In division we will see the relationship between the dividend, divisor, quotient and remainder. The number which we divide is called the dividend. The number by which we divide is called the divisor. The result obtained is called the quotient. The number left over is called the remainder.
55 ÷ 9 = 6 and 1
Dividend Divisor Quotient Remainder
For example:
(i) Divide 217 by 4
(ii) Divide 5679 by 7
Remainder, 55 ÷ 9 can also write as 9) 55 ( or 9) 55Note: dividend = divisor × quotient + remainder
The dividend, divisor, quotient and remainder will help us to verify the answer of division. Add remainder (if any) with the product of divisor and quotient. The sum we get should be equal to the dividend.
Let us consider some examples to verify the answer of division.
(i) Divide 38468 by 17 and verify the answer.
Now let us verify the answer; dividend = divisor × quotient + remainder
38468 = 17 × 2262 + 14 = 38454 + 14 = 38468 So, the answer is correct. 
The quotient is 2262 and the remainder is 14.
(ii) Divide 58791 by 36 and verify the answer.
Now let us verify the answer; dividend = divisor × quotient + remainder
58791 = 36 × 1633 + 3 = 58788 + 3 = 58791 So, the answer is correct. 
The quotient is 1633 and the remainder is 3.
Properties of division:
When zero is divided by a number the quotient is zero.
For example:
(i) 0 ÷ 4 = 0
(ii) 0 ÷ 12 = 0
(iii) 0 ÷ 25 = 0
(iv) 0 ÷ 314 = 0
(v) 0 ÷ 225 = 0
(vi) 0 ÷ 7135 = 0
Division of a number by zero is not possible.
For example, we cannot divide 74 by 0.
If we divide any number by 1, the quotient is the number itself.
For example:
(i) 28 ÷ 1 = 28
(ii) 4558 ÷ 1 = 4558
(iii) 335 ÷ 1 = 335
(iv) 9387 ÷ 1 = 9387
If we divide a nonzero number by itself, the quotient is 1.
For example:
(i) 45 ÷ 45 = 1
(ii) 98 ÷ 98 = 1
(iii) 1371 ÷ 1371 = 1
(iv) 5138 ÷ 5138 = 1
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