# Mixed Number Calculator

Write the given values carefully according to the pattern of the numerator and denominator and then hit on the calculate button to get the solution.

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## What is a mixed number?

It is a group of whole numbers with fractions. It tells us a value that is greater than one, with a fractional part. The different mathematical operations used in it like addition, subtraction, multiplication, and division. It is mostly used to represent quantities that are not whole or integers.

## Types of Mixed Numbers

The types of mixed numbers allow for representing quantities that lie between whole numbers and fractions. Here few types of metal with their characteristics are discussed.

 Mixed Numbers Definition Characteristics Proper Mixed Number It is a mixed number whose value lies between `0 to 1`.For example, 3 1/2 (Three and one-half) The whole number part is greater than zero, and the fractional part is a proper fraction (the numerator is smaller than the denominator). Improper Mixed Number A mixed number of whose values are 1 or below than this.For example, 5 3/4 (Five and three-fourths) The whole number part can be zero or any positive integer, and the fractional part is an improper fraction. Whole Number A mixed number where the fractional part is zero. For example, 7 (Seven) The whole number part is a positive integer, and there is no fractional part Whole Number with Zero A mixed number where both the whole number part and the fractional part are equal to zero. For example, 0 (Zero) The whole number part is zero, and there is no fractional part

## How to solve mixed numbers?

Example 1:

Solve the mixed problem with addition operation.

Solution

Step 1:

a = 4, b = 4, c = 6, d = 8

Mixed numbers to fractions.

15 + 4 / 5 + 32 + 6 / 8

`19 / 5 + 38 / 8`

Step 2:

Simplifying the fraction

`19 / 5 +   19 / 4`

Using formula

A / b + C / d = (a x d) + (b x c) / b x d

Steps 3:

Replacing values

= (19 x 4) + (5 x 19) / (5 x 4)

= 76 + 95 / 20

`= 171 / 20`

`= 8 11/20`

Example 2:

Solve the mixed problem with subtraction operation.

Solution

Step 1:

a = 3, b = 3, c = 5, d = 3

Mixed numbers to fractions.

10 + 3 / 2 - 6 + 5 / 3

`13 / 2 - 11 / 3`

Step 2:

Simplifying the fraction

`13 / 2 - 11 / 3`

Using formula

A / b + C / d = (a x d) + (b x c) / b x d

Steps 3:

Replacing values

= (13 x 3) - (2 x 11) / 2 x 3

= 39 – 22 / 6

= 17 / 6

`= 2 (5/6)`

Example 3:

Solve the mixed problem with multiplication operation.

Solution

Step 1:

a = 2, b = 2, c = 2, d = 2

Mixed numbers to fractions.

30 + 2 / 5 x 14 + 2 / 2

`32 / 5 x 16 / 2`

Step 2:

Simplifying the fraction

32 / 5 x 8 /1

Using formula

`A / b + C / d = (a x d) + (b x c) / b x d`

Steps 3:

Replacing values

= 32 x 8 / 5 x 1

= 256 /5

`= 51 (1/5)`

Which is the required answer to the given data.

Example 4:

Solve the mixed problem with division operation.

Solution

Step 1:

a = 3, b = 3, c = 2, d = 3

Mixed numbers to fractions.

49 + 3 / 7 ÷ 24 + 2/ 3

`52 / 7 ÷ 26 / 3`

Step 2:

Simplifying the fraction

52 / 7 ÷ 26 / 3

Using formula

A / b + C / d = (a x d) + (b x c) / b x d

Steps 3:

Replacing values

= 52 x 3 / 7 x 26

= 156 / 182

`= 6 / 7`