A dividend is a whole number or the number of things that need to be divided into certain equal parts. There are four basic operations on numbers named as addition, subtraction, multiplication, and division. The division is a process of dividing a number into equal parts leaving behind a reminder if the given number cannot be divided into the parts equally. Thus, division with a remainder or Euclidean division contains the following:

Dividend - Dividend is the number that is to be divided by the divisor.

Divisor - The number by which the dividend is to be divided is called the divisor.

Quotient - The resultant of the division is called the quotient.

Remainder - The number that is left after division is called the remainder.

In this article, we are going to discuss the definition and formula of dividends. We will also learn the methods of finding dividend.

Division with No Remainder:

For example, you have 20 candies and you need to divide equally among 4 children. On dividing the candies equally, each one of them gets 5 candies.Consider In this case, the number of candies (i.e, 20) which was to be divided among children is called the dividend, the number of children (i.e, 4) among whom it is to be divided is called the divisor. Remember, the divisor divides the dividend or in other words dividend gets divided by the divisor. The result of the equal distribution, that is the number of candies with each member is called the quotient.

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Dividend = 20

Divisor = 4

Quotient = 5

Remainder = 0

Division with The Remainder:

Consider the same aforementioned example but with a modification. Suppose this time the candies are to be distributed among 3 members, that is 20 candies are to be distributed among three children. The division is shown below:

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Here, the candies are equally distributed among 3 children such that each having 6 candies but 2 candies are left which cannot be divided into three as a whole. Thus, the remainder of this division is called the remainder.

Here,

Dividend = 20

Divisor = 3

Quotient = 6

Remainder = 2.

If the value of divisor, quotient, and remainder is given then we can find dividend divided by the following dividend formula:

Dividend = Divisor x Quotient + Remainder.

It is just the reverse process of division. In the example above we first divided the dividend by divisor and subtracted the multiple with the dividend. That means, we first divided and then subtracted. Thus, to find the dividend we need to do the opposite, that means we first need to multiply instead of dividing and then add instead of subtracting.

Here are dividend examples for you for a better understanding of the concept:

Suppose we need to divide 11 into 2 equal whole parts. The resultant will be with a remainder 1.

Here, dividend = 11, divisor = 2, quotient = 5 and remainder = 1.

As per the dividend formula,

Dividend = Divisor x Quotient + Remainder.

11 = (2 x 5) + 1

11 = 10 + 1

11 = 11

LHS = RHS.

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Hence the formula of dividend is

We can find dividends by using the formula of dividends.

Example: A number is divided by 9 giving 6 as a quotient and leaving behind remainder 1. Find the number.

Solution: Let the dividend be x

x = (9 x 6) + 1

= 54 + 1

= 55

Therefore, the value of the dividend is 55.

Rule 1: Whenever a number is divided by zero, the resultant (quotient) is always zero.

Examples:

(i) 0 ÷ 4 = 0

(ii) 0 ÷ 12 = 0

(iii) 0 ÷ 25 = 0

(iv) 0 ÷ 314 = 0

(v) 0 ÷ 225 = 0

(vi) 0 ÷ 7135 = 0

Rule 2: Whenever a number is divided by one, the resultant (quotient) is always the number itself.

Examples:

(i) 28 ÷ 1 = 28

(ii) 4558 ÷ 1 = 4558

(iii) 335 ÷ 1 = 335

(iv) 9387 ÷ 1 = 9387

(v) 6789754 ÷ 1 = 6789754

Rule 3: Whenever a number is divided by itself, the resultant (quotient) is always 1.

Examples:

(i) 45 ÷ 45 = 1

(ii) 98 ÷ 98 = 1

(iii) 1371 ÷ 1371 = 1

(iv) 5138 ÷ 5138 = 1

(v) 6758 ÷ 6758 = 1

FAQ (Frequently Asked Questions)

1. What are the componendo and dividendo rule in maths?

The componendo and dividendo rule makes life so much easier.

We can consider the following equation:

x/a = y/b

Then, by using componendo and dividendo rule, we can write the above expression as: (x-a)/(x+a) = (y-b)/(y+b)

2. What are the uses of division?

Division is one of the basic operations which is usually introduced to the students of a lower standard to give them the earliest opportunity to step into the real mathematical world. The concept of division familiarises them with the calculations in day to day lives. They can learn to handle money, share items between friends or cut food into equal portions, etc, This way they can begin to develop their division skills as part of their everyday life. Being introduced to these ideas at an early age will not only make them smarter with calculations but also helps them gain confidence in the wider world.

3. What happens when a number is divided by 2?

One of the important properties of division is the division of a number by 2. Whenever you divide a number by 2, the resultant is always half of the number. For example, a dividend 36 is divided by 2, the quotient is 18 which is exactly half of 36. To check we can find the sum of 18 and 18 that is twice of 18, we can see the result is 36.