# Division

Most of the division calculations can be done by approximation techniques without actually finding the original value.

Example

Solution

Let us approximate this value.

There are three golden rules of approximation:

There are three golden rules of approximation:

- Range of approximation should be 2% with respect to the actual result.
- Approximation should be done only if the options are at a considerable gap, say 5% atleast.
- One of the key things to be kept in mind while doing approximation is the direction of the approximation i.e., one should know if the actual result will be more or less than the approximated result.

We should know that in any division, if the numerator and the denominator are both either increased or decreased by the same percentage, then the result will be exactly the same. While it is practically not possible to find such situations always, we will use this to know the direction while doing approximation for the above calculation:

# Approximation 1

Eliminate the unit digit of both the numerator and the denominator

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Now, the objective is to break the numerator into the parts of the denominator.
354 = 209(50% of 418) + 145
145 = 105(25% of 418 approx.) + 40
40 = 10% of 418

Hence, net value = 85% = 0.85
Is this value more or less than the actual value?
Let us compare it with the actual result = 0.8483, which is a slightly less than the approximated result of ours.

# Approximation 2

Eliminate the unit and tens place digit of both the numerator and the denominator

35 = 20.5(50% 0f 41) + 14.5
14.5 = 12(30% of 40 approx.) +2.5 = 30% of 41 + 6% of 41(approx.)
[Since 0.41 = 1% of 41]
Hence, net value = 86% = 0.86. This is slightly more than the actual value.