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Fractions Calculator

Check mixed fraction and improper fraction conversions with clear simplified results.

Whole-number part of the first mixed number.

Fraction numerator for the first mixed number.

Fraction denominator for the first mixed number.

Choose the arithmetic operation.

Whole-number part of the second mixed number.

Fraction numerator for the second mixed number.

Fraction denominator for the second mixed number.

Status: initial

Results

Awaiting calculation

Calculator guide

Introduction

Use this fractions calculator to convert between mixed fractions and improper fractions.

Purpose

Built for common fractions search intent while staying within the verified mixed fraction conversion workflow.

Mixed number method

The calculator converts each mixed number to an improper fraction, applies the selected operation, simplifies the answer, and converts the result back to mixed-number form.

Variable explanations

Whole number

The whole-number part of a mixed number.

Numerator

The top part of the fractional part.

Denominator

The bottom part of the fractional part.

Improper fraction

A fraction where the numerator can be larger than the denominator.

Mixed result

The simplified result written as a whole number plus fraction.

Formula guide

Convert to improper fraction

Improper numerator = whole x denominator + numerator

  • Keep the same denominator.
  • Use the sign of the whole number.

This prepares mixed numbers for fraction arithmetic.

Add or subtract

a/b ± c/d = (ad ± bc) / bd

  • Use a common denominator.

This combines fractions with different denominators.

Multiply or divide

a/b x c/d = ac/bd; a/b ÷ c/d = ad/bc

  • Division multiplies by the reciprocal.

Simplify the final fraction after the operation.

Worked examples

Add mixed numbers

  1. 1 2/3 becomes 5/3.
  2. 1 3/4 becomes 7/4.
  3. 5/3 + 7/4 = 41/12.
  4. 41/12 = 3 5/12.

Multiply mixed numbers

  1. 2 1/2 becomes 5/2.
  2. 1 1/3 becomes 4/3.
  3. 5/2 x 4/3 = 20/6.
  4. 20/6 simplifies to 3 1/3.

Divide mixed numbers

  1. Convert both mixed numbers to improper fractions.
  2. Multiply by the reciprocal of the second fraction.
  3. Simplify the result.

Common mistakes

Adding whole parts and fractions separately without common denominators

The fractional parts still need a common denominator.

Forgetting to convert before multiplying

Mixed numbers should be converted to improper fractions before multiplication or division.

Dividing without using the reciprocal

Fraction division means multiplying by the reciprocal of the second fraction.

Leaving answers unsimplified

Simplify the final fraction and convert to mixed form when appropriate.

FAQs

What does this Mixed Number Calculator do?
It adds, subtracts, multiplies, or divides two mixed numbers.
What is a mixed number?
A mixed number has a whole-number part and a fractional part, such as 2 1/4.
How do you convert a mixed number to an improper fraction?
Multiply the whole number by the denominator, add the numerator, and keep the same denominator.
Can this calculator simplify fractions?
Yes. Results are simplified automatically.
Can it show an improper fraction?
Yes. It shows both mixed-number and improper-fraction forms.
Can it show decimals?
Yes. It includes a decimal result.
Can I subtract mixed numbers?
Yes. Choose subtract as the operation.
Can I multiply mixed numbers?
Yes. The calculator converts both values to improper fractions first.
Can I divide mixed numbers?
Yes. It multiplies by the reciprocal of the second improper fraction.
Can the result be negative?
Yes. Subtraction can produce negative mixed-number results.
Can the numerator be larger than the denominator?
For input mixed numbers, enter a numerator smaller than the denominator. The result can be shown as an improper fraction.
Can I enter a whole number only?
Yes. Use numerator 0 and any positive denominator.
Why convert to improper fractions first?
Improper fractions make addition, subtraction, multiplication, and division more consistent.
Does this use lowest terms?
Yes. The final fraction is reduced to lowest terms.
Is this only for positive numbers?
No. Whole-number parts may be negative, but denominators must be positive.

References

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Last updated and version history

Last updated: 2026-07-10

  • 1.0.0 (2026-07-10): Added fractions keyword variant backed by the mixed fraction calculator engine.