Mixed Numbers Calculator (½)
Add, subtract, multiply, and divide mixed numbers with whole numbers and proper fractions.
Mixed Numbers — interactive calculator, computed instantly in your browser.
Mixed Numbers Arithmetic: Operations, Simplification & Conversion
Anatomy of a Mixed Number: $3 \frac{1}{4}$
Mixed to Improper Conversion: Multiply the whole number by the denominator and add the numerator: $W \times D + N$.
A mixed number combines a non-zero integer with a proper fraction (such as $2 \frac{3}{8}$). Performing arithmetic operations (addition, subtraction, multiplication, division) on mixed numbers requires systematic handling of whole parts and fractional denominators.
1. Operational Rules for Mixed Fractions
- Addition & Subtraction: Convert both terms to improper fractions, find a Common Denominator (LCD), execute numerator addition/subtraction, then reduce to simplest mixed format.
- Multiplication: Always convert to improper fractions first: $\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}$, then simplify.
- Division: Multiply by the reciprocal (invert the second fraction and multiply): $\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}$.
2. Practical Worked Example ($2 \frac{1}{3} + 1 \frac{3}{4}$)
- Convert to improper fractions: $2 \frac{1}{3} = \frac{7}{3}$ and $1 \frac{3}{4} = \frac{7}{4}$
- Find LCD: $\text{LCD}(3, 4) = 12$
- Express with common denominator: $\frac{7 \times 4}{12} + \frac{7 \times 3}{12} = \frac{28}{12} + \frac{21}{12} = \frac{49}{12}$
- Convert back to mixed number: $49 \div 12 = 4$ with remainder $1 \implies \mathbf{4 \frac{1}{12}}$.
🔗 Mixed Number & Fraction Operations
Mixed numbers combine integers and fractional remainders. Explore our ➗ Math & Statistics Hub for complete fraction solutions.
Find Greatest Common Factors or convert fractions to decimals with the tools below.
Frequently Asked Questions (Mixed Numbers)
In algebra, calculus, and scientific computations, improper fractions (like $7/2$) are universally preferred because they avoid confusing the mixed number format with multiplication ($2 \frac{1}{2}$ vs $2 \times \frac{1}{2}$).
If the first fraction is smaller than the second, borrow 1 from the whole number and add the denominator to the numerator (e.g. $4 \frac{1}{5} = 3 \frac{6}{5}$).