Division by 10 and 100 and 1000 are explained here step by step. We know the following facts regarding division process:
1. (i) When any number is divided by 1, the quotient is the number itself.
(a) 7 ÷ 1 = 7
(b) 53 ÷ 1 = 53
(c) 275 ÷ 1 = 275
(ii) When a number (except 0) is divided by itself, the quotient is 1.
(a) 7 ÷7 = 1
(b) 53 ÷ 53 = 1
(c) 275 ÷ 275 = 1
(iii) When zero (0) is divided by any number, the quotient is zero (0), but no number can be divided by zero (0).
(a) 0 ÷ 8 = 0, 0/8 = 0, 0 ÷ 115 = 0, 0/115 = 0
(b) 0 ÷ 0 has no meaning, 10 ÷ 0 has no meaning, 15 ÷ 0 has no meaning.
2.
When a number is divided by 10, the digits, except the digit at the
one's place, make the quotient and the digit at one's place becomes the
remainder.
As for example:
(i) 48 ÷ 10
Quotient = 4 Remainder = 8
(ii) 76 ÷ 10
Quotient = 7 Remainder = 6
(iii) 492 ÷ 10
Quotient = 49 Remainder = 2
(iv) 178 ÷ 10
Quotient = 17 Remainder = 8
(v) 569 ÷ 10
Quotient = 56 Remainder = 9
(vi) 4183 ÷ 10
Quotient = 418 Remainder = 3
Thus, when a. number is
divided by 10, the remainder is always the digit of the unit place and
the quotient is the number made by the remaining digits.
Therefore,
notice that on dividing by 10, the digit in the ONES place forms the
remainder, while the remaining digits form the quotient.
3. When
a number is divided by 100, the quotient is the number made by the
digits, except the digits at one's and ten's places. The number formed
by ten's and one's digit of the dividend number is the remainder.
As for example:
(i) 476 ÷ 100
Will give quotient 4 remainder 76
(ii) 3479 ÷ 100
Will give quotient 34 remainder 79
The number of digits in the remainder is equal to the number of zeros in the divisor.
(iii) 527 ÷ 100
Quotient = 5 Remainder = 27
(iv) 609 ÷ 100
Quotient = 6 Remainder = 9
(v) 7635 ÷ 100
Quotient = 76 Remainder = 35
(vi) 7635 ÷ 100
Quotient = 30 Remainder = 79
Thus, when the
dividend number is divided by 100, the extreme right two digits form the
remainder and the rest of the digits form the quotient.
Therefore,
when we divide by 100, the two digits in the ONES and the TENS place
form the remainder while the remaining digits form the quotient.
4. Following this method, when we divide by 1000, the remainder will have 3 digits.
When
a number is divided by 1000, the quotient is the number made of the
digits except the digits at one's, ten's and hundred's place. The number
formed by these three digits is the remainder.
As for example:
(i) 1379 ÷ 1000
Will give quotient 1 remainder 379
(ii)45362 ÷ 1000
Will give quotient 45 remainder 362
The 3 digits in the ONES, TENS, HUNDREDS places form the remainder.
(iii) 3851 ÷ 1000
Quotient = 3 Remainder = 851
(iv) 9874 ÷ 1000
Quotient = 9 Remainder = 874
(v) 35786 ÷ 1000
Quotient = 35 Remainder = 786
Thus, when the dividend
number is divided by 1000, the extreme right three digits form the
remainder and the rest digit/digits form the quotient.
Division of a number by 20, 30, 40.....
(i) 80 ÷ 20
20 × ____ = 80
2 × 4 = 8
So, 20 × 4 = 80
70 × ____ = 140
7 × 2 = 14
So, 70 × 2 = 140
(iii) 900 ÷30
30 × ____ = 900
3 × 3 = 9
30 × 3 = 90
So, 30 × 30 = 900
(iv) 320 ÷ 80
80 × ____ = 320
8 × 4 = 32
So, 80 × 4 = 320
Related Concept
● Addition
● Check for Subtraction and Addition
● Word Problems Involving Addition and Subtraction
● Estimating Sums and Differences
● Multiply a Number by a 2Digit Number
● Multiplication of a Number by a 3Digit Number
● Word Problems on Multiplication
● Division of TwoDigit by a OneDigit Numbers
● Division of FourDigit by a OneDigit Numbers
● Division by 10 and 100 and 1000
● Division by TwoDigit Numbers
4th Grade Math Activities
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