TFT

Mixed Number Calculator – Add, Subtract, Multiply Mixed Numbers

Calculate with mixed numbers easily using our free online mixed number calculator. Add, subtract, multiply, and divide mixed numbers with instant simplified results and full steps.

Mixed Number Calculator
Perform arithmetic operations with mixed numbers.
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Examples:

Mixed Number Calculator – Add, Subtract, Multiply Mixed Numbers

Mixed numbers combine whole numbers and fractions. Working with them requires converting to improper fractions first, performing the operation, then converting back. This calculator handles all four operations and shows every step of the process.

Enter mixed numbers using the three input fields: whole number, numerator, and denominator. The calculator converts to improper fractions, finds common denominators when needed, performs the operation, simplifies, and converts back to mixed number form.

Mixed Number Operations

Adding Mixed Numbers

  1. Convert both to improper fractions
  2. Find a common denominator (LCM)
  3. Add the numerators
  4. Simplify and convert back to mixed number
1½ + 2¼ = 3/2 + 9/4 = 6/4 + 9/4 = 15/4 = 3¾

Subtracting Mixed Numbers

  1. Convert both to improper fractions
  2. Find a common denominator
  3. Subtract the numerators
  4. Simplify and convert back (may be negative)
3½ − 1¾ = 7/2 − 7/4 = 14/4 − 7/4 = 7/4 = 1¾

Multiplying Mixed Numbers

  1. Convert both to improper fractions
  2. Multiply numerators together
  3. Multiply denominators together
  4. Simplify and convert back to mixed number
2½ × 1⅓ = 5/2 × 4/3 = 20/6 = 10/3 = 3⅓

Dividing Mixed Numbers

  1. Convert both to improper fractions
  2. Multiply by the reciprocal of the second
  3. Simplify the result
  4. Convert back to mixed number
3½ ÷ 1¾ = 7/2 ÷ 7/4 = 7/2 × 4/7 = 28/14 = 2

Converting Between Forms

Mixed to Improper

Multiply the whole number by the denominator, add the numerator, keep the same denominator.

Formula: (whole × denom + num) / denom
2⅗ = (2 × 5 + 3) / 5 = 13/5

Improper to Mixed

Divide numerator by denominator. The quotient is the whole number, remainder is the new numerator.

13 ÷ 5 = 2 R3
13/5 = 2⅗

Worked Examples

Example 1: Add 1½ + 2⅓

Convert: 1½ = 3/2, 2⅓ = 7/3
LCM(2,3) = 6
3/2 = 9/6, 7/3 = 14/6
9/6 + 14/6 = 23/6
Answer: 3⅚

Example 2: Subtract 3¾ − 1½

Convert: 3¾ = 15/4, 1½ = 3/2
LCM(4,2) = 4
15/4 − 6/4 = 9/4
Answer: 2¼

Example 3: Multiply 2½ × 1⅓

Convert: 2½ = 5/2, 1⅓ = 4/3
5/2 × 4/3 = 20/6
Simplify: 20/6 = 10/3
Answer: 3⅓

Example 4: Divide 3½ ÷ 1¾

Convert: 3½ = 7/2, 1¾ = 7/4
7/2 ÷ 7/4 = 7/2 × 4/7
= 28/14 = 2
Answer: 2

Frequently Asked Questions

Why convert to improper fractions first?

It's simpler and less error-prone. Trying to add the whole parts and fraction parts separately requires extra steps and can get confusing with borrowing or carrying. Improper fractions streamline the process.

Can the result be negative?

Yes, when subtracting a larger mixed number from a smaller one. The calculator handles negative results correctly, showing them as negative mixed numbers or improper fractions.

What if the fraction part is improper?

The calculator expects proper fractions (numerator less than denominator) in the input. If you enter an improper fraction part, it will show an error. Convert it to a mixed number first.

How do I simplify the result?

The calculator automatically simplifies by dividing both parts by their greatest common divisor. 8/12 becomes 2/3, and 15/6 becomes 2½.

Can I use this for just fractions (no whole part)?

Yes. Set the whole number to 0. The calculator works fine with proper fractions like 0 3/4 (which is just 3/4).

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