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.
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.
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Frequently asked questions
What is a mixed number?
A mixed number combines a whole number and a proper fraction, such as 2 and a half (written as 2 1/2). It is equivalent to the improper fraction where the numerator is larger than the denominator: 2 1/2 equals 5/2. Mixed numbers are commonly used in everyday measurement, cooking and carpentry because they are easier to visualise than improper fractions.
How do you add mixed numbers?
To add two mixed numbers, convert each to an improper fraction by multiplying the whole number by the denominator and adding the numerator. Then find a common denominator, add the numerators, and convert the result back to a mixed number by dividing the numerator by the denominator to get the whole part and the remainder as the new numerator.
How do you multiply or divide mixed numbers?
To multiply mixed numbers, convert both to improper fractions and then multiply numerator by numerator and denominator by denominator. Simplify the resulting fraction and convert back to a mixed number. To divide, convert both to improper fractions and multiply the first by the reciprocal of the second (flip the second fraction) before simplifying.
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