A dividend is a whole number is being divided. It is the value that must be divided into equal portions. Addition, subtraction, multiplication, and division are the four basic operations of numbers.
The division of a number into equal parts is a method that leaves a remainder of the given number that cannot be divided equally into parts. For example, if 10 is divided by 2, the result is two equal parts of 5, with 10 being the dividend.
Terminologies Applied to Divisional Operations:
When doing division operations in arithmetic, we can see four related terms: dividend, divisor, quotient, and remainder. As a result, division with a remainder, often known as Euclidean division, includes the following:
 Dividend – The number to be divided by the divisor is called the dividend. For example, if we have 20 chocolates to distribute to 5 children, we must divide the 20 chocolates by 5, resulting in 4 chocolates for each child. As a result, the dividend, in this case, is 20.
 Divisor – A divisor is a number by which the dividend is divided or the number that divides the dividend.
 Quotient – The quotient is the consequence of the division.
 Remainder – The remainder is the number that remains after division.
Formula for Dividend
To calculate dividend in division–
Dividend = Divisor x Quotient+Remainder is the formula for calculating the dividend in math.
Normally, when we divide one number by another, we get an answer, such as x/y = z.
The dividend is x, the divisor is y, and the quotient is z.
Important division rules:
Rule 1: The resultant (quotient) is always zero when you divide a number by zero.
Examples:
(i) 0 ÷ 25 = 0
(ii) 0 ÷ 2 = 0
(iii) 0 ÷ 100 = 0
(iv) 0 ÷ 78 = 0
Rule 2: The resultant (quotient) is always the number itself when you divide a number by one.
Examples:
(i) 32 ÷ 1 = 32
(ii) 658 ÷ 1 = 658
(iii) 8 ÷ 1 = 8
(iv) 500 ÷ 1 = 500
Rule 3: When you divide a number by itself, the resultant (quotient) is always 1.
Examples:
 50 ÷ 50 = 1
 108 ÷ 108 = 1
 400 ÷ 400 = 1
 28 ÷ 28 = 1
Example: If a number is divided by 9, the quotient is 6, and the remainder is 1. Determine the number.
Solution: Assume the dividend is x.
Using formula,
Dividend = Divisor x Quotient Remainder
(9 x 6)+1 = x
54+1 = 55
As a result, the dividend is 55.
Example: In total, there are 120 books on 6 shelves in a room. Calculate the number of books on each shelf, knowing that they all have the same number of books.
Solution: Number of books in a room = 120
Using formula,
Dividend = Divisor x Quotient Remainder
Books on each shelf = 120 ÷ 6 = 20
20 books will be there on each shelf.
Formula for Divisor
How do you calculate the divisor? Let us look at the divisor formula when the remainder is 0 and a nonzero number.
If the remainder is zero, Divisor = Dividend x Quotient.
If the remainder is greater than zero, then Divisor = (Dividend – Remainder) ÷ Quotient.
Example: What will be the divisor when dividend = 41, quotient = 7 and remainder = 6.
Solution: Using formula,
Dividend = Divisor x Quotient Remainder
Divisor = (Dividend – Remainder)÷ Quotient.
Divisor = (41 – 6) ÷ 7
Divisor = 35 ÷ 7
Divisor = 5
Example: How much rice will each jute bag contain if 9880 Kg of sugar is packed in 95 jute bags?
Solution: The amount of sugar packed in 95 jute bags equals 9880 kg.
Using formula,
Dividend = Divisor x Quotient Remainder
Divisor = (Dividend – Remainder)÷ Quotient.
The amount of rice packed in one bag is 9880 ÷ 95 = 104.
Dividend = 9880, Divisor = 95
104 is the quotient, and 0 is the remainder.
As a result, each bag will contain 104 kg of sugar.
Formula for Quotient
When one number completely divides another number, the remainder is 0. The divisor is always greater than the remainder. If the remainder is greater than the divisor, the division is considered incomplete. It can be either greater or less than the quotient.
When the remainder is 0
Dividend ÷ Divisor = Quotient.
Consider the following example: 39 ÷ 3 = 13.
Dividend = 39 in this case.
Quotient = 13
Divisor = 3
‘Remainder’ equals ‘0’.
Example: What is the quotient of 26 ÷2?
Ans: Dividend = 26
Divisor = 2
Using Division formula,
Dividend = Divisor x Quotient Remainder
We get,
Dividend / Divisor = Quotient
Quotient= 13
Conclusion
The students should go through the formula, definition and examples based on the dividend. A thorough study and a good amount of practice will help them to be well versed with dividends and their important rules.
Solved Questions
Ques 1. What is the mathematical dividend?
Ans. The dividend is the number that will be split in the division operation in mathematics. It is a whole that is broken down into bits.
Ques 2. What is the formula for calculating the dividend?
Ans. Dividend = Divisor x Quotient Remainder is the formula for calculating the dividend.
Ques 3. If the quotient is 58 and the divisor is 2, find the dividend.
Ans. The dividend is 116 if the quotient is 58 and the divisor is 2.
Because Dividend = Quotient x Divisor
Dividend = 58×2 = 116 as a result.
Ques 4. What are the various terms used in the division procedure?
Ans. The following are the various terminologies used in the division process:

Dividend

Divisor

Quotient

Remainder
Ques 5. If y/2 = 30, find the value of y.
Ans. y has a value of 60. As y = 30 x 2, the result is 60.
Ques 6. What Does the Dividend Divisor Quotient Remainder Formula Mean?
Ans. Dividend, divisor, quotient, and remainder are the four primary components of the dividend divisor quotient remainder formula employed in the division method. The dividend divisor quotient remainder Formula can be used to check if the division procedure was completed correctly using the traditional division method. It’s essentially the division approach in reverse. Dividend = Divisor x Quotient Remainder is the formula.
Ques 7. What Happens When the Dividend Divisor Quotient Remainder Formula is used with a value of zero?
Ans. There are three possibilities when zero is used in the dividend divisor quotient remainder formula:
 The quotient is zero when zero is divided by a number.
 It is not possible to divide a number by zero.
 The remainder is zero if the dividend is completely divisible by the divisor.
Ques 8. Which number is the divisor of all the numbers?
Ans. 1
Ques 9. Find the value of 1000 by 50 by using the division formula. What will be the quotient?
Solution:
To find: The quotient
Dividend = 1000.
Divisor = 50.
Using Division Formula,
Dividend / Divisor = Quotient
(1000/50) = 20
= 20
Ques 10. What is the formula for calculating the divisor if dividend and quotient are given?
Ans. Dividend = Divisor x Quotient+Remainder
Divisor = (Dividend – Remainder)÷ Quotient.