What are Mixed Numbers?

 Mixed numbers, also known as mixed fractions, are a type of numerical unit composed of an integer and a fraction. In the simplest terms, mixed numbers express any number that is not an integer by combining a whole number and a fraction.

 A mixed number contains a whole number combined with a fractional amount of another unit, such as one-quarter or one-half of something.  

 For example, a mixed number can represent a value of three and one half, written as “3 1/2”. In this example, the three is the whole number being expressed, and the one-half is the fractional portion of a unit. Combining these two components means the total value expressed is three and one-half. 

Mixed numbers are used to describe values that are not integers, such as amounts of money, measurements of time, or other measurements that can be described in fraction form.  

Arithmetic Operations on Mixed Numbers  

Arithmetic operations on mixed numbers involve adding, subtracting, multiplying, or dividing mixed numbers.  A composition of an integer and a fraction makes a mixed number. For example, 4 1/2 is a mixed number.  

Here are the steps to perform arithmetic operations on mixed numbers:  

Addition and Subtraction

To add or subtract mixed numbers, convert them into improper fractions, then operate, and finally convert the result back into a mixed number.  

For example, to add 2 1/2 and 3 3/4, follow these steps:  

2 1/2 + 3 3/4  

= (2 x 2 + 1)/2 + (3 x 4 + 3)/4 (convert mixed numbers into improper fractions)  

= 5/2 + 15/4 (add the fractions)  

= 10/4 + 15/4 (find a common denominator)  

= 25/4 (add the numerators)  

= 6 1/4 (convert back into a mixed number)  

To subtract mixed numbers, follow the same process, but subtract the second fraction from the first fraction instead of adding them.  

Multiplication

To multiply mixed numbers, first convert them into improper fractions, then multiply the fractions, and finally convert the result back into a mixed number.  

For example, to multiply 2 1/2 and 3 3/4, follow these steps:  

2 1/2 x 3 3/4  

= (2 x 2 + 1)/2 x (3 x 4 + 3)/4 (convert mixed numbers into improper fractions)  

= 5/2 x 15/4 (multiply the fractions)  

= 75/8 (simplify the fraction)  

= 9 3/8 (convert back into a mixed number)  

Division

To divide mixed numbers, first convert them into improper fractions, then multiply the first fraction by the reciprocal of the second fraction, and finally convert the result back into a mixed number.  

For example, to divide 2 1/2 by 3 3/4, follow these steps:  

2 1/2 ÷ 3 3/4  

= (2 x 2 + 1)/2 ÷ (3 x 4 + 3)/4 (convert mixed numbers into improper fractions)  

= 5/2 ÷ 15/4 (multiply the first fraction by the reciprocal of the second fraction)  

= 5/2 x 4/15 (simplify the fractions)  

= 2/3 (simplify the fraction)  

= 0 2/3 (convert back into a mixed number)  

That is how you perform arithmetic operations on mixed numbers.