Perform arithmetic operations on mixed numbers (whole numbers + fractions). Add, subtract, multiply, and divide mixed numbers with step-by-step solutions.
Step 1: Convert to improper fractions: 2⅓ = 7/3, 1½ = 3/2
Step 2: Find common denominator (6): 14/6 + 9/6 = 23/6
Step 3: Convert back to mixed number: 3⅚
Step 1: Convert to improper fractions: 5¾ = 23/4, 2⅓ = 7/3
Step 2: Find common denominator (12): 69/12 − 28/12 = 41/12
Step 3: Convert back to mixed number: 3⁵/₁₂
Step 1: Convert to improper fractions: 1⅔ = 5/3, 2¼ = 9/4
Step 2: Multiply numerators and denominators: 5/3 × 9/4 = 45/12
Step 3: Simplify: 15/4 = 3¾
Step 1: Convert to improper fractions: 3½ = 7/2, 1¼ = 5/4
Step 2: Multiply by reciprocal: 7/2 × 4/5 = 28/10
Step 3: Simplify: 14/5 = 2⁴/₅
A mixed number consists of a whole number and a proper fraction (e.g., 2⅓). To perform arithmetic operations, the general approach is to convert mixed numbers to improper fractions, perform the operation, then simplify and convert back.
Always convert mixed numbers to improper fractions before performing arithmetic. This avoids errors with whole number and fraction parts.
For addition and subtraction, you must find a common denominator. Use the least common multiple (LCM) for the simplest result.
Always simplify your final fraction and convert back to a mixed number. Simplify by dividing numerator and denominator by their GCD.
Convert your answer back to a decimal to verify. The decimal value of the result should match your manual calculation.
A mixed number is a number that combines a whole number with a proper fraction. For example, 3½ means 3 whole units plus one half. Mixed numbers are commonly used in everyday contexts such as cooking (2⅓ cups of flour), measurements (5¾ inches), and construction (1½ feet).
Performing arithmetic operations with mixed numbers can be challenging because you need to handle both the whole number and fractional parts. The most reliable method is to convert each mixed number to an improper fraction, perform the operation, and then convert the result back to a mixed number. Our Mixed Numbers Calculator automates this process, providing detailed step-by-step solutions to help you understand each stage of the calculation.
Whether you're a student learning fraction arithmetic, a teacher preparing lesson materials, or a professional working with measurements, our calculator simplifies the process. It handles all four basic operations — addition, subtraction, multiplication, and division — and presents results in multiple formats: mixed numbers, improper fractions, simplified fractions, and decimals. The step-by-step breakdown makes it an excellent learning tool for understanding the underlying math.
Mixed numbers appear frequently in real-world scenarios:
Recipes often call for mixed number quantities like 1½ cups or 2¾ teaspoons. Scaling recipes requires adding, subtracting, or multiplying these amounts.
Measurements in feet and inches frequently use mixed numbers. Calculating lumber lengths or room dimensions often involves mixed number arithmetic.
Students from elementary through middle school learn fraction arithmetic. Mixed number operations are a key part of the mathematics curriculum.
Fabric measurements, pattern adjustments, and material calculations frequently involve adding or subtracting lengths given as mixed numbers.