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Do you know that the systematic arrangement of petals in sunflower follows the Fibonacci series of Mathematics? Yes, mathematics is not just limited to your text book but the whole world around us functions on its varied theories and logical explanations.
As a subject, Mathematics always troubles you! From memorizing the formulas to deriving the complex calculations, it can be really strenuous. But this subject can turn quite interesting if you know simple and effective tricks. It will not only turn the boring math sums indulging but also help to do all the calculations fast. We have brought some really cool mathematical tricks which would help you to save time while giving your high school and college examinations. Want to know them? Read on.
In the world of mathematics, there are numerous tricks that will help you to do all your calculations faster. We all tend to make mistakes while performing mathematical operations. Using the simple tricks will give you accurate results in quick time.
Nothing is easier than memorizing the table of 11! We all know that. This time you will learn that multiplying any two digit number is also equally effortless.
Not clear? Let’s show an example.
Say the original number is 43. So, we need to multiply 43 x 11
Step 1:
Adding the two digits we get, 4 + 3 = 7
Step 2:
Putting the result in between them, 4 (7) 3
When the sum exceeds more than 9, simply carry it over and add the first two digits again. Need an example? Here it is.
Let the original number be 59. So, we need to multiply 59 x 11
Step 1:
Adding the two digits we get, 5 + 9 = 14
Step 2:
Putting the result in between them, 5(14)9
Needless to say, it reduces the effort considerably.
Adding numbers which are not the multiple of 10 or 100 always takes away important time during examinations. Rounding off the numbers to the nearest multiples of 10 or 100 will make your job considerably easier. How? Let’s take an example.
154 + 38
If the original numbers are bigger, like
1365 – 492
There are plenty of situations where you need to operate multiplications on two double digit numbers. Obviously sometimes it is cumbersome. So first, find out if both the numbers are between 11 and 19 or not. If yes, then follow this process:
Take an example of 13 x 19
= (13 + 9) x 10 + (3 x 9)
= 220 + 27 = 247
Try practicing it on the paper first. In a few instances, you will be able to do it in your mind.
When the numbers are bigger than 19, you need to follow this algorithm:
So taking the example of 26 x 58,
The result would be,
100 (2 x 5) + 10 (6 x 5) + 10 (2 x 8) + 6 x 8
As it breaks into calculation in stages, it becomes comparatively easier to compute. You might need the help of the paper for the first few times but not beyond that!
Do you know the square results of all the one digit numbers from 1 to 9? Then you can easily find out the square number of any two digit number.
Let us take the example of 48. Then 48 ^{2 }will be
So, 48 ^{2} is 2304
We all know that we can multiply any two numbers ending with zero effortlessly. Similarly, we can use the same process or strategy to multiply another two numbers which are close to the power of 10. But what when we have to multiply any two numbers not ending with zero?
Say for example, 99 with 97. Following the usual process of multiplication, we get 9603.
But, applying a swift procedure, you can do it much more easily.
99 – 100 = – 01
97 – 100 = – 03
This coincides with the original answer. Isn’t it interesting? You can try it yourself using some other examples of your own.
Vedic Math tricks have received wide acknowledgment and appreciation throughout the world. The reason being the principles of Vedic mathematics fasten up calculations and you can perform them mentally without using any paper. Originated in India, it helps you profoundly while you are doing bigger calculations. We will show you an example.
Facing problem in converting kilograms into pounds? Now you can do it even mentally.
Take the example of 78
Multiplying it by 2, you get 78 x 2 = 156
Dividing it by 10, you get 15.6
Adding both the results, you get 156 + 15.6 = 171. 6
Hence, 78 kilos = 171.6 pounds
Taking the example of , there are two groups, the root will be of two digits
The first two digits of the number is 68 which falls between 64 (8^{2}) and 81 (9^{2}). Hence the first figure will be 8 (the number 6889 is situated between 6400 and 8100).
Now, the last digit of the number is 9.
Only the squares of two number end with 9, namely, 3 (9) and 7 (49)
Hence, the square root of the number is either 83 or 87. Since, 85^{2} is 7225, then must be 83
Final answer 83.
Let’s start with a simple example:
The sum of two successive odd numbers is 44. What are those two numbers?
The usual solution goes:
x + (x +2) = 44
Hence, the other number is 23 (x + 2)
But you can solve this question with proper guess work in your mind. Firstly, understand the question and then start thinking about it. If 15 and 17 do not work, try thinking of some bigger number; you will definitely find the solution in your mind.
Like this, there are many effective puzzle solving strategies which can help you to solve all the reasoning and logical problems. So, before beginning your work, remember applying any one these following strategies to resolve the problems.
It is very important to analyze the given problem accurately. Sometimes you can notice some definite pattern in the problem which can lead to the solution. For example,
Find the next 3 numbers of the series 1, 3, 6, 10, 15.
Solution
It is clearly noticeable that the difference between the numbers of the series increases by 1. The series goes like 3-1 = 2, 6 – 3 = 3, 10 – 6 = 4 and so on.
Hence, the next 3 numbers of the series will be 21, 28 and 36.
Sometimes you understand a question only when you make a table on the basis of the given information. It assists you to reach the solution.
Consider the following example:
You save $2 on Sunday. Each day you save double the amount you saved a day before. If this pattern continues, how much will you have on the next Sunday?
Making a table will give the solution
DAY | AMOUNT SAVED |
Sunday | $ 2 |
Monday | $ 4 |
Tuesday | $ 8 |
Wednesday | $ 16 |
Thursday | $ 32 |
Friday | $ 64 |
Saturday | $ 128 |
Sunday | $ 256 |
Making a list can also help to solve the mathematical problems. More or less like a making a table, a complete list will provide you the answer of the questions of simple permutations and combinations.
Example: In how many ways you can throw three balls of different colors namely red, green and blue?
First Throw | Second Throw | Third Throw |
Red Ball | Blue Ball | Green Ball |
Red Ball | Green Ball | Blue Ball |
Blue Ball | Red Ball | Green Ball |
Blue Ball | Green Ball | Red Ball |
Green Ball | Red Ball | Blue Ball |
Green Ball | Blue Ball | Red Ball |
Working backwards is a common technique that can be applied to derive the solution. Going through the steps in reverse order also ensures that you don’t make any mistake.
Take the example of a bus. It started from the place A and took 1 hr 20 minutes to reach B. To arrive in the place C from B, it took another 1 hr 5 minutes. It was 2: 45 pm when it reached C. At what time did the bus leave the place A?
Solution
When the bus reached C it was 2.45 pm.
Subtracting 1 hr 5 minutes, we get 1.40 pm. It reached B at 1.40 pm.
Now, subtracting further 1 hr 20 minutes, we get 12.20 pm. This is the time when the bus left the place A.
Many a times, drawing understandable pictures will help to identify the solution. The relevant diagrams also help to comprehend problems which are never easy to understand in simple sentences.
There are three clocks which ring at the intervals of 15 minutes, 20 minutes and 30 minutes respectively. Which is the closest time when all the three clocks will ring at the same time?
First Clock
Hence, the first time when the rings of all the three clocks coincide is at 60 minutes or one hour.
Mathematics is one such subject which uses logic and theoretical evidence to prove and settle every solution. Always take the right approach to solve all your mathematical problems. These days, the college and high school professors evaluate the performance of the students by assigning them projects and practical coursework. These assignments come with very short deadlines. Hence, you need to be very fast to complete the assignments on time. These tips and mathematical tricks will assist you to complete the tasks on time.
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