Perform addition, subtraction, multiplication, and division on mixed fractions with step-by-step proofs. Compares improper fraction conversions with whole-number borrowing and carrying techniques.
Mixed numbers represent an integer together with a proper fraction. While intuitive for measuring tape readings and recipe quantities, performing arithmetic requires rigorous conversion or whole-number regrouping:
Enter the whole integer, numerator, and denominator for both mixed fractions.
Select Addition (+), Subtraction (-), Multiplication (×), or Division (÷).
Convert each mixed number to improper form: W × D + N over D.
Reduce by GCD and convert the improper result back to a clean mixed number.
Works uniformly across all four operations without exceptions or special cases:
Recommended for multiplication, division, and automated digital calculation.
Operates on whole integers and fractional fractions separately for addition and subtraction:
When subtracting with a smaller first fraction, borrow 1 from the whole number as D/D.
Since 1/4 is smaller than 3/4, borrow 1 from 5: 5 1/4 becomes 4 + (4/4 + 1/4) = 4 5/4. Then subtract:
Convert to improper fractions: 7/3 × 3/2. Cross-cancel 3 with 3 to get 7/1 × 1/2:
Subtracting mixed numbers like 5 1/4 - 2 3/4 requires borrowing whole numbers and regrouping into equivalent fractions. This tool shows both improper fraction and regrouping methods side by side.
Adding timber lengths like 8 3/8 in and 6 3/4 in requires accurate LCD common denominator unification for exact cutting lists.
Scaling recipes by factors like multiplying 2 1/3 cups by 1 1/2 without manual algebra errors.
Prevents students from trying to divide whole numbers and fractions separately, enforcing the mandatory improper conversion step.
Perform Addition, Subtraction, Multiplication, and Division across any two mixed numbers with instant event change response.
Demonstrates both the improper fraction method and the whole number carrying/borrowing method.
Reduces final fraction by GCD, providing both simplified mixed number, improper fraction, and exact 4-decimal value.
| Operation | Can Regroup Wholes Separately? | Standard Method | Key Watchout |
|---|---|---|---|
| Addition (+) | Yes | Add wholes, add fractions with LCD | Carry extra 1 if fractional sum ≥ 1 |
| Subtraction (-) | Yes (with borrowing) | Subtract wholes, subtract fractions with LCD | Borrow 1 from whole number if N1 < N2 |
| Multiplication (×) | No (Avoid FOIL error) | Convert to improper fractions, multiply across | Do not simply multiply whole × whole |
| Division (÷) | No | Convert to improper, multiply by reciprocal | Flip second fraction only after conversion |
Convert mixed numbers into improper fractions with visual pies.
All-in-one arithmetic operations for fractions and mixed numbers.
Cross-cancellation and step-by-step fraction multiplication.
Keep Change Flip reciprocal steps and lowest terms reduction.
Least common denominator steps and visual circle slices.
Reduce fractions to simplest form using Euclidean GCD.
