I don't know approximate division please tell me about it and where to use with examples
As we grow, we tend to get habituated in our day to day calculations and employ conventional methods without thinking whether it is the best for a given scenario. Many a time there will be an approach that is much easier than the conventional methods to solve a given problem. Most of the so called calculation intensive questions are not that scary if we think a bit before solving them. As a rule of thumb, always spend few seconds to identify the best approach before start solving.
Some useful methods are given below which can help in our calculations.
To approximate Actual values
If (and only if) we need to find the actual value of a given fraction, represent the numerator as sum or difference of terms related to denominator.
1449/132 =
1449 = 1320 + 132 – 3
1449/132 = 10 + 1 – a small value ≈ little less than 11 (actual value is 10.977)
36587 / 123 =
36587 = 36900 – 246 – 61.5 - …
36587 / 123 = 300 – 2 - 0.5 – a small value ≈ little less than 297.5 (actual is 297.455)
1569 / 12 =
1569 = 1200 + 360 + 8.4 + 0.6
1569 / 12 = 100 + 30 + 0.7 + 0.05 = 130.75
This method should suffice for the level of accuracy expected in our exams.
Another method is to reduce the complexity of fraction and then solve. Complexity of a fraction can be directly related to the complexity of its denominator. If we simplify denominator, we simplify the fraction. Add to or subtract from the denominator to make it an easier value (like add 2 to 1998 to get 2000 or subtract 16 from 116 to get 100).
While adjusting the denominator always remember to BALANCE the fraction. Balancing fraction is not just adding/subtracting the same number to/from the numerator that we used to change the denominator.
Consider a fraction p/q = n; then p = qn.
If we add a number x to q, we need to add nx to p to balance the fraction. Also if q is reduced by a number x, p needs to be reduced by nx.
Here the approximation comes while fixing n. If the given options are separated well enough from each other and simplification of denominator is pretty obvious, then this method can be employed. If we have closer options it is better to stick with the method we discussed first.
1569 / 12 = ?
Here if we make the denominator as 10 we can tell the value in no time. To do so, we need to subtract 2 from denominator. Numerator is more than 130 times the denominator (n ≈ 130). Hence to balance the fraction we need to subtract 2 * 130 from numerator.
1569 / 12 ≈ 1309 / 10 ≈ 130.9 (actual value is 130.75)
As we grow, we tend to get habituated in our day to day calculations and employ conventional methods without thinking whether it is the best for a given scenario. Many a time there will be an approach that is much easier than the conventional methods to solve a given problem. Most of the so called calculation intensive questions are not that scary if we think a bit before solving them. As a rule of thumb, always spend few seconds to identify the best approach before start solving.
Some useful methods are given below which can help in our calculations.
To approximate Actual values
If (and only if) we need to find the actual value of a given fraction, represent the numerator as sum or difference of terms related to denominator.
1449/132 =
1449 = 1320 + 132 – 3
1449/132 = 10 + 1 – a small value ≈ little less than 11 (actual value is 10.977)
36587 / 123 =
36587 = 36900 – 246 – 61.5 - …
36587 / 123 = 300 – 2 - 0.5 – a small value ≈ little less than 297.5 (actual is 297.455)
1569 / 12 =
1569 = 1200 + 360 + 8.4 + 0.6
1569 / 12 = 100 + 30 + 0.7 + 0.05 = 130.75
This method should suffice for the level of accuracy expected in our exams.
Another method is to reduce the complexity of fraction and then solve. Complexity of a fraction can be directly related to the complexity of its denominator. If we simplify denominator, we simplify the fraction. Add to or subtract from the denominator to make it an easier value (like add 2 to 1998 to get 2000 or subtract 16 from 116 to get 100).
While adjusting the denominator always remember to BALANCE the fraction. Balancing fraction is not just adding/subtracting the same number to/from the numerator that we used to change the denominator.
Consider a fraction p/q = n; then p = qn.
If we add a number x to q, we need to add nx to p to balance the fraction. Also if q is reduced by a number x, p needs to be reduced by nx.
Here the approximation comes while fixing n. If the given options are separated well enough from each other and simplification of denominator is pretty obvious, then this method can be employed. If we have closer options it is better to stick with the method we discussed first.
1569 / 12 = ?
Here if we make the denominator as 10 we can tell the value in no time. To do so, we need to subtract 2 from denominator. Numerator is more than 130 times the denominator (n ≈ 130). Hence to balance the fraction we need to subtract 2 * 130 from numerator.
1569 / 12 ≈ 1309 / 10 ≈ 130.9 (actual value is 130.75)
