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Lesson Posted on 19/09/2017 Life Skills Coaching/Vedic Maths Training Tuition/Class I-V Tuition Exam Coaching/Math Olympiad

Subtraction Of Numbers In An Easy Method

Mamta Mund

I have 4 years of experience in teaching maths. Now I m working as subject matter expert for post graduation...

As we know in decimal system ten digits are used. I.e 0 - 9. Subtracting a number from base 10, 100, 1000. An easy way to calculate is just subtracting all digits of a digit from 9 and last digit by 10.For an example, subtracting 56 from 100: 100 - 56 = (9 - 5) | (10 - 6) = 44Let's check it using... read more

As we know in decimal system ten digits are used. I.e 0 - 9. Subtracting a number from base 10, 100, 1000. An easy way to calculate is just subtracting all digits of a digit from 9 and last digit by 10.

For an example, subtracting 56 from 100:

100 - 56 = (9 - 5) | (10 - 6) = 44

Let's check it using our conventional method, in units place it is 6 there. So carry from tens place, there also 0, so so take carry from hundred places, I.e in units place has value 10 so subtracting 6 from 10 we get 4 and now in tens place there is digit 9. Now subtract 5 from 9 we get 9 - 5 = 4. So our answer is 44. So lengthy using carry.

If we use the first method we have to do just only subtract 9 from all digits and last digit from 10. This is one of the powerful sutra "All From 9 And Last From 10" Of Vedic Mathematics. We also know that complement of 56 is 44. As if we add 56 with 44 we get 100.

Next, try for subtracting 65 from 10000:

10000 - 65 = 10000 - 0065 = 9935.

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Comments 2 Lesson Posted on 17/07/2017 Life Skills Coaching/Vedic Maths Training

Ajinkya

14 23 2 9 9 :8 9 5 3 3 3 1 3 -4 -21 -23 -15 -12 28 18 16 3 27 4 5 3 3 5 6 Quotient Steps: 1.) Place a colon two digits from the right since we now have two digits in flag. 2.) Divide 23 by 5 to get quotient as 4 and remainder as 3. 3.)... read more

14 | 23 | 2 | 9 | 9 | :8 | 9 | ||||

5 | 3 | 3 | 3 | 1 | 3 | |||||

-4 | -21 | -23 | -15 | -12 | ||||||

28 | 18 | 16 | 3 | 27 | ||||||

4 | 5 | 3 | 3 | 5 | 6 | |||||

Quotient |

Steps:

1.) Place a colon two digits from the right since we now have two digits in flag.

2.) Divide 23 by 5 to get quotient as 4 and remainder as 3.

3.) Carry the remainder 3 to the next digit 2 and get 32 as gross dividend.

4.) Now, since there are 2 digits in the flag we will use 2 quotient digits in the flag, we will use 2 quotient digits from the previous two colums to carry out a cross multiplication with the 2 digits of the flag. We will then substract the result from the gross dividend to compute the next dividend.

5.) Since the quotient 4 has only one digit we pad it with a zero on the left and multiply the quotient 04 by the flag 14 as follows:

1 4

0 4

4 x 0 + 1 x 4 = 4

6.) We will subtract 4 from gross dividend 32 to get 28 as net divided.

7.) Divide 28 by 5 to get the quotient as 5 and remainder as 3.

8.) Carry the remainder 3 to the next digit 9 and get 39 as gross dividend.

9.) Now the previous two quotient digits are 4 and 5 which are multiplied by the flag 14 as follows:

1 4

4 5

1 x 5 + 4 X 4 = 21 we will substract 21 from the gross divident 39 to get 18 as net dividend.

Repeat the process for remaining columns.

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Comments Lesson Posted on 17/07/2017 Life Skills Coaching/Vedic Maths Training

Ajinkya

524 6 8 5 1 :2 3 5 6 0 3 3 2 6 8 -5 -2 -29 -10 -25 3 33 2 12 38 1 0 5 0 1 5 Quotient Steps: 1.) Place alon 3 digits from the right since now ther are 3 digits in the flag. 2.) Divide 6 by 6 to get quotient as 1 and remainder as 0. 3.) Carry... read more

524 | 6 | 8 | 5 | 1 | :2 | 3 | 5 | |||

6 | 0 | 3 | 3 | 2 | 6 | 8 | ||||

-5 | -2 | -29 | -10 | -25 | ||||||

3 | 33 | 2 | 12 | 38 | ||||||

1 | 0 | 5 | 0 | 1 | 5 | |||||

Quotient |

Steps:

1.) Place alon 3 digits from the right since now ther are 3 digits in the flag.

2.) Divide 6 by 6 to get quotient as 1 and remainder as 0.

3.) Carry the remainder 0 to the next digit 8 and get 08 as gross dividend

4.) since there are three digits in the flag we will use 3quotient digits from the 3 immediately previous columns and carry out a cross multiplication with the 3digits of the flag. We will then substract the resultfrom the gross dividend to compute the net dividend.

5.) Since the quotient 1 has only one digit, we will pad it with two zeroes on the left and multiply the quotient 001 by the flag 524 as follows.

5 2 4

0 0 1

4 x 0 + 5 x 1 + 2 x 0 = 5

We will substract 5 from gross dividend 8 to get 3 as net divdend.

6.) Divide 3 by 6 to get quotient as 0 and remainder as 3.

7.) Carry the remainder 3 to the next digit 5 to get 35 as gross dividend.

8.) Now the previous two quotient digits are 0 and 1, we pad them with one zero and multiply by the flag 524 as follows

5 2 4

0 1 0

4 x 0 + 5 x 0 + 2 x 1 = 2

We will substract 2 from the gross dividend 35 to get 33 as net dividend.

9.) Divide 33 by 6 to get the quotient as 5 and remainder as 3.

10.) Carry the remainder 3 to the next digit 1 and get 31 as gross dividend.

11.) Now the previous 3 quotuients are 1 , 0 and 5. We multiply by the flag 524 as follows.

5 2 4

1 0 5

4 x 1 + 2 x 0 +5 x 5 = 29

We will substract 29 from gross dividend 31 and get 2 as the net dividend.

Repeat the process for the remaining columns.

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Lesson Posted on 15/07/2017 Life Skills Coaching/Vedic Maths Training

Ajinkya

7 25 3 8 :2 0 0 0 7 4 8 11 7 7 7 -21 -14 -63 -42 -21 42 22 74 49 28 49 28 3 2 9 6 3 6 3 Quotient Case 3: Division with adjustments. Steps: 1.) Place a colon one digit from the right (= number of digits of flag) 2.) Divide 25 by 7 to get quotient... read more

7 | 25 | 3 | 8 | :2 | 0 | 0 | 0 | |||

7 | 4 | 8 | 11 | 7 | 7 | 7 | ||||

-21 | -14 | -63 | -42 | -21 | 42 | |||||

22 | 74 | 49 | 28 | 49 | 28 | |||||

3 | 2 | 9 | 6 | 3 | 6 | 3 | ||||

Quotient |

Case 3: Division with adjustments.

Steps:

1.) Place a colon one digit from the right (= number of digits of flag)

2.) Divide 25 by 7 to get quotient as 3 and remainder as 4.

3.) Carry the remainder 4 to the next digit 3 and get 43 as gross dividend.

4.) Multiply the quotient 3 by the flag to get 21 and substract it from 43 to get 22 as net dividend.

5.) Divide 22 by 7 to get quotient as 3 and remainder as 1.

6.) Carry the remainder 1 to the next digit 8 and get 18 as gross dividednd.

7.) Multiply the quotient 3 by 7 to get 21 and subtract it from 18 to get -3 as net dividend.

8.) Now we have a negative net dividend.The process cannot go further with this. so we have to make an adjustment.

9.) We will go one step backward and instead of writing the quotient as 3 while dividing 22 by 7 we will write down only 2 as the quotient and carry forward a bigger remainder of 8 (i.e. 22-2x7).

10.) Carry the remainder 8 to the next digit 8 and get 88 as gross dividend

11.) Multiply the quotient 2 by the flag 7 to get 14 and substract it from 88 to get 74 as net dividend which is now positive.

Carry out the process in the remaining columns, making an adjustment whenever the net divident is negative.

The final answer is 329 and remainder 49 or in decimal form, it is 329.6363.

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Comments Lesson Posted on 14/07/2017 Life Skills Coaching/Vedic Maths Training CBSE/Class 6/Maths/Playing With Numbers/Divisibility Test

Ajinkya

4 8 7 1 0 :8 8 0 3 7 2 -4 0 -12 -28 3 31 58 0 1 0 3 7 0 Quotient Remainder Case 1 : Division of a number with a flag of one digit (no remainder) Steps: 1.) Place a colon one digit from right (= number of digits of flag). 2.) Divide 8 by 8 to get quotient... read more

4 | 8 | 7 | 1 | 0 | :8 | |

8 | 0 | 3 | 7 | 2 | ||

-4 | 0 | -12 | -28 | |||

3 | 31 | 58 | 0 | |||

1 | 0 | 3 | 7 | 0 | ||

Quotient | Remainder |

Case 1 : Division of a number with a flag of one digit (no remainder)

Steps:

1.) Place a colon one digit from right (= number of digits of flag).

2.) Divide 8 by 8 to get quotient as 1 and remainder as o.Carry the remainder 0 to the next digit 7 and get 7 ( called gross dividend, GD).

3.) Multiply the quotient 1 by the flag 4 to get 4 and subtract it from 7 to get 3 (called net dividend, ND).

4.) Divide 3 by 8 to get quotient as 0 and remainder as 3.

5.) Carry the remainder 3 to the next digit and get 31 as GD.

6.) Multiply the quotient 0 by the flag 4 to get 0 and subtract it from 31 to get 31 as ND.

7.) Divide 31 by 8 to get quotient as 3 and remainder as 7.

8.) Carry the remainder 7 to the next digit 0 and get 70.

9.) Multiply the quotient 3 by the flag 4 to get 12 and substract it from 70 to get 58.

10.) Divide 58 by 8 to get the quotient as 7 and reaminder as 2.

11.) At this point we have obtained the integer part of the final quotient as we have reached the colon.All the balance digits would be the decimal part.

12.) Carry the remainder 2 to the next digit 8 and get 28.

13.) Multiply the quotient 7 by flag 4 to get 28 and substract it from 28 to get 0.

14.) Since the difference is now 0 the division is completed and we get the answer as 1037.

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Comments Lesson Posted on 14/07/2017 Life Skills Coaching/Vedic Maths Training

Ajinkya

7 26 3 8 :2 0 0 0 7 5 4 6 6 4 5 -221 -28 -14 -42 -14 -21 32 20 48 18 26 29 3 4 2 6 2 3 Quotient Case 2: Division of a number with a flag of one digit ( with remainder). Consider 26382/77 The quotient is 342 and the reaminder is 48, which appears... read more

7 | 26 | 3 | 8 | :2 | 0 | 0 | 0 | |||

7 | 5 | 4 | 6 | 6 | 4 | 5 | ||||

-221 | -28 | -14 | -42 | -14 | -21 | |||||

32 | 20 | 48 | 18 | 26 | 29 | |||||

3 | 4 | 2 | 6 | 2 | 3 | |||||

Quotient |

Case 2: Division of a number with a flag of one digit ( with remainder).

Consider 26382/77

The quotient is 342 and the reaminder is 48, which appears under the column just after the colon. The final answer in decimal form is 342.623.

Steps:

1.) The steps as explained before are carried out till we reach the column after the colon which shows the reaminder as 48. If we want to get the answer in decimal form we have to carry out division further by using the same procedure.

2.) Divide 48 by 7 to get the quotient as 6 and remainder as 6.

3.) Now we attach a zero to the dividend and write the remainder to its left giving the next number as 60.

4.) Multiply the quotient 6 by the flag 7 to get 42 and substract it from 60 to get 18.

5.) Divide 18 by 7 to get quotient as 2 and remainder as 4.

6.) Carry the remainder 4 to the next digit 0 (attached as before) and get 40.

7.) Multiply the quotient 2 by flag 7 to get 14 and substract it from 40 to get 26.

8.) Divide 26 by 7 to get the quotiuent as 3 and remainder as 5.

The process can be carried out further to any number of digits.

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Lesson Posted on 23/06/2017 Life Skills Coaching/Vedic Maths Training

Square Root Of Perfect Squares

Ajinkya

Method: I request the students to remember the square of numbers from 1 to 10. Number: 1 2 3 4 5 6 7 8 9 10 Squares: 1 4 9 16 25 36 49 64 81 100 Also the same applies for numbers from 10 to 100 and the numbers ending in 5. Let us take... read more

Method:

I request the students to remember the square of numbers from 1 to 10.

Number: 1 2 3 4 5 6 7 8 9 10

Squares: 1 4 9 16 25 36 49 64 81 100

Also the same applies for numbers from 10 to 100 and the numbers ending in 5.

Let us take an example:

Find the square root of 7744:

The number ends in 4 so looking at the above table we can conclude that the square root ends in either 2 or 8.

Next we take the complete number 7744. This number lies between 6400 which is square of 80 and 8100 which is square of 90. So our possible answer lies in between 80 and 90. i.e.: 81,82,83,84,85,86,87,88,89. But only two numbers end in 2 and 8 i.e. 82 and 88.

Now in betwenn 82 and 88 what is the answer. So in the previous lessons, we learned how to find the square of numbers ending in 5. Similarly we find the square of 85 which is = 7225.

Lastly as our number 7744 is more than 7225 our answer is obviously 88.

Similarly try for 9801.

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Comments Lesson Posted on 21/06/2017 Life Skills Coaching/Vedic Maths Training

Vedic Math Method For Finding Cube Root Of Perfect Cubes

Ajinkya

I request the students to memorize the cubes of numbers 1 to 10. The list is below: 1 1 2 8 3 27 4 64 5 125 6 216 7 343 8 512 9 729 10 1000 Remeber the last digit of the cubes for the corresponding number. Like the number 7 and last digit 3 On the basis of above cube roots we can draw the conclusion... read more

I request the students to memorize the cubes of numbers 1 to 10.

The list is below:

1 1

2 8

3 27

4 64

5 125

6 216

7 343

8 512

9 729

10 1000

Remeber the last digit of the cubes for the corresponding number. Like the number 7 and last digit 3

On the basis of above cube roots we can draw the conclusion as below.

The last digit of the cube The last digit of the cube root

1 1

2 8

3 7

4 4

5 5

6 6

7 3

8 2

9 9

0 0

We can conclude that all cubes end with the same number except 3, 7 and 2

Method:

If the cube given to you is 39304, split it into 39|304.

Q.) Cube root of 287496

A.) Split it to 287|496. Since it ends in 6, the cube root also ends in 6, so now we have the right hand part.

Now take the part on LHS i.e.: 287. We need two perfect cubes between which the number 287 lies.

From the above table we find that 287 lies between 216 (6^3) and 343 (7^3).We take the smaller number 6 and put it in the left hand part of our number. Thus the answer is 66.

Q.) 205379

A.) Split 205|379.

The cube ends in 9. So the root also ends in 9. Left hand part is 205. It lies between 125 and 216. Out of 5 and 6 we take the smaller number and put it on the left hand side of the answer.

Thus our answer is:** 59**

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Comments Lesson Posted on 16/03/2017 Life Skills Coaching/Vedic Maths Training

Find squares of any number that ends with 5.!!

Ameer Hasshan J

Enthusiastic Middle School Math Teacher committed to creating an atmosphere that encourages productive...

Take a two digit number, Say 25. To find the square for 25. 25 × 25 = 625 Step 1: 5X5 = 25 Step 2: 2×3 = 6 25X 25 = 6 25

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Answered on 24/05/2016 Life Skills Coaching/Vedic Maths Training

Mamta D.

Certified Vedic Maths Trainer

Abacus is limited. Vedic maths is unlimited. Abacus is more about addition subtraction. Whereas Vedic maths trains you in everything like addition subtraction, multiplication division, squares, square root, cube root..so on.. Vedic mathematics can be taught to the kid as small as 8 yrs old..

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