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\ 30-Sep-2025 Bharat Arora Proof-9 Reader’s Sign _______________________ Date __________

2. Division by Itself: When a number (other than 0) is divided by itself, the quotient Step 5: Divide 23 tens by 3. We get the quotient 7 and remainder 2.
is 1. Step 6: Bring down the ones digit 1 next to the

Examples: (a) 32 ÷ 32 = 1 (b) 13 × 1 = 13 (c) 340 × 1 = 340 remainder 2, making it 21. 3 4731 1577 Q
3
3. Division of 0 by a Number: Zero divided by any Step 7: Now, divide 21 ones by 3. We get the 17
non-zero number gives the quotient zero. Think Tank quotient 7 and remainder 0. 15
023
Examples: (a) 0 ÷ 18 = 0 (b) 0 ÷ 324 = 0 State true or False. So, the quotient is 1577 and the remainder is 0. 21
Dividing 0 by any number
Thus, Q = 1577 and R = 0.
4. Division by 0: The division of any number by zero always gives a quotient Checking: We have: 021
is not defined. greater than zero. 21
Quotient × Divisor + Remainder 00 (R)
= 1577 × 3 + 0 = 4731 = Dividend
Practice time 4A Hence, the answer is correct.

Fill in the blanks. Example 2: Divide: 5437 ÷ 6.

1. The division of 153 ÷ 9 has Solution: Dividend

dividend = ______, divisor = ______, quotient = ______, remainder = ______ Divisor 6 5437 906 Q

2. The division of 215 ÷ 8 has 54 If the number formed after bringing down a
037
dividend = ______, divisor = ______, quotient = ______, remainder = ______ 36 digit is smaller than the divisor, put a ‘zero’ in
the quotient and bring down the next digit of
3. 4216 ÷ ________ = 4216 4. ______ ÷ 712 = 1 1 R the dividend to continue the process of division.

5. _______ ÷ 152 = 0 6. ______ ÷ 278 = 0 Thus, Q = 906, R = 1.
7. 0 ÷ 1024 = ______________ 8. ______ ÷ 3247 = 1 Checking: Quotient × Divisor + Remainder = 906 × 6 + 1 = 5437 = Dividend
Hence, the answer is correct. 11888
Division of 4- anD 5-Digit numbers by 1-Digit number Example 3: Divide 83218 by 7 and verify your answer. 7 83218
7
In the previous class, we have learnt the division of 3-digit numbers by 1-digit numbers. Solution: Step 1: Divide the ten thousands by 7. 13
Here, we will extend our learning by dividing 4- and 5-digit numbers by 1-digit numbers. 8 ten thousands ÷ 7 = 1 ten thousand and remainder = 1 7
62
Example 1: Divide 4731 by 3. Step 2: Bring down the thousands digit. Divide the thousands, 56
by 7.
Solution: We write the dividend inside the division brackets and the 3 4731 13 thousands ÷ 7 = 1 thousand and remainder = 6 61
56
divisor outside the brackets as shown. Step 3: Bring down the hundreds digit. Divide the hundreds by 7. 58

Step 1: Start dividing from the highest place. Since 4 > 3. Divide 4 62 hundreds ÷ 7 = 8 hundreds and remainder = 6 56
2
thousands by 3. We get the quotient 1 and the remainder 1. Step 4: Bring down the tens digit. Divide the tens by 7.

Step 2: Bring down 7 hundreds along with the remainder 1, making it 17 61 tens ÷ 7 = 8 tens and remainder = 5
hundreds. Step 5: Now, bring down the ones. Be Aware

Step 3: Divide 17 hundreds by 3. We get the Be Aware Divide the ones by 7. The remainder in the division
process should always be less
quotient 5 and the remainder 2. At each step, when 58 ones ÷ 7 = 8 ones than the divisor. If a remainder
another digit is required is more than the divisor, then
Step 4: Bring down the tens digit 3 next to the for division, it is called and remainder = 2 check the division because in
remainder 2, making it 23 tens. “bringing down”. Thus, 83218 ÷ 7 gives Q = 11888 and R = 2. such a case it is incorrect.

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