Free mixed number calculator with step-by-step solutions. Add, subtract, multiply, and divide mixed numbers and fractions with visual results.
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Working with mixed numbers like 2½ or 3¾? Our mixed number calculator handles all arithmetic operations—addition, subtraction, multiplication, and division—with visual step-by-step solutions. Whether you're a student tackling math homework, a parent helping with fraction problems, a chef scaling recipes, or a carpenter working with fractional measurements, this calculator shows you exactly how to solve any mixed number problem with clear, LaTeX-rendered mathematical steps.
A mixed number combines a whole number with a proper fraction, like 3½ (three and one-half) or 2¾ (two and three-quarters). The whole number represents complete units, while the fraction represents the remaining part. Mixed numbers are commonly used in everyday measurements—cooking recipes (2½ cups of flour), construction (8⅝ inches), and time (1¾ hours). To perform arithmetic operations with mixed numbers, we typically convert them to improper fractions first, perform the calculation, then convert the result back to mixed form and simplify.
Conversion Formulas
Mixed to Improper: a b/c = (a × c + b) / c | Improper to Mixed: n/d = q r/d where n = q × d + rEvery calculation shows detailed steps with LaTeX-rendered mathematical notation—from converting to improper fractions, finding common denominators, performing the operation, to simplifying the final result.
Add, subtract, multiply, or divide any two mixed numbers in one comprehensive tool. No need to switch between different calculators.
Get your answer as a simplified mixed number, improper fraction, decimal, and percentage—all displayed simultaneously for maximum flexibility.
See fractions rendered beautifully with proper numerator/denominator stacking, making it easier to understand and verify your calculations.
Results are always reduced to lowest terms using GCD (Greatest Common Divisor), so you get the cleanest possible answer.
Full support for negative mixed numbers with proper sign handling throughout all calculations.
Load common textbook problems instantly to learn the process, check your work, or practice similar problems.
Completely free to use with unlimited calculations. No account required, no ads blocking your work.
Check your fraction homework, learn the step-by-step process for solving mixed number problems, and prepare for math tests with clear explanations of each calculation step.
Double or halve recipes that use fractional measurements. Calculate what 1½ cups times 3 equals, or divide 2¾ cups of flour between 4 batches.
Add and subtract measurements in inches and fractions when cutting lumber, calculating total lengths, or figuring out material needs. What's 8⅝ inches minus 3⅜ inches?
Calculate fabric lengths, seam allowances, and pattern adjustments using fractional yard and inch measurements common in sewing projects.
Work with fractional interest rates, stock prices, and financial ratios that are often expressed as mixed numbers or fractions.
Demonstrate mixed number operations to students with clear visual steps. Perfect for teachers, tutors, and parents explaining fraction arithmetic.
To add mixed numbers: (1) Convert each mixed number to an improper fraction by multiplying the whole number by the denominator and adding the numerator, (2) Find a common denominator (LCD) for both fractions, (3) Convert both fractions to have this common denominator, (4) Add the numerators while keeping the denominator the same, (5) Simplify by finding the GCD and dividing, (6) Convert back to a mixed number if the result is an improper fraction.
First, convert both mixed numbers to improper fractions. Then find the LCD (Least Common Denominator) of both fractions. Convert each fraction to an equivalent fraction with the LCD as denominator. Subtract the numerators. If the result is negative, the answer will be negative. Simplify and convert back to a mixed number. Sometimes you need to 'borrow' from the whole number if the first fraction is smaller than the second.
Multiplication is simpler than addition/subtraction: (1) Convert both mixed numbers to improper fractions, (2) Multiply the numerators together to get the new numerator, (3) Multiply the denominators together to get the new denominator, (4) Simplify by dividing both by their GCD, (5) Convert back to a mixed number. For example: 1½ × 2⅓ = 3/2 × 7/3 = 21/6 = 7/2 = 3½.
To divide mixed numbers: (1) Convert both to improper fractions, (2) Take the reciprocal (flip) of the divisor (second fraction), (3) Multiply the first fraction by this reciprocal, (4) Simplify and convert to a mixed number. Remember: dividing by a fraction is the same as multiplying by its reciprocal. For example: 4½ ÷ 1½ = 9/2 ÷ 3/2 = 9/2 × 2/3 = 18/6 = 3.
Multiply the whole number by the denominator, then add the numerator. This becomes your new numerator over the original denominator. Formula: a b/c = (a × c + b)/c. For example: 3⅖ = (3 × 5 + 2)/5 = 17/5.
Divide the numerator by the denominator. The quotient becomes the whole number, and the remainder becomes the new numerator over the original denominator. For example: 17/5 → 17 ÷ 5 = 3 remainder 2 → 3⅖.
A mixed number combines a whole number with a proper fraction (like 2½), while an improper fraction has a numerator greater than or equal to its denominator (like 5/2). They represent the same value in different forms. Mixed numbers are often easier to visualize (2½ pizzas), while improper fractions are easier to calculate with.
Converting to improper fractions: 2½ = 5/2 and 3¾ = 15/4. Finding common denominator (4): 5/2 = 10/4. Adding: 10/4 + 15/4 = 25/4. Converting back: 25/4 = 6¼. So 2½ + 3¾ = 6¼.
To convert 3½ to a decimal, divide the numerator by the denominator (1 ÷ 2 = 0.5) and add the whole number: 3 + 0.5 = 3.5. You can also convert to an improper fraction first (7/2) and divide: 7 ÷ 2 = 3.5.
Yes! A negative mixed number like -2⅓ represents a value less than zero. The negative sign applies to the entire mixed number. When calculating with negative mixed numbers, follow the standard rules for negative numbers: negative × negative = positive, negative + negative = more negative, etc.
Converting to improper fractions gives us a single fraction to work with, making the multiplication straightforward (just multiply numerators and denominators). If we tried to multiply mixed numbers directly, we'd need to distribute: (2 + ½) × (3 + ¼) requires FOIL-like expansion, which is much more complex than 5/2 × 13/4.
Yes! 2½ and 5/2 represent exactly the same value, just written in different forms. 2½ means '2 whole units plus half a unit,' while 5/2 means '5 halves.' Converting: 2½ = (2 × 2 + 1)/2 = 5/2. Both equal 2.5 in decimal form.
First convert the mixed numbers to improper fractions, then find the LCD (Least Common Denominator) of the denominators. The LCD is the smallest number that both denominators divide into evenly. For 1⅓ and 2¼, the fractions are 4/3 and 9/4. LCD of 3 and 4 is 12. Convert: 4/3 = 16/12, 9/4 = 27/12.
Yes! Simply leave the whole number field empty or enter 0. The calculator will work with simple fractions like ¾ + ⅔ just as easily as with mixed numbers.