# How do I calculate mixed numbers?

Adds, subtracts, multiplies, or divides two mixed numbers or fractions exactly, as a mixed number, an improper fraction, and a decimal.

- Page: https://www.acalculator.org/math/mixed-numbers-calculator
- JSON spec: https://www.acalculator.org/math/mixed-numbers-calculator.json
- Version: 6d35aca36e3e

## Default answer

Example with the default inputs (First number 1 2/3, Operation +, Second number 2 1/4): 1 2/3 + 2 1/4 = 3 11/12.

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| a | First number | A mixed number, fraction, or whole number, such as 1 2/3, 5/3, or 2. |
| operation | Operation | Add, subtract, multiply, or divide the first number by the second. |
| b | Second number | A mixed number, fraction, or whole number, such as 2 1/4, 9/4, or 3. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| result | Result | The answer in lowest terms, as a mixed number such as 3 11/12 or -1 1/4. |
| improper | As an improper fraction | The answer as one fraction in lowest terms. |
| decimal | As a decimal | The answer as a decimal. |

## Method

Turn each mixed number into an improper fraction, apply the operation, reduce by the GCF, and write the result as a mixed number.

## Assumptions

- A minus sign applies to the whole mixed number: −1 1/2 means −(1 + 1/2) = −3/2.
- All arithmetic is exact with whole-number numerators and denominators of any size.
- Dividing by 0 has no answer.

## Worked examples

1. a = 1 2/3, operation = +, b = 2 1/4 gives result = 3 11/12, improper = 47/12, decimal = 3.916667. Source: OpenStax, Prealgebra 2e, §4.6 Add and Subtract Mixed Numbers. https://openstax.org/books/prealgebra-2e/pages/4-6-add-and-subtract-mixed-numbers.
2. a = 7/4, operation = +, b = 5/6 gives result = 2 7/12, improper = 31/12. Source: OpenStax, Prealgebra 2e, §4.6 Add and Subtract Mixed Numbers. https://openstax.org/books/prealgebra-2e/pages/4-6-add-and-subtract-mixed-numbers.
3. a = 3 1/4, operation = -, b = 1 1/2 gives result = 1 3/4, improper = 7/4, decimal = 1.75. Source: OpenStax, Prealgebra 2e, §4.6 Add and Subtract Mixed Numbers. https://openstax.org/books/prealgebra-2e/pages/4-6-add-and-subtract-mixed-numbers.
4. a = 2 2/3, operation = *, b = 1 1/2 gives result = 4, improper = 4, decimal = 4. Source: OpenStax, Prealgebra 2e, §4.6 Add and Subtract Mixed Numbers. https://openstax.org/books/prealgebra-2e/pages/4-6-add-and-subtract-mixed-numbers.
5. a = 2 1/3, operation = /, b = 1 1/4 gives result = 1 13/15, improper = 28/15. Source: OpenStax, Prealgebra 2e, §4.6 Add and Subtract Mixed Numbers. https://openstax.org/books/prealgebra-2e/pages/4-6-add-and-subtract-mixed-numbers.
6. a = -2 1/3, operation = *, b = -1 2/3 gives result = 3 8/9, improper = 35/9. Source: OpenStax, Prealgebra 2e, §4.6 Add and Subtract Mixed Numbers. https://openstax.org/books/prealgebra-2e/pages/4-6-add-and-subtract-mixed-numbers.
7. a = -1 1/2, operation = +, b = 1/4 gives result = -1 1/4, improper = -5/4, decimal = -1.25. Source: OpenStax, Prealgebra 2e, §4.6 Add and Subtract Mixed Numbers. https://openstax.org/books/prealgebra-2e/pages/4-6-add-and-subtract-mixed-numbers.

## FAQ

### What is a mixed number?

A mixed number is a combination of a whole number and a proper fraction. For example, 2 3/4 means 2 whole units plus 3/4 of another unit. Mixed numbers are commonly used in everyday measurements like cooking (1 1/2 cups) or construction (3 1/4 feet).

### How do I convert a mixed number to an improper fraction?

To convert a mixed number to an improper fraction: 1) Multiply the whole number by the denominator, 2) Add the numerator to that product, 3) Write the result over the original denominator. For example, 2 3/4 becomes (2 × 4 + 3)/4 = 11/4.

### How do I convert an improper fraction to a mixed number?

To convert an improper fraction to a mixed number: 1) Divide the numerator by the denominator, 2) The quotient becomes the whole number, 3) The remainder becomes the numerator of the fraction, 4) Keep the same denominator. For example, 11/4 becomes 2 3/4.

### How do I add mixed numbers?

To add mixed numbers: 1) Convert them to improper fractions, 2) Find a common denominator, 3) Add the numerators, 4) Convert the result back to a mixed number if needed. For example, 2 1/3 + 1 1/4 = 7/3 + 5/4 = 28/12 + 15/12 = 43/12 = 3 7/12.

### How do I subtract mixed numbers?

To subtract mixed numbers: 1) Convert them to improper fractions, 2) Find a common denominator, 3) Subtract the numerators, 4) Convert the result back to a mixed number if needed. If the first fraction is smaller, you may need to borrow from the whole number.

### How do I multiply mixed numbers?

To multiply mixed numbers: 1) Convert them to improper fractions, 2) Multiply the numerators and denominators, 3) Simplify the result, 4) Convert back to a mixed number if needed. For example, 2 1/3 × 1 1/4 = 7/3 × 5/4 = 35/12 = 2 11/12.

### How do I divide mixed numbers?

To divide mixed numbers: 1) Convert them to improper fractions, 2) Invert the second fraction (reciprocal), 3) Multiply the fractions, 4) Simplify and convert back to a mixed number if needed. For example, 2 1/3 ÷ 1 1/4 = 7/3 ÷ 5/4 = 7/3 × 4/5 = 28/15 = 1 13/15.

### When should I use mixed numbers vs. improper fractions?

Mixed numbers are better for everyday measurements and when you want to emphasize the whole number part. Improper fractions are better for mathematical calculations and when you need to perform operations. Our calculator can work with both formats and convert between them.

### How do I simplify mixed numbers?

To simplify a mixed number: 1) Convert to an improper fraction, 2) Simplify the fraction by dividing numerator and denominator by their greatest common factor, 3) Convert back to a mixed number if needed. For example, 2 8/12 simplifies to 2 2/3.

### What are some real-world applications of mixed numbers?

Mixed numbers are used in cooking (recipe measurements), construction (lengths and measurements), time (hours and minutes), money (dollars and cents), and many other everyday situations where you need to express whole units plus fractional parts.

### How do negative mixed numbers work?

The minus sign belongs to the whole mixed number. −1 1/2 means −(1 + 1/2) = −3/2, not −1 + 1/2. For example, −1 1/2 + 1/4 = −6/4 + 1/4 = −5/4 = −1 1/4, and −2 1/3 × −1 2/3 = (−7/3) × (−5/3) = 35/9 = 3 8/9.

## Sources

- OpenStax, Prealgebra 2e, §4.1 Visualize Fractions (mixed numbers and improper fractions). https://openstax.org/books/prealgebra-2e/pages/4-1-visualize-fractions
- OpenStax, Prealgebra 2e, §4.6 Add and Subtract Mixed Numbers. https://openstax.org/books/prealgebra-2e/pages/4-6-add-and-subtract-mixed-numbers