Mixed Number & Fraction Calculator Guide

What This Calculator Does

Simplify, convert, add, subtract, multiply, divide or compare ordinary fractions and mixed numbers. Keep the original separate numerator/denominator fields or choose a single fraction/mixed-number field. Exact integer arithmetic reduces fraction results, with mixed, decimal, percentage and common-denominator views.

When to Use It

Check mixed-number homework, convert improper fractions, perform two-number arithmetic or compare values. For decimal input, use the decimal fraction converter. For separate factor work, use GCF or LCM.

Inputs Explained

Choose simplify, convert, arithmetic or compare, then select the input format. Separate numerator and denominator fields accept signed integers, including negative denominators. Single-field syntax is an integer such as 3, a fraction such as -7/3, or a mixed number such as -2 1/3. Spaces around the slash are allowed; whitespace must separate a mixed number's whole and fraction parts.

A mixed number's leading sign applies to its whole magnitude. -2 1/3 = -(2+1/3) = -7/3; -0 1/3 = -1/3. The fractional part must satisfy 0 ≤ numerator < positive denominator. 2 3/2 is invalid mixed syntax; enter an improper fraction instead. Ordinary fractions may have negative denominators, which are normalized to positive denominators. Zero reduces to 0/1.

Each integer component is limited to ±1,000,000,000; single-field input is at most 50 characters. Decimal input, scientific notation and expressions are unsupported. Denominators and divisor fractions cannot be zero. Editing clears the old result; calculate again to update it. Calculating saves inputs through the existing URL fields, so old numerator/denominator shared links still work.

How the Calculation Works

A mixed number becomes w n/d = (w×d+n)/d, applying any minus sign to the entire numerator. Euclid's algorithm finds gcd(|numerator|,denominator) for reduction. The original simplify input is retained for truthful GCD display: 8/12 uses GCD 4.

For a/b and c/d, the common denominator is L=lcm(b,d)=b/gcd(b,d)×d. Addition/subtraction first form a(L/b)/L and c(L/d)/L, combine their numerators, then reduce. Multiplication uses ac/bd; division uses ad/bc. Comparison checks the scaled numerators. An arithmetic result's GCD refers to the unreduced result of that operation.

Example

• -2 1/3 + 1 1/2 becomes -7/3 + 3/2, then -14/6 + 9/6 = -5/6.
• 2 1/3 × 1 1/2 becomes 7/3 × 3/2 = 21/6 = 7/2 = 3 1/2.
• Convert -7/3 to the mixed form -2 1/3.
• Compare 2/3 and 3/5: LCM 15 gives 10/15 > 9/15.
• Simplify -6/-8: normalize to 6/8, divide by GCD 2, get 3/4.

How to Understand the Result

The reduced fraction is exact. Mixed form separates the whole number and remainder; values below one stay ordinary fractions. Decimal and percentage displays have at most 8 decimal places and do not replace exact repeating fractions. The common-denominator line and LCM help check addition/subtraction and comparison; multiplication/division still use their numerator/denominator products.

Common Mistakes

Reading -2 1/3 as -2+1/3; adding another sign inside a mixed fractional part; entering decimals in integer fields; zero denominators; division by zero fractions; treating rounded decimals as exact.

FAQ

Can I type a mixed number directly?

Use an integer, signed fraction or mixed number such as -2 1/3. The leading minus applies to the entire mixed number. Mixed fractional parts must be proper and positive.

What does -2 1/3 mean?

It means -(2 + 1/3) = -7/3, not -2 + 1/3.

Are fraction results exact?

Each entered integer part is limited to ±1,000,000,000. Exact integer arithmetic preserves fraction results; decimal and percent displays are rounded to 8 places. No decimal inputs or expressions.

Notes

Each entered integer part is limited to ±1,000,000,000. Exact integer arithmetic preserves fraction results; decimal and percent displays are rounded to 8 places. No decimal inputs or expressions.