Quick Vedic Maths Trick For Binary Subtraction

Quick Vedic Maths Trick For Binary Subtraction

Subtraction is the very common and important part of Mathematics. The traditional western technique that we have learned in our schools is complex because of the carry and borrow thing. With Vedic Maths you can do subtraction very easily without  having to worry about this carry and borrow things.  There are two categories of substation in Vedic mathematics

1. Subtraction of any number from bases

2. General Subtraction

Case 1: Subtraction of number from its base

For subtraction of number from a base number will use the sutra ‘All from 9 and last from 10′  which we have used to find the complement. For example to subtract 3246 from 10000 , we will simply calculate the complement of 3246 by applying the formula All from 9 and last from 10 .

So 10000-3246 = 6754   ( 9-3,9-2, 9-4. 10-6)

As you can see here this method removes the mental  strain of borrowing

You should note here that this method is applicable when the number of digits in the number to be subtracted is equal to the number of 0′s in the base.

Case 2: Subtraction of a number from a bigger base

If you have to subtract a number from a bigger base then make the number of digits in the number to be subtracted equal to the number of 0′s in the base by adding the required 0′s to the  beginning of the number.

lets say we have to subtract 24 from 10000 , as base here has four zeros and 24 is a two digit number we will put two 0′s in front of 24 so the calculation actually becomes 10000 -0024 , now we can apply the same ‘all from 9 and last from 10′ formula to get the answer as 9976 , the addition of 0′s can be done mentally.

case 3: When the number involves decimals 

In case of decimals also the same formula is applied, only thing we have to check is that the number of digits before the decimal should be equal to the number of 0′s in the base, if they are not then we have to append the 0′s in front

for example if we have to solve 1000- 24.35 , then we will actually solve 1000-024.35 , by applying the same ‘all from 9 and last from 10′ we get the answer as 975.65

Case 4: Subtraction of number from multiple  of bases 

When we have to do subtraction of numbers from multiple of bases like 200, 4000, 8000 etc then we will simply split the number to the nearest base. Lets see with an example

600 – 63

we will split this calculation as 500+100 – 63  and solve it as 500+(100-63) using the same technique to get 500+37 = 537 as answer. You can make it faster by simply reducing 1 from the  multiple of base mentally and then write the complement of the number as answer. Lets take another example to understand it.

4000 – 248

Reduce 1 from 4 to get 3 at thousand’s place

Write the complement of 248 as 752

so 4000- 248 = 3752

Case 5: When both the numbers have same number of digits 

In this case subtract the digits on the left most side of both the numbers and further reduce it by one and finally take the complement of the other digit of the number to be subtracted

Example 8000 – 4246

subtracting left most digits of both the number i.e. 8-4 = 4

on further subtracting 1 we get 4-1 = 3

taking of complement of 246 we get 754

so our final answer becomes 3754

I hope you have understood this basic subtraction technique of vedic mathematics , if you are having any problem anywhere let us know in comments and we will help you to solve it.  In the next post we will see the advance subtraction technique.

How To Find Square Roots of Numbers Quickly

How To Find Square Roots of Numbers Quickly

In our previous post we saw how to find the cube root of a perfect cube in seconds. Today we will discuss a vedic maths trick to find out square root of perfect squares quickly. This method uses the same approach which we have seen in the cube root method.  To proceed its very necessary for us to memorize the square of first ten natural numbers.

Number	Square
1	1
2	4
3	9
4	16
5	25
6	36
7	49
8	64
9	81
10	100

From the above table you can observe that we have 1 in the number column and 1 in the square column. In the same way, in the 9th row we have 9 in the number column and 1 in the square column. From this we can conclude that if the number ends in 1, the square root ends in 1 or 9 . Similarly if the number ends in 4 the square root ends in 2 or 8. If the number ends in 9, the square root ends in 3 or 7. If the number ends in 6, the square root ends in 4 or 6. If the number ends in 5, the square root ends in 5. If the number ends in 0, the square root also  ends in 0. The below table summarize this thing. You should memorize this table.

Last digit of square	Last digit of square root
1	1 or 9
4	2 or 8
9	3 or 7
6	4 or 6
5	5
0	0

From the above tables you can find that a perfect square never ends  with 2,3,7, or 8

Below is the another table of square of numbers from 10 to 100.  This table will help us to find the square roots quickly.

Number	Square
10	100
20	400
30	900
40	1600
50	2500
60	3600
70	4900
80	6400
90	8100
100	10000

Lets now try to find the square root of 9801

Step 1: The last digit of the number 9801 is 1 therefore the last digit of the square root will be either 1 0r 9. The answer for now will be _1 or _9

Step: 2 The number 9801 lies between 8100 (square of 90) and 10000 ( square of 100). Therefore the answer lies between 90 and 100.  From the first step we know that the  square  ends in either 1 or 9. So the answer can be 91 or 99

Step 3: Now we pick the number which is closer to the square. Since 9801 is closer to the bigger number 10,000 we will take the number number 99 as the answer.   So our answer becomes 99

Lets find the square root of 5184 through the same shortcut method

Step 1: Number ends in 4. So square root ends in either 2 or 8. Answer at this stage can be _2 or _8

Step 2: 5184 lies between 4900 and 6400, the square of 70 and 80.  From the first step the answer at this stage becomes 72 or 78

Step 3: 5184 is closer to the smaller number 4900. Thus we take smaller number 72 as our correct answer.

I hope you have understood the method, if you have any problem let us know in comments and we will do our best to help you.

Vedic Maths Sutras For quick Calculation

Vedic Maths Sutras For quick Calculation

Vedic Math is a popular calculation technique developed by ancient Indian sages. With this technique one can do very fast mathematical calculations, even faster than a calculator. To master this technique one has to be through with its formulas which are called as sutras. There are around 16 vedic maths sutras. With these sutras you can quickly do almost any kind of mathematical calculation.  This sutras are originally in Sanskrit.  We have made simple translation, you that you can understand them in English. 

1. एकाधिकेन पूर्वेण  one more than the previous one

2. निखिलं नवतश्चरमं दशतः All from 9 and the last from 10

3. ऊर्ध्वतिर्यग्भ्याम्: Vertically and crosswise (multiplications)

4. परावर्त्य योजयेत्  Transpose and apply

5. शून्यं साम्यसमुच्चये If the Samuccaya is the same (on both sides of the equation, then) that Samuccaya is (equal to) zero

6. (आनुरूप्ये) शून्यमन्यत्  If one is in ratio, the other one is zero.

7. संकलनव्यवकलनाभ्याम् By addition and by subtraction

8. पूरणापूरणाभ्याम् By the completion or non-completion

9. चलनकलनाभ्याम् Differential calculus

10. यावदूनम् By the deficiency

11. व्यष्टिसमष्टिः Specific and general

12. शेषाण्यङ्केन चरमेण The remainders by the last digit

13. सोपान्त्यद्वयमन्त्च्यम् The ultimate (binomial) and twice the penultimate (binomial) (equals zero)

14. एकन्यूनेन पूर्वेण By one less than the one before

15. गुणितसमुच्चयः The product of the sum

16. गुणकसमुच्चयः All the multipliers

Its good if you by heart these sutras, understanding them is more important than mugging them up. You will see in our upcoming posts how you can employ the above sutras in your calculation.