Mathematics · Updated 2026

Mixed Number Calculator

Add, subtract, multiply and divide mixed numbers. Shows the full step-by-step solution including improper fraction conversion. Results given in simplest form with mixed number and decimal equivalents.

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Mixed Number Calculator
Add, Subtract, Multiply, Divide
whole
and
fraction
Enter whole = 0 if it is a proper fraction only (e.g. 0 and 3/4)
whole
and
fraction

Enter two mixed numbers and choose an operation to calculate.

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Mixed Number Arithmetic Operations

To add, subtract, multiply or divide mixed numbers, turn each one into an improper fraction first (2 1/2 = 5/2), do the operation, then convert the answer back. For example, 1 1/2 + 2 1/3 = 3/2 + 7/3 = 23/6 = 3 5/6. The calculator above does this for all four operations and shows every step, plus the improper fraction, decimal and percent.

A mixed number combines a whole number and a proper fraction, such as 2 and 1/2 or 3 and 3/4. To perform arithmetic on mixed numbers, the standard approach is to convert them to improper fractions first, perform the operation, then convert the result back to a mixed number.

Converting to improper fraction: multiply the whole number by the denominator, add the numerator, keep the same denominator. Example: 2 and 1/2 = (2×2+1)/2 = 5/2.

Adding Mixed Numbers

1 and 1/2 + 2 and 1/3. Convert: 3/2 + 7/3. LCD = 6: 9/6 + 14/6 = 23/6. Convert back: 3 and 5/6.

Subtracting Mixed Numbers

3 and 3/4 − 1 and 1/2. Convert: 15/4 − 3/2 = 15/4 − 6/4 = 9/4. Convert back: 2 and 1/4.

Multiplying Mixed Numbers

2 and 1/2 × 1 and 1/3. Convert: 5/2 × 4/3 = 20/6 = 10/3. Convert back: 3 and 1/3.

Dividing Mixed Numbers

3 and 1/2 ÷ 1 and 3/4. Convert: 7/2 ÷ 7/4. Flip and multiply: 7/2 × 4/7 = 28/14 = 2.

More Worked Examples

Subtraction with borrowing: 5 1/4 − 2 2/3

Improper fractions: 21/4 − 8/3. Over the common denominator 12 that is 63/12 − 32/12 = 31/12 = 2 7/12. Done by hand in mixed form, 1/4 (3/12) is smaller than 2/3 (8/12), so you borrow 1 from the 5: 5 3/12 becomes 4 15/12, and 4 15/12 − 2 8/12 = 2 7/12. Same answer.

Multiplication: 3 1/3 × 2 1/4

10/3 × 9/4 = 90/12. The greatest common factor is 6, so 90/12 = 15/2 = 7 1/2.

Division: 4 1/2 ÷ 1 1/8

9/2 ÷ 9/8 = 9/2 × 8/9 = 72/18 = 4. A whole-number answer means 1 1/8 fits into 4 1/2 exactly four times.

Scaling a recipe: 1 3/4 cups × 1 1/2

Making one and a half batches of a recipe that needs 1 3/4 cups of flour: 7/4 × 3/2 = 21/8 = 2 5/8 cups.

A negative mixed number: −1 1/2 + 3/4

−1 1/2 means −(1 + 1/2) = −3/2, not −1 + 1/2. So −3/2 + 3/4 = −6/4 + 3/4 = −3/4. In the calculator, type −1 in the whole box and 1/2 in the fraction boxes.

Mixed Numbers as Improper Fractions and Decimals

Digits in brackets repeat, so 1.(3) means 1.333...

Mixed numberImproper fractionDecimal
1 1/45/41.25
1 1/34/31.(3)
1 1/23/21.5
1 2/35/31.(6)
1 3/47/41.75
2 1/49/42.25
2 1/25/22.5
2 2/38/32.(6)
2 3/411/42.75
3 1/825/83.125
3 3/827/83.375
4 5/629/64.8(3)
5 7/1687/165.4375

The rule behind every row: a b/c = (a × c + b)/c. For 5 7/16 that is (5 × 16 + 7)/16 = 87/16.

Mistakes to Avoid

  • Multiplying the parts separately. 2 1/2 × 2 1/2 is not 4 1/4 (2 × 2 plus 1/2 × 1/2). Convert first: 5/2 × 5/2 = 25/4 = 6 1/4.
  • Subtracting the fractions backwards. In 5 1/4 − 2 2/3 you cannot take 1/4 from 2/3 and hope it works out. Borrow 1 from the whole part, or use improper fractions.
  • Leaving the fraction part unsimplified. 2 4/8 should be written 2 1/2.
  • Leaving an improper fraction inside a mixed number. 3 5/4 is really 4 1/4, because 5/4 = 1 1/4.
  • Splitting the sign. −2 1/3 is −7/3. Treating it as −2 + 1/3 gives −5/3, which is wrong.

For plain fractions without a whole part, the fraction calculator is quicker. To turn a decimal measurement such as 2.375 into a mixed number, use the decimal to fraction calculator.

Method and sources. Mixed numbers are converted with a b/c = (a × c + b)/c, combined with standard fraction arithmetic (least common denominator for addition and subtraction, reciprocal for division) and reduced by the greatest common divisor, as in the Common Core State Standards for Mathematics fraction standards for grades 4 to 6. Every example and table value above was computed with the same integer arithmetic the calculator uses.
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Mixed Number Questions

A mixed number has a whole number part and a fractional part. Examples: 2 and 1/2, 3 and 3/4, 5 and 1/6. They represent quantities between two whole numbers and are used extensively in everyday measurement (1 and 1/2 cups, 2 and 3/4 inches). They are equivalent to improper fractions: 2 and 1/2 = 5/2, 3 and 3/4 = 15/4.

Multiply the whole number by the denominator and add the numerator, keeping the same denominator. Formula: a and b/c = (a×c + b) / c. Examples: 2 and 1/2 = (2×2+1)/2 = 5/2. 3 and 3/4 = (3×4+3)/4 = 15/4. 4 and 1/6 = (4×6+1)/6 = 25/6. This conversion is always the first step when doing arithmetic on mixed numbers.

Divide numerator by denominator. The quotient is the whole number; the remainder is the new numerator over the original denominator. Example: 17/5. 17 ÷ 5 = 3 remainder 2. Mixed number: 3 and 2/5. Another: 22/7 = 3 remainder 1 = 3 and 1/7. If the remainder is 0 (like 15/5 = 3), the result is a whole number.

Best method: convert both to improper fractions, find a common denominator, add numerators, simplify, convert back. Example: 1 and 1/2 + 2 and 1/3 = 3/2 + 7/3. LCD = 6: 9/6 + 14/6 = 23/6 = 3 and 5/6. Alternative: add whole number parts separately, add fraction parts, combine. If the fraction part exceeds 1, carry over to the whole number.

Always convert to improper fractions first, then multiply numerators together and denominators together, then simplify. Example: 2 and 1/2 × 1 and 1/3 = 5/2 × 4/3 = 20/6 = 10/3 = 3 and 1/3. Never multiply the whole number parts and fraction parts separately: that gives a wrong answer. The improper fraction conversion is essential.

Convert both to improper fractions, then multiply the first by the reciprocal of the second (Keep-Change-Flip). Example: 3 and 1/2 ÷ 1 and 3/4 = 7/2 ÷ 7/4 = 7/2 × 4/7 = 28/14 = 2. The KCF rule works because dividing by a fraction equals multiplying by its reciprocal. Always simplify before or after multiplying.

Convert both to improper fractions and subtract. The result will be negative. Example: 1 and 1/4 − 2 and 3/4 = 5/4 − 11/4 = −6/4 = −3/2 = −1 and 1/2. Converting to improper fractions removes the ambiguity of working with negative mixed numbers. The result is simply a negative fraction which converts to a negative mixed number.

Mixed numbers are better for communication and measurement: "2 and a half cups of flour" is clearer than "5/2 cups." Improper fractions are better for calculation: arithmetic operations are simpler and less error-prone. In practice, you communicate in mixed numbers and calculate in improper fractions, converting between the two as needed. This calculator does both automatically.

2.5. Convert: 2 and 1/2 = 5/2 = 5 ÷ 2 = 2.5. More examples: 3 and 1/4 = 13/4 = 3.25. 1 and 2/3 = 5/3 = 1.6666... (repeating). 4 and 3/8 = 35/8 = 4.375. To convert any mixed number to decimal: convert to improper fraction, then divide numerator by denominator.

Cooking: recipes use 1 and 1/2 cups, 2 and 3/4 teaspoons. Construction: lumber dimensions like 3 and 1/2 inches (a standard 2x4). Distance: races of 1 and 1/2 miles. Time: 2 and 1/4 hours. Sewing and fabric: 1 and 3/8 yards. Stock prices historically quoted in fractions (now decimals). Any situation where quantities fall between whole numbers naturally produces mixed numbers.

Put the minus sign on the whole number only. For −2 1/3, type −2 in the whole box and 1 over 3 in the fraction boxes; the calculator reads it as −7/3. For a negative proper fraction such as −3/4, leave the whole number at 0 and type −3 as the numerator. Denominators must be positive.

Borrow 1 from the whole number. For 5 1/4 − 2 2/3, rewrite over 12: 5 3/12 − 2 8/12. Since 3/12 is less than 8/12, turn 5 3/12 into 4 15/12. Then 4 15/12 − 2 8/12 = 2 7/12. Converting both to improper fractions (63/12 − 32/12 = 31/12) avoids borrowing altogether.
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