Mixed Number Multiplication

Mixed number is a combination of a whole number and a proper fraction. A mixed number can be converted into an improper fraction and vice versa. All of the arithmetic operations can be performed by using the mixed numbers. For example, 2 (1)/(2) is a mixed numbers. In this example, the 2 is called as the whole number and (1)/(2) is called as the improper fraction

It will be easier to perform arithmetic operations on mixed numbers by first converting them to improper fractions

Rules for the multiplication of mixed number

There are many rules are followed for the multiplication of mixed numbers, They are given as follows,

In the first step, we have to convert the given mixed number into the improper fraction.
In the next step, we have to perform the multiplication for the numerator part
In the next step, we have to perform the multiplication in the denominator part
Then, the next step we have put this in an improper fraction.
Then the next step is simplify those improper fractions.
Then the result is converted into a mixed number.


Example problem for the mixed number multiplication

Problem 1: Multiply the given mixed numbers, 2 (4)/(6) with 1  (6)/(9) .

Solution:

Step 1: Write the mixed numbers

2(4)/(6) xx 1 (6)/(9)

Step 2: Convert the given mixed numbers into improper fractions

(16)/(6) xx (15)/(9)

Step 3: Perform the multiplication operation for the numerator terms,

16 xx 15 =240

Step 4: Perform the multiplication operation for the denominator terms,

6 xx 9 =54

Step 5: The result obtained for step 3 and 4 can be combined to an improper fractions

(240)/(54)

= (120)/(17)

This is the required solution for the multiplication of mixed numbers.

Problem 2: Multiply the given mixed numbers, 4 (2)/(7) with 7  (2)/(8) .

Solution:

Step 1: Write the mixed numbers

4 (2)/(7) xx 7 (2)/(8)

Step 2: Convert the given mixed numbers into improper fractions

(30)/(7) xx (56)/(8)

Step 3: Perform the multiplication operation for the numerator terms,

30 xx 56 = 1680

Step 4: Perform the multiplication operation for the denominator terms,

7 xx 8 = 56

Step 5: The result obtained for step 3 and 4 can be combined to an improper fractions

(1680)/(56)

= (840)/(28)

=(420)/(14)

=(210)/(7)

= 30

This is the required solution for the multiplication of mixed numbers.