Math
Mixed Number Calculator
Use this mixed number calculator to convert an improper fraction to a mixed number (or the reverse) and to add, subtract, multiply, or divide two mixed numbers.
Every answer is computed with exact integer math, fully reduced with the GCD, and shown as a mixed number, an improper fraction, and a decimal approximation, with the classroom steps written out.
Use 0 for a plain fraction. A minus sign here makes the entire first value negative.
Try an example
Result
Result
—
- Mixed number
- —
- Improper fraction
- —
- Decimal (approximate)
- —
Student quick launch
Grade planning, algebra checks, and formulas students reach for most.
Study path
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Follow these when you want the formula behind the answer, a short lesson, or nearby tools in the same topic.
What the mixed number calculator solves
Use this A whole number written next to a fraction, like 2 1/3. calculator to convert an A fraction whose top number is at least as big as its bottom number, like 7/3. to a mixed number (or the reverse) and to add, subtract, multiply, or divide two mixed numbers. Every answer is computed with exact integer math, fully reduced with the The largest number that divides evenly into every number in a set., and shown as a mixed number, an improper fraction, and a decimal approximation, with the classroom steps written out.
Formula
How to use it
- Pick a mode: convert between improper fractions and mixed numbers, or do arithmetic on two mixed numbers.
- Enter each value as a whole number, The top number of a fraction; it counts how many parts you have., and The bottom number of a fraction; it says how many equal parts make one whole.. Use 0 for the whole part when you only have a fraction like 22/8.
- For a negative value, put the minus sign on the whole number; if the whole part is 0, put it on the numerator instead.
- In arithmetic mode, choose add, subtract, multiply, or divide.
- Read the exact answer as both a mixed number and an improper fraction, use the decimal to sanity-check it, and follow the steps to see the work.
How to read the answer
The mixed number and the improper fraction are the same exact value written two ways, and both are fully reduced. The decimal is a rounded approximation for checking your work; repeating decimals such as 1/3 = 0.333333... can never be written exactly. The sign convention is that a minus sign applies to the whole value: -2 3/4 means -(2 + 3/4) = -11/4, not -2 + 3/4.
Common mistakes and edge cases
- Reading -2 3/4 as -2 + 3/4. The sign covers the entire value: -2 3/4 = -(2 + 3/4) = -11/4.
- Multiplying whole parts and fraction parts separately: 2 1/2 × 3 1/2 is 8 3/4, not 6 1/4. Convert to improper fractions first.
- Adding fraction parts without carrying: in 2 3/4 + 1 5/6 the fraction parts alone total 19/12, which carries an extra whole into the answer.
- Flipping the wrong fraction when dividing. Keep the first fraction, change ÷ to ×, and flip only the second fraction.
- Leaving the answer unreduced, such as writing 22/8 instead of 11/4 (2 3/4). Divide numerator and denominator by their GCD.
- Entering a zero or negative denominator. Denominators must be positive whole numbers; the calculator reports an error otherwise.
Worked examples
Add mixed numbers with carrying
2 3/4 + 1 5/6 becomes 33/12 + 22/12 = 55/12 = 4 7/12.
Result
4 7/12
Multiply mixed numbers
2 1/2 × 3 1/2 = 5/2 × 7/2 = 35/4 = 8 3/4, not 6 1/4.
Result
8 3/4
Divide with a negative mixed number
-2 3/4 ÷ 1 1/2 = -11/4 × 2/3 = -22/12 = -11/6 = -1 5/6.
Result
-1 5/6
Whole-number result
1 1/2 + 2 1/2 = 3/2 + 5/2 = 8/2 = 4 exactly.
Result
4
Improper fraction to mixed number
22/8 reduces to 11/4, and 11 ÷ 4 = 2 remainder 3, so 22/8 = 2 3/4.
Result
2 3/4
Mixed number to improper fraction
2 3/4 = (2 × 4 + 3)/4 = 11/4.
Result
11/4
Division by zero is undefined
Result
Error
Frequently asked questions
How do I turn an improper fraction into a mixed number?+
Divide the numerator by the denominator. The whole-number quotient is the whole part, the remainder is the new numerator, and the denominator stays the same. For 11/4: 11 ÷ 4 = 2 remainder 3, so 11/4 = 2 3/4.
How do I add mixed numbers with different denominators?+
Convert each mixed number to an improper fraction, rewrite both over the least common denominator, add the numerators, reduce with the GCD, and convert back. For 2 3/4 + 1 5/6: 11/4 + 11/6 = 33/12 + 22/12 = 55/12 = 4 7/12.
How do I enter a negative mixed number?+
Put the minus sign on the whole number, so -2 3/4 is whole -2, numerator 3, denominator 4. The sign applies to the entire value: -2 3/4 = -11/4. If the whole part is 0, put the minus sign on the numerator instead.
Why is 2 1/2 × 3 1/2 not 6 1/4?+
Multiplying the whole parts and the fraction parts separately skips the cross terms. Convert first: 5/2 × 7/2 = 35/4 = 8 3/4. The distributive property produces 6 + 1 + 3/2 + 1/4, which also totals 8 3/4.
What does it mean when the answer has no fraction part?+
The numerator divided evenly by the denominator, so the exact answer is a whole number. For example, 1 1/2 + 2 1/2 = 8/2 = 4, which is 4/1 as an improper fraction.
Is the decimal answer exact?+
Not always. The mixed number and improper fraction are exact because they are computed with integer math, but the decimal is rounded to six places. Fractions like 1/3 or 5/12 have repeating decimals that no rounded value can capture exactly.
About this calculator
- Written by
- mathcheck editorial team
- Last reviewed
- May 8, 2026
Method
- Uses the values entered by the user and stable formulas documented on the page.
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Last updated: May 8, 2026