Multiply Mixed Numbers

  Here in this page we are going to discuss about multiplying mixed numbers.Mixed numbers can be written in form of improper fraction. The mixed numbers have summation of whole number and proper fraction. Proper fraction is nothing but the numerator of the fraction is less that that the denominator of the fraction. By multiplying the mixed numbers, we must follow certain procedure as follow.

How to Multiply Mixed Numbers

Let's see the procedure-

Step 1: Convert the given mixed numbers to improper fraction.

To make the mixed numbers to improper fraction, we multiply the whole number and denominator of the fraction and add the result to the numerator of the fraction.

Example: 2 ¼

Multiply 2 and 4 we get 8

Add the number 8 to the numerator of the fraction 1, we get 8 + 1 = 9.

Now get the improper fraction of the mixed number 2 ¼ = `(9)/(4)`

Step 2: Multiply the numerator and denominator of the improper fraction separately.

Example: consider the two improper fractions.

`(a)/(b)` * `(c)/(d)` , where, a > b and c > d

`(a * c)/(b * d)`  = `(p)/(q)`

Step 3: Now convert the improper fraction by mixed number as following procedure.

Example: `(8)/(5)`

5) 8 ( 1

       5

_________

        3

___________

Mixed number can be written as, quotient as the whole number, remainder is the numerator of the proper fraction and divisor is the denominator of the proper fraction.

`(8)/(5)`  = 1`(3)/(5)`

Examples:

Here are the examples on Multiplying Mixed Numbers

Example 1:

Multiplying the mixed numbers 3 ½ and 6 ¼.

Solution:

Step 1: Convert the mixed numbers 3 ½ to improper fraction, we get

3 ½ = `(7)/(2)`

Step 2: Convert the mixed numbers 6 ½ to improper fraction, we get

6 ¼ =  `(25)/(4)`

Step 3: Multiplying the improper fractions  `(7)/(2)` and `(25)/(4)`, we get

`(7)/(2)` * `(25)/(4)` =  `(175)/(8)`

Step 4: Convert the improper fraction  `(175)/(8)` to mixed number.

8) 175 (21

    16

___________

       1 5

          8

___________

           7

Mixed number  `(175)/(8)` =  `21(7)/(8)`

Answer:  `21(7)/(8)`

Example 2:

Multiplying the mixed numbers 4 ½ and 2 ¾.

Solution:

Step 1: Convert the mixed numbers 4 ½ to improper fraction, we get

4 ½ = `(9)/(2)`

Step 2: Convert the mixed numbers 2 ¾ to improper fraction, we get

2 ¾ = `(11)/(4)`

Step 3: Multiplying the improper fractions `(9)/(2)` and `(11)/(4)`, we get

`(9)/(2)` * `(11)/(4)` = `(99)/(8)`

Step 4: Convert the improper fraction `(99)/(8)` to mixed number.

8) 99 (12

    8

___________

     1 9

     1 6

___________

         3

Mixed number `(99)/(8)` =   `12(3)/(8)`

Answer:   `12(3)/(8)`