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Calculator Answers

Mixed Fraction Calculator

Blake Boege
Written by Blake Boege · Founder, Calculator Answers

A mixed fraction calculator is an arithmetic utility that performs addition, subtraction, multiplication, and division on mixed numbers and improper fractions. It automatically converts mixed numbers to improper fractions, computes the selected mathematical operation, reduces the resulting fraction using its greatest common divisor (GCD), and yields both the simplified mixed fraction and its decimal equivalent with step-by-step work.

Add, subtract, multiply, and divide mixed numbers or improper fractions. Renders the simplified mixed number and step-by-step calculations.

Quick Answer

Add, subtract, multiply, or divide mixed numbers and improper fractions. Renders the simplified mixed fraction and improper fraction results.

First Mixed Number

Operation

Second Mixed Number

Mixed Fraction Result

Simplified Result

3 3/4

Improper Fraction: 15/4

Improper fraction15/4
Decimal value3.75

Step-by-Step Solution:

  1. Convert 1 1/2 to improper fraction: 3/2
  2. Convert 2 1/4 to improper fraction: 9/4
  3. Find a common denominator: (3 × 4) / (2 × 4) + (9 × 2) / (4 × 2)
  4. Calculate: 12/8 + 18/8 = 30/8
  5. Simplify fraction by dividing by GCD (2): 15/4
  6. Convert improper fraction back to mixed number: 3 3/4
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How it works

How to calculate with mixed numbers

Operating directly on mixed numbers is prone to errors. The safest mathematical approach involves these three stages:

1. Convert to Improper Fractions

Multiply the whole number by the denominator, then add the numerator to get the new numerator:

Improper Numerator = (Whole × Denominator) + Numerator

2. Perform the Fraction Arithmetic

  • Addition/Subtraction: Cross-multiply to find a common denominator, then add/subtract numerators.
  • Multiplication: Multiply the numerators together and denominators together.
  • Division: Invert the second fraction (the reciprocal) and multiply.

3. Simplify and Reconvert

Reduce the resulting fraction by dividing the numerator and denominator by their greatest common divisor (GCD). If the numerator is larger than the denominator, convert it back into a mixed number.

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Mixed Number CalculatorConvert improper fractions to mixed numbers and back. Returns the simplified form and the decimal equivalent.

Frequently asked questions

A mixed fraction (or mixed number) is a combination of a whole number and a proper fraction, such as 1 1/2. It represents the sum of the whole number and the fraction.

To add mixed fractions, first convert each mixed fraction into an improper fraction. Find a common denominator, add the numerators, and then convert the resulting improper fraction back into a mixed fraction if necessary.

Convert both mixed numbers to improper fractions, then multiply the numerators together and the denominators together. Simplify the resulting fraction and convert it back to a mixed number.

No, division requires converting them to improper fractions first. After converting, multiply the first fraction by the reciprocal (the inverted version) of the second fraction.