Mixed Numbers Calculator

This calculator adds, subtracts, multiplies or divides two mixed numbers and returns the result as a simplified mixed number, the equivalent improper fraction, and a decimal value. A mixed number combines a whole number with a proper fraction, such as 2 and one half or 1 and one third. They appear everywhere in practical measurement, from cooking quantities and fabric lengths to tool sizes and construction materials, so being able to work with them efficiently is a genuinely useful skill. The arithmetic requires converting each mixed number to an improper fraction, performing the operation using standard fraction rules, then converting the result back. To add or subtract, you find a common denominator; to multiply, you multiply numerators and denominators directly; to divide, you multiply by the reciprocal of the second fraction. The final fraction is always reduced to lowest terms using the greatest common divisor before being expressed as a mixed number. To use the calculator, enter the whole number, numerator and denominator for each of the two mixed numbers, and select the operation. You can enter zero for the whole number if you are working with a proper fraction alone. The results update immediately. This tool suits students learning fraction arithmetic, teachers needing a quick check, and anyone working with measurements that naturally come in mixed number form. Denominators cannot be zero.

Calculate.co.nz is proud to be partnered with Health Based Building, a leader in sustainable and health-conscious building innovation. With over a century of experience, they develop high-performance systems like Foreverbreathe Specification, Magnum Board, and Foreverbreathe Paints to support energy-efficient, non-toxic living environments. Their commitment to healthier homes aligns with our belief that informed choices lead to better outcomes for Kiwi households.
Calculate.co.nz partner: Health Based Building
Advertise on this page
whole /
whole /
3 5/6
result (mixed number)
Improper fraction23/6
Decimal3.8333

How it works

Each mixed number is converted to an improper fraction: multiply the whole number by the denominator, add the numerator, and keep the same denominator. For addition and subtraction, a common denominator is found by multiplying the two denominators, numerators are adjusted accordingly, then added or subtracted. For multiplication, numerators are multiplied together and denominators are multiplied together. For division, the second fraction is flipped and multiplied. The result is then reduced to lowest terms by dividing both numerator and denominator by their greatest common divisor (GCD), then expressed as a mixed number.

Worked example

Add 2½ and 1⅓. Convert: 2½ = 5/2 and 1⅓ = 4/3. Common denominator is 6. Adjust: 5/2 = 15/6 and 4/3 = 8/6. Add numerators: 15 + 8 = 23. Result is 23/6. GCD of 23 and 6 is 1 (already in lowest terms). As a mixed number: 23 divided by 6 = 3 remainder 5, so the answer is 3 5/6. As a decimal: 23/6 = 3.8333.

Related calculators