Use this free mixed number calculator to add, subtract, multiply, or divide any two mixed numbers. Enter the whole number, numerator, and denominator for each fraction, choose an operation, and get an instant answer with a full step-by-step solution showing every conversion and simplification.
Mixed Number Calculator
Num / Den
Num / Den
How Do You Calculate with Mixed Numbers?
A mixed number (also called a mixed fraction) is a whole number combined with a proper fraction, such as 2 ¾. To perform any operation on mixed numbers, follow this three-step process that works for addition, subtraction, multiplication, and division.
Convert to improper fractions. Multiply the whole number by the denominator, add the numerator, and place the result over the original denominator.
Perform the operation. For addition or subtraction, find a common denominator first. For multiplication, multiply straight across. For division, flip the second fraction and multiply.
Simplify and convert back. Reduce the fraction to lowest terms, then divide the numerator by the denominator to get the mixed-number form.
For example, to evaluate 2 ¾ + 1 ⅔: convert to 11/4 and 5/3, find a common denominator of 12, rewrite as 33/12 + 20/12 = 53/12, and convert back to 4 5/12.
Tip: For multiplication and division you don't need a common denominator — just convert to improper fractions, multiply (or flip and multiply for division), and simplify.
How Do You Convert a Mixed Number to an Improper Fraction?
To convert a mixed number to an improper fraction, multiply the whole number by the denominator, add the numerator, and place the result over the original denominator. The formula is: W n/d = (W × d + n) / d.
For example, 3 2/5 converts as follows: 3 × 5 = 15, then 15 + 2 = 17, giving the improper fraction 17/5. To convert back, divide the numerator by the denominator — 17 ÷ 5 = 3 remainder 2, which gives 3 2/5.
What Are Some Mixed Number Calculation Examples?
Example 1 — Addition: 1 ½ + 2 ¾
Convert to improper fractions: 1 ½ = 3/2 and 2 ¾ = 11/4. Find a common denominator of 4: 3/2 = 6/4. Add: 6/4 + 11/4 = 17/4. Convert back: 17 ÷ 4 = 4 remainder 1, so the answer is 4 ¼.
1 ½ + 2 ¾ = 3/2 + 11/4 = 6/4 + 11/4 = 17/4 = 4 ¼
Example 2 — Subtraction: 5 ⅓ − 2 ⅚
Convert: 5 ⅓ = 16/3 and 2 ⅚ = 17/6. Common denominator is 6: 16/3 = 32/6. Subtract: 32/6 − 17/6 = 15/6. Simplify 15/6 = 5/2, then convert: 2 ½.
Convert: 3 ½ = 7/2 and 1 ¾ = 7/4. Flip the second fraction and multiply: 7/2 × 4/7 = 28/14 = 2. The answer is simply 2.
3 ½ ÷ 1 ¾ = 7/2 ÷ 7/4 = 7/2 × 4/7 = 28/14 = 2
Frequently Asked Questions About Mixed Numbers
A mixed number combines a whole number with a proper fraction, such as 2 ¾. It represents a value greater than one whole unit. Mixed numbers are widely used in everyday measurement — for instance, a recipe might call for 1 ½ cups of flour.
Convert each mixed number to an improper fraction, find a common denominator, add the numerators, then simplify and convert back to a mixed number. For example, 1 ½ + 2 ¾ = 3/2 + 11/4 = 6/4 + 11/4 = 17/4 = 4 ¼.
Convert both mixed numbers to improper fractions, find a common denominator, subtract the second numerator from the first, then simplify and convert back. If the result is negative, the sign applies to the entire mixed number.
Convert each mixed number to an improper fraction, then multiply the numerators together and the denominators together. Simplify the resulting fraction and convert back to a mixed number. No common denominator is needed for multiplication.
Convert both mixed numbers to improper fractions. Flip the second fraction (find its reciprocal), then multiply straight across. Simplify and convert back to a mixed number. For example, 3 ½ ÷ 1 ¾ = 7/2 × 4/7 = 28/14 = 2.
Multiply the whole number by the denominator, add the numerator, and place the result over the original denominator. For example, 3 2/5 becomes (3 × 5 + 2)/5 = 17/5. For more detail, see our mixed-to-improper converter.
Divide the numerator by the denominator. The quotient becomes the whole number, and the remainder becomes the new numerator over the original denominator. For example, 17/5: 17 ÷ 5 = 3 remainder 2, so the mixed number is 3 2/5. Try our improper-to-mixed converter.
Yes. A negative mixed number like −2 ⅓ means the entire value is negative, equal to −7/3 as an improper fraction. In this calculator, enter a negative whole number to indicate a negative mixed number.
A mixed number has a whole-number part and a fractional part (e.g. 3 ½), while an improper fraction has a numerator equal to or larger than its denominator (e.g. 7/2). They represent the same value in different forms. Use our improper-to-mixed converter to switch between them.
No. A common denominator is only required for addition and subtraction. For multiplication, simply multiply numerators and denominators after converting to improper fractions. For division, flip the second fraction and multiply.