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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

Frequently Asked Questions

What are mixed numbers and how do they work?
A mixed number combines a whole number with a proper fraction (e.g., 3 1/4). They represent values greater than 1, where the fractional part is less than 1. Mixed numbers provide an intuitive way to express quantities in everyday life.
How do I convert between mixed numbers and improper fractions?
To convert to improper fraction: multiply the whole number by the denominator, add the numerator, and place over the original denominator. To convert back: divide the numerator by the denominator to get the whole number, with the remainder as the new numerator.
How do I add or subtract mixed numbers?
Convert both mixed numbers to improper fractions, find a common denominator, perform the operation on the numerators, then convert the result back to a mixed number. The calculator handles all these steps automatically with detailed explanations.
How do I multiply or divide mixed numbers?
Convert to improper fractions first, then multiply numerators and denominators (for multiplication) or multiply by the reciprocal (for division). Simplify the result and convert back to mixed number format if needed.
What educational standards does this calculator follow?
This calculator follows NCTM Principles and Standards, Common Core State Standards for Mathematics (CCSS-M) for grades 3-8, and Khan Academy curriculum standards for fraction operations and mixed number arithmetic.
Can I convert mixed numbers to decimals?
Yes, the calculator converts mixed numbers to decimal format by adding the whole number to the decimal equivalent of the fraction. For example, 3 1/4 = 3 + 0.25 = 3.25.

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