Mixed Number Calculator — Add & Divide
Add, subtract, multiply, and divide mixed numbers. Converts between mixed numbers, improper fractions, and decimals with step-by-step working.
What Is the Mixed Number Calculator — Add & Divide?
A mixed number combines a whole number and a proper fraction (e.g. 2¾). To perform arithmetic on mixed numbers, the standard method converts them to improper fractions first, applies the operation, then converts the result back. This calculator shows every step and also displays results as decimals.
Formula
How to Use
Enter each mixed number as whole, numerator, and denominator parts (the whole-number part can be 0 for a plain fraction). Select the operation (+, −, ×, ÷), then click Calculate. The result is shown as a mixed number, an improper fraction, and a decimal.
Example Calculation
2¾ + 1½: Convert to improper fractions: 11/4 + 3/2. Find LCD = 4: 11/4 + 6/4 = 17/4. Convert back: 17 ÷ 4 = 4 remainder 1 → 4¼. Decimal: 4.25.
Understanding Mixed Number — Add & Divide
Mixed numbers arise naturally whenever a quantity exceeds one whole unit but is not itself a whole number — cooking recipes (1¾ cups), construction measurements (2⅜ inches), and time intervals (1½ hours) are everyday examples.
The improper fraction conversion method is computationally reliable because it reduces all arithmetic to the same set of fraction rules, avoiding the special cases that arise from borrowing in subtraction or carrying in addition.
The GCD (greatest common divisor) algorithm is applied after every calculation to ensure the resulting fraction is in lowest terms before conversion back to a mixed number.
When dividing mixed numbers, the standard algorithm is "multiply by the reciprocal": convert both to improper fractions, flip the second (the divisor), and multiply. For example, 2½ ÷ 1¼ = 5/2 ÷ 5/4 = 5/2 × 4/5 = 2.
Frequently Asked Questions
What is a mixed number?
A mixed number has a whole-number part and a fractional part, like 3½ or 7⅔. It is always equal to the corresponding improper fraction: 3½ = 7/2.
How do you add mixed numbers?
Convert each to an improper fraction, find a common denominator, add the numerators, then simplify and convert back to a mixed number if the result is improper.
How do you subtract mixed numbers when the fraction part of the first is smaller?
You "borrow" 1 from the whole-number part, converting it to a fraction, then subtract. For example, 3¼ − 1¾: borrow to get 2⁵⁄₄ − 1¾ = 1²⁄₄ = 1½. The improper fraction method handles this automatically.
Can the result be negative?
Yes, if the result is negative (e.g. 1½ − 3¼), the calculator displays a negative mixed number or fraction.