Mixed Numbers Calculator

Mixed numbers calculator to add, subtract, multiply and divide mixed numbers (mixed fractions), fractions and integers.

Mixed Numbers Calculator: A Complete Guide to Working with Fractions and Mixed Numbers

The Mixed Numbers Calculator is an essential online tool for performing mathematical operations on mixed numbers, fractions, integers, and decimals. Whether you are dealing with addition, subtraction, multiplication, or division, this calculator simplifies the process and provides results in reduced fractions or mixed numbers whenever applicable. Below, you'll find an in-depth guide to using the calculator and understanding the formulas it employs.

What is a Mixed Number?

A mixed number is a combination of a whole number and a fraction, such as 1341 \frac{3}{4} (one and three-fourths). Mixed numbers are commonly used in everyday life but often need to be converted to improper fractions for easier mathematical operations.

How to Use the Mixed Numbers Calculator

The calculator supports various input formats, making it versatile for different types of numbers. Here's how you can input your values:

Input Formats

  1. Mixed Numbers: Enter as 1 1/2 (one and one-half) or 25 3/32 (twenty-five and three thirty-seconds). Always include one space between the whole number and the fraction, and use a forward slash for the fraction.
  2. Whole Numbers: Enter integers up to three digits long, such as 123.
  3. Fractions: Input fractions in the form 3/4 (three-fourths) or 3/100 (three one-hundredths). The numerator and denominator can each be up to three digits.

Performing Operations on Mixed Numbers

The calculator handles addition, subtraction, multiplication, and division of mixed numbers. Let’s explore how each operation works.

Adding Mixed Numbers

To add mixed numbers:

  1. Convert the mixed numbers into improper fractions.
  2. Use the formula for adding fractions: \frac{a}{b} + \frac{c}{d} = \frac{(a \cdot d) + (b \cdot c)}{b \cdot d}
  3. Simplify the resulting fraction and, if applicable, convert it back to a mixed number.

Example: Add 1 \frac{2}{6} and 2 \frac{1}{4}

  • Convert:
    • 1 \frac{2}{6} = \frac{8}{6}
    • 2 \frac{1}{4} = \frac{9}{4}
  • Apply the formula: \frac{8}{6} + \frac{9}{4} = \frac{(8 \cdot 4) + (9 \cdot 6)}{6 \cdot 4} = \frac{32 + 54}{24} = \frac{86}{24}
  • Simplify: \frac{86}{24} = 3 \frac{7}{12}

Subtracting Mixed Numbers

To subtract mixed numbers:

  1. Convert the mixed numbers into improper fractions.
  2. Use the formula for subtracting fractions: \frac{a}{b} - \frac{c}{d} = \frac{(a \cdot d) - (b \cdot c)}{b \cdot d}
  3. Simplify the result.

Example: Subtract 2 \frac{1}{4} from 1 \frac{2}{6}

  • Convert:
    • 1 \frac{2}{6} = \frac{8}{6}
    • 2 \frac{1}{4} = \frac{9}{4}
  • Apply the formula: \frac{8}{6} - \frac{9}{4} = \frac{(8 \cdot 4) - (9 \cdot 6)}{6 \cdot 4} = \frac{32 - 54}{24} = \frac{-22}{24}
  • Simplify: \frac{-22}{24} = -\frac{11}{12}

Multiplying Mixed Numbers

To multiply mixed numbers:

  1. Convert the mixed numbers into improper fractions.
  2. Use the formula for multiplication: \frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}
  3. Reduce the resulting fraction.

Example: Multiply 1 \frac{2}{6} by 2 \frac{1}{4}

  • Convert:
    • 1 \frac{2}{6} = \frac{8}{6}
    • 2 \frac{1}{4} = \frac{9}{4}
  • Apply the formula: \frac{8}{6} \cdot \frac{9}{4} = \frac{8 \cdot 9}{6 \cdot 4} = \frac{72}{24}
  • Simplify: \frac{72}{24} = 3

Dividing Mixed Numbers

To divide mixed numbers:

  1. Convert the mixed numbers into improper fractions.
  2. Use the formula for division: \frac{a}{b} \div \frac{c}{d} = \frac{a \cdot d}{b \cdot c}
  3. Simplify the resulting fraction.

Example: Divide 1 \frac{2}{6} by 2 \frac{1}{4}

  • Convert:
    • 1 \frac{2}{6} = \frac{8}{6}
    • 2 \frac{1}{4} = \frac{9}{4}
  • Apply the formula: \frac{8}{6} \div \frac{9}{4} = \frac{8 \cdot 4}{6 \cdot 9} = \frac{32}{54}
  • Simplify: \frac{32}{54} = \frac{16}{27}

Related Tools for Fraction Operations

  • Fractions Calculator: For simpler operations on proper or improper fractions, use the Fractions Calculator. It handles basic addition, subtraction, multiplication, and division.
  • Simplify Fractions Calculator: This tool reduces any fraction to its lowest terms, making it easier to interpret or use in further calculations.
  • Greatest Common Factor (GCF) Calculator: Understanding how to factor numbers to find the GCF is critical for simplifying fractions. This calculator provides a step-by-step explanation.
  • Long Division with Remainders Calculator: When working with large fractions, this calculator helps find whole numbers and remainders, simplifying the process of reducing fractions.

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