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Let us try this with an example: 582 ÷ 6 =?

By decomposing the dividend, we can solve it
as shown alongside.

We can also solve it in a different way.
20 + 20 + 20 + 20 + 10 + 7 We will simply use the method where we will not

6 5 8 2 multiply 6 to get closer to 582. Instead, we will reach
– 1 2 0 582 by applying the concept of simple multiplication
4 6 2 by multiples of 10.

– 1 2 0 Here, the quotient is 20 + 20 + 20 + 20 + 10 + 7 = 97.
3 4 2
– 1 2 0 Let us do this in some other way.
2 2 2 90 + 7

– 1 2 0 6 5 8 2
1 0 2 – 5 4 0
– 6 0 4 2
4 2 – 4 2

– 4 2 00
00

Sometimes, a dividend does not get completely 20 + 1 = 21
divided and leaves a remainder. 25 5 3 5

In this case, there is a relationship between the – 5 0 0
dividend, divisor, quotient and remainder which 3 5

is: Dividend = Divisor × Quotient + Remainder. – 2 5
535 = 25 × 21 + 10 1 0

example 1. Divide 9913 by 23.
Solution. 400 + 30 + 1

23 9 9 1 3
– 9 2 0 0 Here, quotient = 400 + 30 + 1 = 431

7 1 3 What did you observe so far?
– 6 9 0 We are basically taking away the largest
2 3 possible groups of divisors in multiples
– 2 3 of 10s and 100s. This can be extended to

00
multiples of 1000, 10000, or even more.

52 Mathematics 5