What is Multiplication and Division in Maths?

In mathematics, there are four basic operations.

  • Addition (+)
  • Subtraction (-)
  • Multiplication (×)
  • Division (÷)

What is Multiplication?

Multiplication is the repeated addition of a number. If we multiply m by n, that means m is repeatedly added to itself for n times. The symbol for multiplication is ‘×’.

For instance, 8 multiplied by 4 is equal to 32. How? Adding 8, 4 times to itself,  we get;

8 + 8 + 8 + 8 = 32

Therefore, we can write,

8 x 4 = 32

What is Division?

The division is a method of dividing or distributing a number into equal parts, For example, if 16 is divided by 4, then 16 is divided into 4 equal parts. Therefore, the resultant value is 4.

16 ÷ 4 = 4

Parts of division

Dividend ÷ Divisor = Quotient

15 ÷ 3 = 5

In the above example, there are three parts for division.

  • 15 is dividend
  • 3 is divisor
  • 5 is quotient (R.H.S)

Multiplication and Division Relationship

Multiplication and division, are inverse operations of each other. If we say, a multiplied by b is equal to c, then c divided by b results in a. Mathematically, it can be represented as:

  • a × b = c
  • c ÷ b = a

For example, 

  • 4 x 5 = 20   [4 multiplied by 5 results in 20]
  • 20 ÷ 5 = 4   [20 divided by 5 returns back 4]

Multiplication and Division Rules

For every mathematical computation, we need to follow the rules. Thus even to multiply and divide the numbers, there are some rules which we need to follow.

Rule 1: Order of operations

The order of operations for multiplication does not matter. It means if we arrange the number in a different order while multiplying them, then the result will be the same. 

Examples are:

3 x 4 = 12

4 x 3 = 12

In the above example, we can see, even if we have swapped the position of 3 and 4, the product of the two integers is equal to 12.

But this rule is not applicable for division. Let us take another example.

12 ÷ 3 = 4

3 ÷ 12 ≠ 4  (it is equal to 0.25)

Thus, we cannot change the order of numbers in division method.

Rule 2: Multiplying and Dividing by Positive Numbers

If any real number is multiplied or divided by the positive real number, then the sign of the resulting number does not change.

Examples are:

2 x 3 = 6

-2 x 3 = -6

Since, 2 and 3 both are positive integers, therefore the product of 2 and 3 is also positive. But the product of -2 and 3 is a negative number.

4 ÷ 2 = 2

-4 ÷ 2 = -2

Since, 4 and 2 both are positive, therefore, 4 divided by 2 is also a positive number. But -4 divided by 2 is a negative number.

Thus, we can conclude that:

  • (+)  x  (+)   = (+)
  • (+)  ÷  (+)   = (+)
  • (-)   x  (+)   =  (-)
  • (-)  ÷  (+)   = (-)

Rule 3: Multiplying and Dividing by Negative Numbers

Multiplication and division of any real number by a negative number will change the sign of the resulting number. Examples are given below.

  1. Multiply 5 by -2.

5 x -2 = -10

  1. Multiply -5 by -2.

-5 x -2 = 10

  1. Divide 10 by 2.

10 ÷ -2 = -5

-10 ÷ -2 = 5

Thus we can conclude that:

  • (+) x (-) = (-)
  • (+) ÷ (-) = (-)
  • (-) x (-) = (+)
  • (-) ÷ (-) = (+)