Mixed Numbers Calculator

What is Mixed Fractions (Mixed Numbers)?

A mixed number consists of a whole number and a fraction together. It generally represents a number between any two whole numbers.

For example, 2 ¾ represents a mixed number between two whole numbers 2 and 3. It is a fraction which is greater than 2 but less than 3.

A fraction can be classified into different types, namely proper fraction, improper fraction, and mixed fraction.

How to use the Mixed Numbers Calculator?

A Mixed number calculator can be used to perform arithmetic operations on Mixed numbers, whole numbers and fractions. Numbers can be added in the following format into the calculator:

1. A whole number followed by a space followed by a fraction like ‘a b/c’ to represent mixed numbers
2. Whole numbers
3. Simple Fractions

Use the mixed fractions calculator to perform all mathematical operations

• Step 1: Enter the mixed fractions in the respective input field
• Step 2: Click the “Calculate” button to get the results
• Step 3: Finally, the resultant fraction will be displayed below with detailed steps on the right.

You can also use below free fractions calculators

Fractions

• Fraction calculator – To perform mathematical Operations (addition, subtraction, multiplication, division)
• Fraction Simplifier calculator – To simplify fractions
• Fraction Converter
  • Fraction to Decimal calculator
  • Decimal to Fraction calculator
  • Fraction to Percent calculator
  • Percent to Fraction calculator

Mixed Fractions

• Mixed Fraction calculator – To perform mathematical Operations (addition, subtraction, multiplication, division)
• Mixed Fraction Simplifier calculator – To simplify Mixed fractions
• Mixed Fraction Converter
  • Mixed Fraction to Decimal calculator
  • Mixed Fraction to Percent calculator
  • Mixed Fraction to improper fraction calculator

Addition of Mixed Numbers

1. In order to perform addition on mixed numbers, they have to be converted into improper fractions. For example, a b/c can be written as ((a*c)+b)/c.
2. After converting the mixed numbers into improper fractions, we have to follow the same steps like addition of fractions
3. Find a common denominator for the fractions either by multiplying the numerator and denominator of each fraction involved in the operation with the denominator of all the fractions OR finding the LCM of all the denominators of the fractions.
4.  In the case of LCM, multiply the numerator and denominator of all the fractions with a value that makes the denominator equal to LCM.
5. Perform addition on numerators of the fractions, keeping the denominator as common
6. Simplify the fraction by reducing, if possible

For example, 2 ¾ + 5 ⅔

• = ((2*4)+3)/4 + ((5*3)+2)/3
• = 11/4 +17/3
• = (11*3)/(4*3) + (17*4)/(3*4)
• = 33/12 + 68/12 = (33+68)/12
• = 101/12 Simplifying, 101/12 = 8 5/12

Alternatively, we can perform addition on the whole number separately and on fractions separately and then add the whole number result with the whole number of mixed numbers created by simplifying the fraction result.

For example, 2 ¾ + 5 ⅔ Solving the whole number parts = 2 + 5 = 7

Solving the fraction parts ¾ + ⅔ = 3*3/4*3 + 2*4/3*4 = 9/12 + 8/12 = 17/12 Simplifying, 17/12 = 1 5/12

Adding the whole number result with mixed number whole number (7+1) 5/12 = 8 5/12

Subtraction of Mixed Numbers

Subtraction of mixed numbers is very similar to Addition. A common denominator is required to perform the operation after converting the mixed number to improper fraction.

Refer to the addition section to know how to find the common denominator in detail. For example, 2 ¾ – 5 ⅔

• = ((2*4)+3)/4 – ((5*3)+2)/3
• = 11/4 -17/3
• = (11*3)/(4*3) – (17*4)/(3*4)
• = 33/12 – 68/12 = -35/12
• = -2 11/12

Multiplication of Mixed Numbers

Convert mixed numbers into improper fractions. A common denominator is not required for multiplication. Simply, multiply the numerators and the denominators to obtain a new fraction with new numerator and denominator. Simplify the result, if required.

For example, 2 ¾ * 5 ⅔ = ((2*4)+3)/4 * ((5*3)+2)/3

= 11/4 * 17/3

= 187/12 = 15 7/12

Division of Mixed Numbers

Convert mixed numbers into improper fractions. In order to calculate the result of division of fractions, the numerator fraction is multiplied by the reciprocal of the denominator fraction. In case of fractions, the position of numerator and denominator are interchanged in reciprocal i.e. reciprocal of a/b would become b/a. Simplify the result, if required.

For example, (2 ¾) / (5 ⅔) = (((2*4)+3)/4) / (((5*3)+2)/3)

= (11/4) / (17/3)

= 11/4 * 3/17 = 33/68