Dividend, Divisor, Quotient and Remainder
Division is the process of sharing
things into equal groups.
Suppose we have 15 balls
and these are to be shared equally into 3 children.
You can see from the
following figure that each group has 5 balls. It means each child will get 5
balls.
Division is denoted by the symbol ‘÷’.
So, the statement when 15 balls are shared
equally among 3 children, each child will get 5 balls, can be written in
division form as:
15 ÷ 3 = 5
In the above division equation, 15 is called dividend, 3 is
divisor and 5 is quotient.
Thus,
The number which is to
be divided is called the dividend.
The number which divides
the dividend is called the divisor.
The result is called the
quotient.
The leftover, if any, is
called the remainder. Here, no balls are leftover, therefore the
remainder is 0.
Division is a repeated subtraction.
Division can be done using repeated subtraction.
Let us divide 15 by 5. Subtract 5 from 15
again and again until you get zero.
Step 1: Subtract 5 from
15.
15 – 5 = 10
Step 2: Subtract 5 from
10.
10 – 5 = 5
Step 3: Subtract 5 from
5.
5 – 5 = 0
We subtracted 3 times.
Thus, 15 ÷ 5 = 3
Dividend, Divisor,
Quotient and Remainder Formula
There is a relationship between the
dividend, divisor, quotient and the remainder. This relationship is called the
dividend, divisor, quotient and the remainder formula.
Let us divide 122 by 5 and find the
quotient and the remainder.
Here, quotient is 24 and remainder is 2. The dividend is 122 and the divisor is 5.
If we multiply quotient (24) by the
divisor (5) and add the remainder (2), we get the dividend (122).
The above relation is called the dividend, divisor, quotient and remainder formula.
According to this formula:
Quotient
× Divisor + Remainder = Dividend
Or
Dividend
= Quotient × Divisor + Remainder
Dividend
Definition
As discussed
earlier, the number to be divided is called the dividend.
For example: If 12 is divided by 3, 12 is called the
dividend.
Divisor
Definition
As discussed
earlier, the number by which the dividend is divided is called the divisor.
For example: If 12 is divided by 3, 12 is called the
dividend and 3 is called the divisor.
You can see the divisor is shown in
the above division problem.
Quotient
Definition
We
know that the result obtained after division is called the quotient.
For example: If 13 is divided by 5, the quotient is 2.
Remainder Definition
The number which is
leftover after finding the quotient is called the remainder.
For example: If 13 is divided by 5, the quotient is 2.
After division, 3 is left over. Therefore, 3 is the remainder.
You can see the remainder is shown in
the above division problem.
Properties of
Division
1. If we divide 0 by another number, the quotient is always
zero.
For example:
(i) 0 ÷ 8 = 0
(ii) 0 ÷ 16 = 0
(iii) 0 ÷ 245 = 0
(iv) 0 ÷ 136 = 0
(v) 0 ÷ 2748 = 0
2. If a number is divided by 1, the quotient
is always the number itself.
For example:
(i) 6 ÷ 1 = 6
(ii) 36 ÷ 1 = 36
(iii) 216 ÷ 1 = 216
(iv) 475 ÷ 1 = 475
(v) 6812 ÷ 1 = 6812
3. If a number is divided by itself,
the quotient is always 1.
For example:
(i) 9 ÷ 9 = 1
(ii) 57 ÷ 57 = 1
(iii) 375 ÷ 375 = 1
(iv) 1746 ÷ 1746 = 1
(v) 7583 ÷ 7583 = 1
Let us consider a few examples to
verify the answer of division.
Example 1: Divide 67 by 3. Find the quotient and
remainder.
Solution: Let us divide 67 by 3.
Here, Dividend = 67
Divisor = 3
Quotient = 22
Remainder = 1
Example 2: Divide 962 by 15. Find the quotient and
remainder.
Solution: Let us divide 962 by 15.
Here, Dividend = 962
Divisor = 15
Quotient = 64
Remainder = 2
Example 3: Divide 4368 by 9. Verify the answer.
Solution: Let us divide 4368 by 9.
Here, Dividend = 4368
Divisor = 9
Quotient = 485
Remainder = 3
Now, let us verify the answer.
Quotient × Divisor + Remainder =
Dividend
485 × 9 + 3 = 4368, which is dividend.
Hence, verified.
Example 4: Divide 8569 by 6. Verify the answer.
Solution: Let us divide 8569 by 6.
Here, Dividend = 8569
Divisor = 6
Quotient = 1428
Remainder = 1
Now, let us verify the answer.
Quotient × Divisor + Remainder =
Dividend
1428 × 6 + 1 = 8569, which is
dividend.
Hence, verified.