
Multiplication
To multiply mixed numbers: (1) Convert each to an improper fraction. (2) Multiply numerators together and denominators together. (3) Simplify and convert back. Multiplication is simpler than addition because no common denominator is needed.
Division
To divide mixed numbers: (1) Convert each to an improper fraction. (2) Multiply the first fraction by the reciprocal of the second. (3) Simplify and convert back. "Dividing by a fraction" means "multiplying by its flip."
Converting Between Forms
Mixed to improper: Multiply the whole number by the denominator, add the numerator, and keep the same denominator. For 3 ⅖: (3 × 5) + 2 = 17, so 3 ⅖ = 17/5.
Improper to mixed: Divide the numerator by the denominator. The quotient is the whole number, the remainder is the new numerator, and the denominator stays the same. For 17/5: 17 ÷ 5 = 3 remainder 2, so 17/5 = 3 ⅖.
Simplifying Fractions
A fraction is in simplest form when the numerator and denominator share no common factors other than 1. To simplify, find the greatest common divisor (GCD) of the numerator and denominator, then divide both by the GCD. For example, 12/18: GCD(12, 18) = 6, so 12/18 = 2/3.
This calculator automatically simplifies all results. If you need more detailed fraction simplification, try our dedicated Simplify Fractions Calculator for a more comprehensive analysis.
Tips for Working with Mixed Numbers
Always convert first: The most common mistake is trying to operate on mixed numbers without converting to improper fractions first. Conversion makes the arithmetic much more straightforward. Simplify early: When multiplying, you can cross-cancel common factors before multiplying to keep numbers smaller. Check your work: Convert your result to a decimal and compare it to the decimal values of the original numbers to verify your answer makes sense.