Bank jobs are one of the most sought after government jobs in India, where the competition is increasing every year. Form all the sections that are asked in bank exams, Maths is the most important. If you are good in Maths, you are sure to grab more marks in quantitative aptitude. You can score full marks in Maths if your calculation is accurate, as well as what matters the most during these exams is speed and accuracy. Mathematics is all about calculations, which by nature is time consuming, so here I have bring some rapid calculation tips that will help you do speed calculations with accuracy.
Here in this article, I will discuss following topics in detail for faster and accurate calculations to help you score good in bank exams.
- Fast Calculation of huge number multiplication by 9’s
- Multiplication of big number will be easy and rapid by Crisscross method
- Faster Calculation Trick for Square of 3 digits & 4 digits number
- Square estimation technique for Rapid calculation at Bank Exams
- Fast calculation tricks to get Cube of numbers
- Rapid division method
- Addition Guestimation
Crack your bank exams with vedic maths, let’s get started…..
Fast Calculation of huge number multiplication by 9’s
This technique is for the multiplication of any numbers with 9’s; either its 9 or 99 or 999 or so on.
It can be done by combination of 2 ways (sutras):
One less than before
All from 9 and last from 10
Let’s understand this method by an example:
e.g.: 756 x 999
Step 1: according to first sutra ( one less than before ), deduct 1 number from 756. i.e.: 756 – 1 = 755
Step 2: applying the second sutra ( all from 9 and last from 10) on 756. i.e.: 9-7 = 2 ; 9 – 5 = 4 ; 10 – 6 = 4
The new number is 244.
Now combining both steps to get an answer, we get 755244.
Therefore: 756 x 999 = 755244
(Tip: How to get answer within few seconds from the options of the problem sum?
If options are having different last digits at the end then you can directly get the answer by multiplying last digits of the multiplying numbers. e.g.: 756 x 999 ; 6 x 9 = 54 ; option with last digit 4 is your answer)
Multiplication of big number will be easy and rapid by Crisscross method
It is the one of the traditional method of doing multiplication of small and big numbers, in a comparatively short time span.
This method is known as ‘ Urdhva – Tiryak Sutra‘, means vertical and cross wise, which has been modified to Crisscross method.
It helps to multiply any length of number or any combination of number. It means it is applicable to all type of multiplication.
Let’s learn it with some examples with different digit numbers:
Crisscross method with 3 digits number
Lets multiply – 328 x 261
Simplify the numbers (328 x 261) ≈ (abc x pqr)
a=3, b=2, c=8 & p=2, q=6, r=1
Pattern for multiplication:
(a x p) / (a x q) + (b x p) / ( a x r) + (b x q) + (c x p) / (b x r) + (c x q) / (c x r)
As per the method,
= (3 x 2) / (3 x 6) + (2 x 2) / ( 3 x 1) + (2 x 6) + (8 x 2) / (2 x 1) + (8 x 6) / (8 x 1)
= 6 / 18 + 4 / 3 + 12 + 16 / 2 + 48 / 8
= 6 / 22 / 31 / 50 / 8
Here, is the step you need to take care, how to write final answer? You need to start from last digit, that is 8, then move to 2nd last number that is 50, take 0 as the second last digit of the answer number and carry of 5 to middle number that is 31 (31 + 5), so the new number is 36, take 6 as the third last digit of the answer number and carry 3 to the second number 22 (22 + 3), so the new number is 25, take 5 as the four last digit of the answer number and carry 2 to the first number 6 ( 6 + 2) , so the new number is 8.
Therefore, final answer is 85,608.
Crisscross method with 4 digits number
Lets multiply – 6952 x 1980
Simplify the numbers (6952 x 1980) ≈ (abcd x pqrs)
a=6, b=9, c=5, d=2 & p=1, q=9, r=8, s=0
Pattern for multiplication:
(a x p) / (a x q) + (b x p) / ( a x r) + (b x q) + (c x p) / (a x s) +
(b x r) + (c x q) + (d x p) / (b x s) + (c x r ) + (d x q) / (c x s) + (d x r) / (d x s)
As per the method,
= (6 x 1) / (6 x 9) + (9 x 1) / ( 6 x 8) + (9 x 9) + (5 x 1) / (6 x 0) +
(9 x 8) + (5 x 9) + (2 x 1) / (9 x 0) + (5 x 8) + (2 x 9) / (5 x0) + (2 x 8) / (2 x 0)
= 6 / 54 + 9 / 48 + 81 + 5 / 0 + 72 + 45 + 2 / 0 + 40 + 18 / 0 + 16 / 0
= 6 / 63 / 134 / 119 / 58 / 16 / 0
Here, is the step you need to take care, how to write final answer?
As we have done in previous example, we need to carry the digit to the before numbers and need to add with them to get new number. By doing that sequential calculations, the final answer is 13,764,960.
Faster Calculation Trick for Square of 3 digits & 4 digits number
Squaring big numbers is an impressive feat of mental prestidigitation.
It can be done by rounding up and down to the nearest multiple of 10s (i.e.: 10, 100, 100,…). Let’s see the examples:
Square of 3 digits number:
Square of 3 digits number can be done by rounding up and down to the nearest multiple of 100.
e.g.: Find the square of 298.
Step 1: nearest multiple of 298 is 300 ( 298 + 2 = 300)
Step 2: now you need to subtract 2 from 298, new number is 296.
Step 3: Now Multiplying both new numbers:
300 x 296 ( first multiply 3 x 296 = 888 ; 888 x 100 = 88800)
Step 4: New number from step 3 that is 88800 + square of 2 (the number which is used for rounding up the main number)
Therefore, the answer is 88804.
Square of 4 digits number close to 1000:
- It can be done by a very simple method of squaring and addition.
- Let’s understand by an example: Find the square of 1015.
Step 1: Nearest number to 1000 = 1015 – 15
Step 2: Square of 15 = 225
Step 3: Now let’s add 15 to 1015, therefore the new number we got is 1030
Step 4: Combining both new answers from step 2 and 3, the final answer is 1030225
Square root estimation technique for Rapid calculation at Bank Exams
Normally a Square root of any number ‘a’, is the number which, when is multiplied by itself, will give you ‘a’.
e.g.: The square root of 4 is 2 because 2 x 2 = 4.
To find a square root of any number is time consuming and calculator operative process.
But by the vedic maths method of estimation, we can get accurate estimate of the answer.
In this method of estimation, our goal is to get a number that when multiplied by itself approximates the main or original number. Therefore, the square root of most numbers is not a whole number, it may be fraction or decimal number.
Let’s take an example, where we can start by guesstimating the square root of 26.
Step 1: Get the number that when multiplied by itself comes closest to 26. The answer is 5. As, 5 x 5 = 25, that is closest to 26.
Step 2: Now divide 26 by 5, the new answer will be, 5.2.
By this, we can conclude that, the square root of 26 is between 5 and 5.2. To get nearest accurate answer, get an average of both the numbers: (5 + 5.2) / 2 = 5.1.
You can check by multiplying number 5.1 by itself to check our Guestimation. (5.1 x 5.1 = 26.01). So our Guestimation is quite nearer to the answer.
Fast calculation tricks to get Cube of numbers
Cube of any digit is three times multiplication of that same digit.Here we can learn by the algebraic method of calculation. For that here is the algebraic formula:A3 = (A – x) A(A + x) + x2AHere x = is the number, which is nearest to the tens digit in the main or original number.e.g.: Find the Cube of 12As per the Algebraic formula:
123 = [(12 – 2) x 12 x (12 + 2)] + [22 x 12]
= [10 x 12 x 14] + [ 4 x 12]
= (1680) + ( 48)
Rapid Division Method
To start with rapid division, first we need to figure out from the original number, that how many digits will be in our answer.
This can be done easily and mentally with this vedic maths trick for division. Here is an example elaborating the concept more clearly.
e.g.: Solve 224 ÷ 6
Step 1: Here the number 224, lies between 6×10 = 60 and 6×100 = 600. This means that our answer will be of 2 digits.
Step 2: Now let’s determine the largest multiple of 10 that can be multiplied by 6 whose answer is below 224.
6 x 20 = 120
6 x 30 = 180
6 x 40 = 240
Above calculations, clarify that the number 224, lies between 30 and 40, this shows that our answer lies between 30 and 40.
Step 3: Now 224 – 180 = 44
Step 4: Divide this new number 44 by 6, this is the nearest one to 6 x 7 = 42, which is 2 away from 44.
Step 5: Here is the answer, Where 7 is added to 30, that will be 37 and 4 ( we take this first digit from 6 x 7 = 42) is the reminder
Therefore, the final answer is 37
Guestimation is the best method to get approximate and nearby answers.
This method is used to make easy and rapid long calculations by converting the numbers to its round figure.
e.g.: 8327 + 5817
Let’s get their approximate round figures,
8000 + 6000 = 14000
If you check the main digit calculation, then
8327 + 5817 = 14144
In this way by guessing proper round figure for the number, we can get approximate answers very rapidly.
In this article we have gone through with different calculation methods, some are quick calculation tricks, where as some are very helpful for rapid calculations. By crisscross multiplication you can rapidly get answer for big number multiplications, whereas Square and square root calculations become easy and faster. Guestimation method and Cubing method makes the calculation Fast. In this way Vedic Maths techniques and methods are very useful to solve big problems very fast during Competitive exams especially bank exams.
Try these tricks for faster calculation and share your experience with us via comments!