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\\November 3, 2023 10:57 AM Surender Prajapati Proof 5 Reader _________________________ Date: ___________________74

When a number is divided by another number and a number smaller than the divisor is
left over, the left over number is called the remainder (R).

Larger numbers are divided in the same way as smaller numbers.

Example 1: Divide 504085 by 6 and check the answer.

Solution: 8 4 0 1 4 Quotient Step 1: Since 5 < 6, we divide 2-digit number
Divisor 6 5 0 4 0 8 5 Dividend 50 by 6. 6 × 8 = 48 < 50 and 6 × 9 =
– 4 8 54 > 50. So, subtract 48 from 50 and
2 4
– 2 4 bring down 4.
0 8 Step 2: 24 is the new dividend. Here, 6 × 4
– 6 = 24. Subtract 24 from 24 and bring
2 5 down 0.
– 2 4
1 Remainder Step 3: Since 0 < 6, put 0 in quotient and
bring down 8. Now, 08 is the new

Checking: partial dividend. Here, 6 × 1 = 6 < 8
Quotient × Divisor + Remainder and 6 × 2 = 12 > 8. So, subtract 6
= Dividend from 8 and bring down 5.
84014 × 6 + 1 = 504084 + 1 Step 4: 25 is the new dividend. Here, 6 × 4 =

= 504085. 24 < 25, Subtract 25 – 24 = 1. Now,
The division is correct. no number is left to bring down, so,
stop the process.

Thus, Quotient = 84014 and Remainder = 1

Example 2: Find the quotient and remainder for the following and check the answer.
(a) 86345 ÷ 23 (b) 621575 ÷ 25

Solution: 3 7 5 4 Q Step 1: Since 8 < 23, we divide 86 by 23.
(a) Divisor 23 8 6 3 4 5 Dividend We do not know the table of 23,
– 6 9
1 7 3 so think: 2 8 is 4. 23 86 is about 4.
– 1 6 1 Multiply 23 × 4 = 92 > 86

1 2 4 so, take 23 × 3 = 69 < 86.
– 1 1 5 Subtract 69 from 86 and bring down 3.

9 5 Step 2: Now, the new dividend is 173 > 23.
– 9 2
3 R Divide 23 173
Think: 2 17 is about 8.

Thus, 23 173 is about 8.
Multiply 23 × 8 = 184 > 173,

so take 23 × 7 = 161 < 173
Subtract 161 from 173 and bring down 4.

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