Math & Algebra Tool

Mixed & Improper Fractions

Convert between Mixed Numbers and Improper Fractions.

Σ The Formula

Mixed to Improper: (whole × den + num) / den | Improper to Mixed: num ÷ den = whole remainder/den

Real World Examples

Mixed to Improper
2 1/2 = (2×2+1)/2 = 5/2
Improper to Mixed
5/2 = 2 remainder 1 = 2 1/2
Whole Number
4/2 = 2
Large Conversion
13/3 = 4 1/3

# About This Calculator

Mixed Numbers (like 2 1/2) and Improper Fractions (like 5/2) are two ways to represent values greater than 1 that aren't whole numbers. Being able to convert between them is a key skill in arithmetic and algebra.

An Improper Fraction has a numerator larger than the denominator (top > bottom). It's simpler for multiplication and division. A Mixed Number has a whole number part and a fraction part. It's easier to verify visually (e.g., "2 and a half pizzas").

To convert Mixed to Improper: Multiply the whole number by the denominator, add the numerator, and put it all over the original denominator. To convert Improper to Mixed: Divide numerator by denominator to get the whole number and finding the remainder.

This tool handles both conversions instantly with step-by-step explanations, ensuring you understand the logic behind the change.

How To Use

  1. Select conversion type (Mixed to Improper OR Improper to Mixed).
  2. Enter the values.
  3. Click Calculate.

Frequently Asked Questions

What is an improper fraction?+

A fraction where the numerator (top) is greater than or equal to the denominator (bottom), like 5/2 or 7/3. It represents a value ≥ 1.

What is a mixed number?+

A combination of a whole number and a proper fraction, like 2 1/2. It explicitly shows the whole parts and the fractional remainder.

Which form is better?+

It depends! Improper fractions are better for math operations (multiplying, dividing). Mixed numbers are better for real-life measurement and understanding magnitude (like '2 and a half inches').

How do I convert improper to mixed manually?+

Divide top by bottom. The answer is the whole number. The remainder becomes the new numerator. Denominator stays the same. E.g., 7/3: 7÷3=2 R1, so 2 1/3.

Can I convert a whole number to an improper fraction?+

Yes! Any whole number 'n' can be exacted as n/1. For example, 5 = 5/1.

Is Mixed & Improper Fractions free to use?+

Yes, Mixed & Improper Fractions on Matheric is completely free to use. We believe in accessible education and utility for everyone.

About

Mixed Numbers (like 2 1/2) and Improper Fractions (like 5/2) are two ways to represent values greater than 1 that aren't whole numbers. Being able to convert between them is a key skill in arithmetic and algebra.

An Improper Fraction has a numerator larger than the denominator (top > bottom). It's simpler for multiplication and division. A Mixed Number has a whole number part and a fraction part. It's easier to verify visually (e.g., "2 and a half pizzas").

To convert Mixed to Improper: Multiply the whole number by the denominator, add the numerator, and put it all over the original denominator. To convert Improper to Mixed: Divide numerator by denominator to get the whole number and finding the remainder.

This tool handles both conversions instantly with step-by-step explanations, ensuring you understand the logic behind the change.

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