There are many types of mathematical operations. One of them is __multiplication__ and others are addition, subtraction and division. Multiplication is an important operation. In Mathematics, the term multiplication means repeated addition.

**Example: **4 5 = 4 + 4 + 4 + 4 + 4 = 20

Along with the whole numbers, we can also multiply by fractions, decimals, and more.

**Example: **5 2 = 5 + 5 + (half of 5) = 12.5

## Terms of Multiplication

There are two terms of multiplication namely multiplicand and multiplier.

**Multiplicand:**A multiplicand is a number that is multiplied by another number known as a multiplier.**Multiplier:**A multiplier is a number that tells how many times multiplicand should be multiplied by the multiplier.**Product:**A product is nothing but the result of multiplying the numbers.

**Example: **6 5 = 30

**Solution:**

Here:

6 is the multiplicand

5 is the multiplier

30 is the product

## Multiplication Symbol

There are a number of multiplication symbols but the most renowned symbol is “ ”(it is read as times). The other symbols of multiplication are “.” (read as a dot), “()” ( read as opening and closing parentheses, and “*” (read as asterisk). For example, 5 4 can be written as 5.4, or 5(6), or 5 * 6.

**Multiplication By 0 and 1**

**Multiplication by 0:** Whenever any number is multiplied by 0 it obtains the product equals zero.

**Example: **8 0 = 0 and 5 0 = 0

**Multiplication by 1: **Whenever any number is multiplied by 1 it obtains the product as the number itself.

**Example: **8 1 = 1 and 5 1 = 1

## Multiplication Properties

**Commutative Property:** This property states that p q = q p. In other words, the commutative property states that products remain the same even if we change the orders of numbers. For example: 8 2 = 16 and 2 8 = 16

** ****Associative Property: **This property states that if p,q, and r are any three whole numbers then (p q) r = p (q r). In other words, the associative property states that whenever three or more numbers are multiplied, the product remains the same regardless of their order. For example: (5 3) 4 = 60, 5 (3 4).= 60, (5 4) 3 = 60

**Distributive Property: This property states that **if p,q, and r are any three whole numbers then:

p (q r) = (p q) + (p r)

(q r) p = (q p) + (r p)

In other words, the distributive property states that the multiplication of the whole number distributes over addition. For example:

5 ( 4 + 3) = (5 4) + (5 3) = 20 + 15 = 35

(4 3) 5 = (4 5) + (3 5) = 20 + 15 = 35

# Division

The next operation is division. This is also somewhat opposite to multiplication. The __division__ is a method of splitting a given value or quantity into equal parts or groups.

** ****For example**, There are 15 biscuits and 3 friends want to share them, how do their friends distribute chocolates.

**Solution: **15 divided by 3 is 5. Hence, each friend gets 5 biscuits.

## Terms of Division

There are four terms of multiplication namely dividend, divisor, quotient, and remainder.

**Dividend:**It is the number that is being divided by in the division process.**Divisor:**It is the number by which dividend is divided in the division process.**Quotient:**It is the result that is obtained in the division process.**Reminder:**It is the number that is left over after the division process.

**Example: **54 6 = 9

6) 54(9

– __54__

__0__

Here:

54 is dividend

6 is divisor

9 is quotient

0 is remainder

## Division Symbol

There are a number of division symbols but the most renowned symbol is “( ”(it is read as obeluses or obeli). The other symbols of division are “/” (read as slash), and “-” (read as fraction or division bar). For example, 20 4 can be written as 20/4, or .

## Division By 0 and 1

**Division by 0:** Whenever any number is divided by 0 it is considered undefined.

**Example: **8 0 is undefined as the denominator here is 0.

**Division by 1: **Whenever any number is divided by 1 it obtains the quotient as the number itself.

**Example: **8 1 = 8, 5 1 = 5

## Division Properties

- Whenever any number is divided by itself, it obtains the quotient as 1.
**For example: 50****50 = 1** - When zero is divided by any number, it obtains the quotient as 0.
**For example: 0****50 = 0** - If any whole number excluding 0 is divided by any other whole number, the quotient obtained is not necessarily a whole number.
**For example : 27****2 = 13.5** - If there are three whole numbers and out of the three whole numbers, one number is dividend and the other two numbers are divisor and quotient. Now, if the value of the divisor and dividend are not equal to zero then the divisor multiplied by quotient obtains dividend. This topic can be practiced in a engaging way from cuemath.
**For example : 24****2 = 12.**Here, 24 is the dividend, 2 is the divisor, and 12 is the quotient. According to the property, the divisor multiplied by the quotient obtains the product as a dividend. Hence, 2 12 = 24.