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Mixed Number Calculator

Perform arithmetic operations with mixed numbers, convert between mixed numbers, improper fractions, and decimals. Essential for elementary and middle school mathematics, following NCTM and Common Core standards.

Mixed Number Calculator

Operation
Input Format
First Number (for add)
Second Number (for add)

Enter the second mixed number for add operation

Output Format

Calculation Results

3 1/4
Result
Mixed Number
3 1/4
Improper Fraction
13/4
Decimal
3.25

Formula

Mixed Number = Whole Number + (Numerator / Denominator)
A mixed number combines a whole number with a proper fraction

Calculation Steps

  1. Result: 3 1/4

Notes

  • Mixed number calculations follow standard mathematical conventions

What are Mixed Numbers?

A mixed number is a combination of a whole number and a proper fraction. It represents a value greater than 1, where the fractional part is less than 1. Mixed numbers are commonly used in everyday life and provide an intuitive way to express quantities.

Examples

  • • 3 1/4 = 3 + 1/4 = 3.25
  • • 2 3/8 = 2 + 3/8 = 2.375
  • • 5 2/3 = 5 + 2/3 ≈ 5.667

How to Work with Mixed Numbers

Converting to Improper Fractions

Multiply the whole number by the denominator, add the numerator, and place over the original denominator.

3 1/4 = (3 × 4 + 1) / 4 = 13/4

Converting to Decimals

Add the whole number to the decimal equivalent of the fraction.

3 1/4 = 3 + (1 ÷ 4) = 3 + 0.25 = 3.25

Arithmetic Operations

Convert to improper fractions, perform the operation, then convert back to mixed number if needed.

Mathematical Standards

Educational References

  • • NCTM Principles and Standards: Number and Operations standards for grades 3-8
  • • Common Core State Standards: 4.NF.3, 5.NF.1, 5.NF.2 for fraction operations
  • • Khan Academy: Arithmetic with fractions and mixed numbers curriculum
  • • Wolfram MathWorld: Mathematical definitions and algorithms

Example Calculations

Addition: 3 1/4 + 1 2/3

1. Convert to improper fractions: 13/4 + 5/3
2. Find common denominator: 39/12 + 20/12
3. Add numerators: 59/12
4. Convert to mixed number: 4 11/12

Multiplication: 2 1/3 × 1 1/2

1. Convert to improper fractions: 7/3 × 3/2
2. Multiply numerators and denominators: 21/6
3. Simplify: 7/2
4. Convert to mixed number: 3 1/2

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Frequently Asked Questions

What's the difference between a mixed number and an improper fraction?
A mixed number combines a whole number with a proper fraction (e.g., 3 1/4), while an improper fraction has a numerator equal to or greater than the denominator (e.g., 13/4). They represent the same value but in different formats.
How do I add mixed numbers?
Convert both mixed numbers to improper fractions, find a common denominator, add the numerators, and convert the result back to a mixed number if needed. The calculator handles all these steps automatically.
Can I use negative numbers?
This calculator focuses on positive mixed numbers and fractions. For negative numbers, you would typically work with the absolute values and apply the negative sign to the final result.
What if my result is an improper fraction?
The calculator automatically converts improper fractions to mixed numbers. You can also choose to display results as improper fractions, decimals, or mixed numbers using the output format options.
How accurate are the decimal conversions?
Decimal conversions are accurate to 6 decimal places. For most practical purposes, this provides sufficient precision. The calculator uses standard mathematical algorithms for conversion.
What educational standards does this follow?
This calculator follows NCTM Principles and Standards, Common Core State Standards for Mathematics (CCSS-M), and Khan Academy curriculum standards for fraction operations and mixed number arithmetic.
Mixed Number Calculator - Convert & Calculate Mixed Numbers