Fraction and Mixed Number Calculator
Add, subtract, multiply, and divide fractions and mixed numbers with step-by-step simplification.
Fraction & Mixed Number Calculator
Add, subtract, multiply, and divide proper, improper, or mixed fractions with step-by-step working
How Does It Work?
Free client-side fraction calculator. Add, subtract, multiply, and divide proper, improper, and mixed fractions with common denominators, GCD reduction, mixed number conversions, and step-by-step arithmetic working.
Fractions are converted to improper format, evaluated using cross-multiplication or common denominator LCD arithmetic, and simplified by dividing numerator and denominator by their greatest common divisor (GCD).
Real-World Worked Example
Adding two mixed fractions: 1 1/2 + 2 3/4.
- •Convert 1 1/2 to improper fraction: (1 × 2 + 1) / 2 = 3/2
- •Convert 2 3/4 to improper fraction: (2 × 4 + 3) / 4 = 11/4
- •Find Least Common Denominator (LCD) of 2 and 4 = 4
- •Scale first fraction: (3 × 2) / (2 × 2) = 6/4
- •Add numerators: (6 + 11) / 4 = 17/4
- •Convert to Mixed Number: 17 ÷ 4 = 4 with remainder 1 -> 4 1/4
- •Decimal Equivalent: 17 / 4 = 4.25
Takeaway: Converting mixed fractions to improper fractions upfront prevents mistakes with whole number borrowing during subtraction and cross-multiplying.
Complete Guide & Practical Explanations
Fractions represent parts of a whole and are ubiquitous in daily life, cooking recipes, carpentry measurements, school mathematics, and financial ratios. Yet, arithmetic involving fractions—especially when combining unlike denominators or mixed numbers—remains one of the most frequent stumbling blocks for students.
The fundamental rule of fraction arithmetic depends on the mathematical operation:
1. Addition and Subtraction: You cannot combine fractions with different denominators directly. If you have 1/2 of a pizza and 1/4 of a pizza, you cannot say you have 2/6 of a pizza. You must find a Common Denominator (the LCM of the denominators). The LCM of 2 and 4 is 4. We scale 1/2 into (1 × 2) / (2 × 2) = 2/4. Now with identical denominators: 2/4 + 1/4 = 3/4.
2. Multiplication: Multiplication is straightforward. Multiply the numerators together, and multiply the denominators together: (a/b) × (c/d) = (a × c) / (b × d). For example, (2/3) × (4/5) = 8/15.
3. Division: Dividing fractions uses the "Keep, Change, Flip" rule. Keep the first fraction, change division to multiplication, and flip the second fraction into its reciprocal: (a/b) ÷ (c/d) = (a/b) × (d/c) = (a × d) / (b × c). For instance, (3/4) ÷ (2/5) becomes (3/4) × (5/2) = 15/8 = 1 7/8.
Handling Mixed Numbers: A mixed number combines a whole number with a fraction, such as 2 1/3. Before performing operations, convert mixed numbers into improper fractions: multiply the whole number by the denominator, add the numerator, and place it over the original denominator. For 2 1/3: (2 × 3 + 1) / 3 = 7/3. Once evaluated, convert the result back into a mixed number by dividing numerator by denominator to find the whole quotient and remainder.
Our interactive Fraction Calculator automates this entire process: it shows your answer as a simplified fraction, a mixed number, and an exact decimal, accompanied by step-by-step arithmetic derivations.
Practical Tips
- ✓Leave the whole number box as 0 if you are working with simple proper fractions like 1/2 or 3/4.
- ✓Remember that dividing by a fraction is mathematically identical to multiplying by its reciprocal (inverting the numerator and denominator).
- ✓Review the step-by-step drawer to inspect GCD reduction and common denominator scaling.
Common Mistakes to Avoid
- ⚠Adding denominators together directly (e.g. 1/2 + 1/2 = 2/4 = 1/2 instead of 2/2 = 1). Denominators must always share a common base before adding.
- ⚠Attempting division when the second fraction evaluates to zero, which is mathematically undefined.
Related Guides & Calculation Deep Dives
All guidesHow to Find LCM and HCF (3 Methods with Examples)
The Highest Common Factor (HCF / GCD) is the largest positive integer that divides each number without remainder. The Least Common Multiple (LCM) is the smallest positive integer divisible by all numbers. For any two positive integers a and b, HCF(a, b) × LCM(a, b) = a × b.
Adding and Subtracting Fractions: Simple Steps
To add or subtract fractions with different denominators, find their Least Common Denominator (LCD), convert each fraction into an equivalent fraction with that common denominator, add or subtract the numerators, and reduce to simplest form using the GCD.
Fraction Calculator FAQs
Common questions, calculation formulas, and usage rules.
To add fractions with different denominators, find their Least Common Denominator (LCD), convert each fraction to an equivalent fraction with that denominator, add the numerators together, and keep the denominator unchanged before simplifying.
To divide fractions, keep the first fraction, change the division sign to multiplication, and flip the second fraction (use its reciprocal). Then multiply numerators and denominators straight across.