8/9/2019 Multiply Any Number by 9-99-999 Etc.

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Vedic Math Handouts by Swati Dave Page 1

Multiply numbers by 9, 99, 999, 9999 etc. 

Rule: Application of “All from 9 and the last from 10”  

Objective: Learn to quickly multiply any number by 9, 99, 999, 9999 etc. when

  Number of digits in the number is same as the number of digits in 9’s

(e.g. 75 x 99; 8765 x 9999)

Pre-requisite: Understanding of the rule “All from the 9 and the last from 10” 

GUIDED INSTRCUTION 

85 x 99

Step 1: For LHS of the answer

  Take away 1 from 85

  85-1 = 84 

Step 2: For RHS of the answer

 

Apply “All from 9 and the last from 10”

to 85

8 5

1 5

Step 3: Answer: 8,415

854,673 x 999,999

Step 1: For LHS of the answer

  Take away 1 from 854,673

  854, 673 – 1 = 854,672 

Step 2: For RHS of the answer

 

Apply “All from 9 and the last from 10”

to 854,673

8 5 4 6 7 3

1 4 5 3 2 7

Step 3: Answer: 854,672,145,327

8/9/2019 Multiply Any Number by 9-99-999 Etc.

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Vedic Math Handouts by Swati Dave Page 2

Multiply numbers by 9, 99, 999, 9999 etc. 

Rule: Application of “All from 9 and the last from 10”  

Objective: Learn to quickly multiply any number by 9, 99, 999, 9999 etc.

  Number of digits in the number is less than the number of digits in 9’s

(e.g. 75 x 999; 876 x 9999)

Pre-requisite: Understanding of the rule “All from the 9 and the last from 10” 

GUIDED INSTRCUTION 

56 x 999

Step 1: For LHS of the answer

  Take away 1 from 56

  56-1 = 55 

Step 2: For RHS of the answer

  Write 0 before 56, to make the

number of digits the same as in 9 ’s

  Then, apply “All from 9 and the last

from 10” to 056 

0 5 6

9 4 4

Step 3: Answer: 55, 944

673 x 999,999

Step 1: For LHS of the answer

  Take away 1 from 673

  673 – 1 = 672

Step 2: For RHS of the answer

 

Here, add three 0’s before 673, to make

the number of digits the same as in 9 ’s

  Then, apply “All from 9 and the last from 10”

to 000,673

0 0 0 6 7 3

9 9 9 3 2 7

Step 3: Answer: 672, 999, 327 

(Please remember to add as many 0’s as needed before the number, to make the number of digits the same as

in 9 ’ s , before applying “ All from 9 and the last from 10)  

8/9/2019 Multiply Any Number by 9-99-999 Etc.

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Vedic Math Handouts by Swati Dave Page 3

Multiply numbers by 9, 99, 999, 9999 etc  

Rule: Application of “All from 9 and the last from 10”  

Objective: Learn to quickly multiply any number by 9, 99, 999, 9999 etc.

  Number of digits in the number is more than the number of digits in 9’s

(e.g. 775 x 99; 87,654 x 9999)

Pre-requisite: Understanding of the rule “All from the 9 and the last from 10” 

GUIDED INSTRCUTION 

775 x 99

Step 1:

Split the number in such a way, that the right hand

side contains digits equal to the number of digits in

9’s 

7 75

673,456 x 999

Step 1:

Split the number in such a way, that the right hand

side contains digits equal to the number of digits in

9’s 

673 456

Step 2:

  Add 1 to the number

7 + 1 = 8

  Then, take away 8

from 775

  775 – 8 = 767 

  Apply “All from 9

and the last from

10” to 75 

7 5

2 5

Step 2:

  Add 1 to the number

673 + 1 = 674

 

Then, take away 674

from 673,456

  673,456 – 674 =

672, 782 

  Apply “All from 9

and the last from

10” to 456

4 5 6

5 4 4

Answer: 76, 725 Answer: 672, 782, 544 

8/9/2019 Multiply Any Number by 9-99-999 Etc.

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Vedic Math Handouts by Swati Dave Page 4

Multiply numbers by 9, 99, 999, 9999 etc. 

Rule: Application of “All from 9 and the last from 10”  

Objective: Learn to quickly multiply any number by 9, 99, 999, 9999 etc. when

  Number of digits in the number is same as the number of digits in 9

(e.g. 75 x 99; 8765 x 9999)

  Number of digits in the number is less than the number of digits in 9’s

(e.g. 75 x 999; 876 x 9999)

  Number of digits in the number is more than the number of digits in 9’s

(e.g. 775 x 99; 87,654 x 9999)

Pre-requisite: Understanding of the rule “All from the 9 and the last from 10” 

Examples 

1.  578 x 999 = 577,422 

2. 

43, 567 x 99,999 = 4,356,656,433

3. 

78,965 x 99,999 = 7,896,421,035 

4. 

56 x 999 = 55,944

5.  5,675 x 999,999 = 5,674,994,325

6. 

912 x 99,999 = 91,199,088

7. 

5,675 x 99 = 561, 825

8.  675,468 x 99 = 66,871,332 

9.  47,652 x 999 = 47,604,348

10. 

543,652 x 999,999 = 543,651,456,348

Explanation

1.  (578 – 1 = 577); (1000 – 578 = 422) 

2. 

(43,567 – 1 = 43,566); (100,000 – 43,567 = 56,433)

3. 

(78,965 – 1 = 78,964); (100,000 – 78,965 = 21,035) 

4. 

(56 – 1 = 55); (1000 – 056 = 944)

5.  (5675 – 1 = 5,674); (1,000,000 – 005675 = 994,325)

6. 

(912 – 1 = 911); (10,000 – 009,912 = 990,088)

7. 

(56 75); (56 + 1 = 57; 5,675 – 55 = 5,618); (100 – 75 = 25)

8.  (6754 68); (6,754 + 1 = 6,755; 675,468 – 6,755 = 668,713);

(1,000 – 68 = 32)

9.  (47 652); (47 + 1 = 48; 47,652 – 48 = 47,604);

(1,000 – 652 = 348)

10. 

(543,652 – 1 = 543,651); (1,000,000 – 543,652 = 456,348)