Multiplication and Division Methods

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Multiplication and Division

Multiplication and division of numbers are the base of mathematics. All the problems of mathematics depend upon the multiplication and division of numbers. Suppose you want to distribute 5 chocolates among 15 of your friends so how many total chocolates do you need ? what will you do to get the result you will add 5 , 15 times isn’t it. But multiplication is the shorthand for repeated addition by using multiplication you can directly multiply 15 × 5 = 75.to distribute  Isn't that quick and easy. Similarly if you want to distribute 60 chocolates among  your 20 friends equally,  how will you calculate? Here comes the division, division will let you find this easily 60 ÷ 20 = 3. So you can distribute 3 chocolates to each of them. But to understand multiplication and division it becomes mandatory to memorize the multiplication table of the numbers. 

So let us study what is multiplication, and how to divide a number, and methods of division.


What is Multiplication?

Multiplication  is an arithmetic operation for finding the product of two numbers which will result in a third number.Multiplication of positive integers consists of adding a number to itself a specified number of times. Multiplication is called repeated addition because it makes repeated addition easier. For example, 5 + 5 + 5 = 5 × 3 = 15. However, as we multiply by whole numbers, we can also multiply by fractions, decimals and more. For example in below figure:

  • The number that is to be multiplied is called the multiplicand here 3 is multiplicand

  • The number by which the multiplicand is multiplied is called the multiplier, here 5 is the multiplier or multiplicator.

  • The result of the multiplication is called the product here 15 is the product.

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Multiplication Methods

The single digit numbers are easily multiplied as we know the multiplication tables. So what about 2 digit multiplication , 3 digit multiplication and so on. So let us study the easy method for multiplication of two or more digit numbers.

Multiplication Using Grid Method

Example: Find the product of 48 and 9

Step 1: Split 48 into 40 and 8

Step 2: Place the numbers in the grid


40

8

9



Step 3: multiply 9 by 40 = 360 and place it below 40 

Step 4: multiply 9 by 8 = 72 place it below 8 


40

8

9

360

72

Step 5: Add 360 and 72 = 432

Therefore 48 x 9 = 432


Multiplication Using Column Method

Column multiplication method is a method used to solve multiplication problems with large numbers.

Example: 469 x 32

Solution:

Step 1: Write down the numbers on top of each other.

Step 2: We begin with the ones placed in the bottom number. This is the 2 in 32. We multiply 2  with 469 and write it down under the line. 

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Step 3: Place a zero at tens place

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Step 4: Multiply the 3 by the top number (469) and write this number next to the zero. 

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Step 5: If there were more numbers we would add more rows and continue to add more zeros. For example, if there were a 3 in the hundreds spot (i.e. the number on the bottom was 332) we would add two zeros in the next row and then multiply 469 by 3. 

Step 6: After we have multiplied all the numbers on the bottom, we add up the rows of numbers to get the answer.

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Division of Numbers

Division is repeated subtraction. Division means sharing in equal numbers, 

In the process of division, the number which is to be divided is called the dividend. The number which is dividing is called the divisor. The number of times the divisor divides dividend is quotient and the number left over after division is called remainder.

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For example in the above figure, the dividend is 68, the divisor is 5 and the quotient is 13 and the remainder is 0.


Methods of Division

How to divide 425 ÷ 5

Solution:

Step 1:  Write the divisor, which is 5 before the division bracket, and write the dividend (425) under it.     

               5)425

Step 2: Consider the first digit of the dividend that is 4. It is smaller than 5 therefore we cannot divide it by 5, so take the first two numbers of the dividend (42) and determine how many 5''s it holds. In this case 42 holds five eights (5*8=40) but not  (5*9=45). Write the 8 as the quotient on top of the division bracket.

   8 

5)425

Step 3: Multiply the 5 by 8 and write the result (40) below 42 of the dividend.

     8 

5)425

    40

Step 4: Put a line under the 40 and subtract it from 42 (42-40=2) and write 2 below 40 of the dividend. Bring down the next number, which is 5 from the 425, and write it to the right of the 2.

   8 

5)425

-  40

-------

   25

Step 5: Divide 25 by 5. In this case 25 contains five fives. Write 5 next to 8 as quotient on top of the division bracket to the right of the 8.

   85

5)425

   40

--------

     25

Step 6: Multiply the 5 of the quotient by the divisor that is 5, and write the result under the dividend. Subtract 25 from 25 to get an answer 0. This results in that there is nothing left over and 5 can be evenly divided into 425 to get a quotient of 85.

   85

5)425

    40

------

      25

      25

--------

      00


Solved Examples

1. Multiply 562 x 22

Solution:

5 6 2

X 2 2 

     -----------------

         1  1  2 4

      1 1  2  4  0

-----------------------

     1  2  3  6  4

2. Divide 342 ÷ 6

Solution:

    5 7

  6 ) 3 4 2

    3 0

-----------

4 2

4 2

---------------

0  0


Quiz Time

  1. Multiply

    1. 67 x 7

    2. 561 x 89

  2. Divide

    1. 678 ÷ 7

    2. 543 ÷ 5


Fun Facts

The Chinese method for multiplication originally involved using bamboo sticks to help them with multiplication, arranging them horizontally and vertically.

Division is the inverse of multiplication.

FAQs (Frequently Asked Questions)

1. What is the Lattice Method of Multiplication?

Answer: Although the lattice method for multiplication is no longer being used right now in school, it is easy to understand.

Example

Multiply 42 and 35

Step 1: Arrange 42 and 35 around a 2 × 2 grid as shown below.

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Step 2: Draw the diagonals of the small squares as shown below.

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Step 3: Multiply 3 by 4 to get 12 and put 12 in the intersection of the first row and the first column as shown below.

Step 4:  multiply 5 and 2 and put the answer in the intersection of the second row and the second column.

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Step 5: Then, going from right to left, add the numbers down the diagonals as indicated with the arrows.

Step 6: The first diagonal has only 0. Bring zero down.

The second diagonal has 6, 1, 0. Add these numbers and bring it down. And so on.

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Step 7: After the grid is completed, what you see in red is the answer that is 1470.

2. What are the Properties of Division?

Answer: 

  • When a non-zero number is divided by 1 , the quotient is the number itself and the remainder is zero

Example: 259 ÷ 1 = 259

  • When zero is divided by a non-zero number, the quotient is zero.

Example: 0 ÷ 34 = 0

  • When a non-zero number is divided by itself we get the quotient as 1 and the remainder is zero.

Example: 78 ÷ 78 = 1

  • We cannot divide a number by zero.

Example: 56 ÷ 0 = not defined

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