Mixed Numbers Calculator – Add, Subtract, Multiply & Divide Mixed Numbers
Calculating mixed numbers
Solve math problems with mixed numbers (also known as mixed fractions) with ease. The mixed numbers calculator lets you effortlessly add, subtract, multiply, and divide all types of numbers, including common fractions, whole numbers, and improper fractions.
Understanding Mixed Numbers
A mixed number is simply a combination of a whole number and a common fraction. A whole number is a regular number without decimal places (like 1, 2, or 3). A common fraction occurs when the top number is smaller than the bottom number (like 1/2 or 3/4).
How this calculator can help you
Working with fractions and whole numbers manually takes a lot of time. Our online mixed numbers tool helps you solve basic mathematics and advanced algebra problems instantly. When you perform calculations, the tool displays a complete step-by-step resolution, showing you exactly how the final answer was calculated.
Steps to Add Mixed Numbers
- Convert each mixed number into an improper fraction.
- Multiply the whole number by the denominator, then add the numerator. Place this result over the original denominator.
- Find a common denominator for the two fractions.
- Add the numerators together and keep the common denominator.
- Simplify the resulting fraction and convert it back to a mixed number if possible.
Formula for Addition
Addition Example
The easiest way to add mixed numbers is to convert them to improper fractions first. The following example shows exactly how to find a common denominator and solve the problem step by step. To get fast and accurate results without manual calculation, just use our free Mixed Numbers Calculator above.
Let's add 1 3/5 and 2 2/7:
This results in 136/35, which easily simplifies to 3 31/35.
Steps to Subtract Mixed Numbers
- Convert each mixed number into an improper fraction.
- Multiply the whole number by the denominator and add the numerator. Place this result over the original denominator.
- Use the mathematical rule for subtracting fractions: a/b − c/d = (a×d − b×c) / (b×d)
- Simplify your final result if possible.
Formula for Subtraction
Subtraction Example
Let's subtract 2 1/4 from 1 2/6:
Simplify the fraction to get −11/12.
Steps to Multiply Mixed Numbers
- Convert each mixed number into an improper fraction.
- Multiply the whole number by the denominator and add the numerator. Place this over the denominator.
- Use the mathematical rule for multiplying fractions: a/b × c/d = (a×c) / (b×d)
- Reduce and simplify your final result.
Formula for Multiplication
Multiplication Example
Let's multiply 1 2/6 by 2 1/4:
Simplify the fraction to get 3/1, which becomes simply 3.
Steps to Divide Mixed Numbers
- Convert your mixed numbers into improper fractions.
- Multiply the whole number by the denominator and add the numerator. Keep the original denominator.
- Use the mathematical rule for dividing fractions: a/b ÷ c/d = (a×d) / (b×c)
- Simplify the final fraction as much as possible.
Formula for Division
Division Example
Let's divide 1 2/6 by 2 1/4:
Reduce the fraction to get 16/27.
Related Calculators
- To perform mathematical operations on simple proper or improper fractions, use the Fraction Calculator, which easily converts improper fractions to mixed numbers.
- To reduce a single fraction to its simplest form, use our Simplify Fractions Calculator.
- To understand how to factor numbers and determine the greatest common divisor (GCD), explore the Größeatest Common Divisor Calculator.
- For manual simplification of large fractions, the Long Division with Remainders Calculator helps to quickly identify both the integer and the exact remainder.