Between the years 1911 to 1918, the eminent Indian mathematician Jagadguru Shri Bharathi Krishna Tirthaji established a branch of mathematics known as Vedic maths. He was regarded as the first mathematician to examine earlier mathematical methods. He published his studies and findings in the book Tirthaji Maharaj: Vedic Mathematics. Vedic maths, often known as mental maths, uses straightforward techniques to answer complicated problems quickly and efficiently. Vedic maths, as opposed to conventional approaches, is thought to boost the brain’s analytical capacity five times more. The 16 sutras and 13 sub-sutras that makeup Vedic mathematics are used to mentally solve a variety of issues in all areas of mathematics.
Multiplication of 4-digit number with 1111
let us consider a 4-number digit number abcd.
We use basic tricks to solve the multiplication problem.
- The multiplication of any 4-digit number with 1111 will mostly consist of 7-digit numbers.
- The first digit of the answer will be the first digit of the given number.
It is the number in the thousands place.
=> a
- The last digit of the answer will be the last digit of the given number.
It is the number in one place.
=> d
- The second last digit is the sum of the last two numbers.
It is the sum of numbers in ten’s place and one’s place.
=> c+d
- The third last digit is the sum of the last three numbers.
It is the sum of numbers in hundreds’ place, ten’s place and one’s place.
=> b+c+d
- The middle digit of the answer is the sum of all 4 digits.
It is the sum of numbers in the thousand’s place, hundreds’ place, ten’s place and one’s place.
=> a+b+c+d
- The third digit is the sum of the first three numbers.
It is the sum of numbers in the thousand’s place, hundreds’ place and ten’s place.
=> a+b+c
- The second digit is the sum of the first 2 digits of the given number.
It is the sum of numbers in the thousand’s place and hundreds’ place.
=> a+b
Note: During the addition of digits if the sum of the digits is more than 9 place the unit digit and position and carry the one’s position to the next digit.
eg: abcd X 1111
=> Solution is a 7 digit number: _ _ _ _ _ _ _
=> a _ _ _ _ _ d
=> (a) (a+b) (a+b+c) (a+b+c+d) (b+c+d) (c+d) (d) is the solution.
Solved Examples
Question: Multiply 2222 X 1111
Answer:
The solution is a 7-digit number: _ _ _ _ _ _ _
=> 2 _ _ _ _ _2
=> 2 (2+2) (2+2+2) (2+2+2+2) (2+2+2) (2+2) (2)
=> 2 4 6 8 6 4 2
Therefore 2222 X 1111 is 2468642
Question: Multiply 1340 X 1111
Answer:
The solution is a 7-digit number: _ _ _ _ _ _ _
=> 1 _ _ _ _ _ 4
=> 1 (1+3) (1+3+4) (1+3+4+0) (3+4+0) (4+0) 0
=> 1 4 8 8 7 4 0
Therefore 1340 X 1111 is 1488740
Question: Multiply 4221 X 1111
Answer:
The solution is a 7-digit number: _ _ _ _ _ _ _
=> 4 _ _ _ _ _ 1
=> 4 (4+2) (4+2+2) (4+2+2+1) (2+2+1) (2+1) 1
=> 4 6 8 9 5 3 1
Therefore 4221 X 1111 is 4689531
Question: Multiply 6021 X 1111
Answer:
The solution is a 7-digit number: _ _ _ _ _ _ _
=> 6 _ _ _ _ _ 1
=> 6 (6+0) (6+0+2) (6+0+ 2+1) (0+2+1) (2+1) 1
=> 6 6 8 9 3 3 1
Therefore 6021 X 1111 is 6689331
Question: Multiply 4832 X 1111
Answer:
The solution is a 7-digit number: _ _ _ _ _ _ _
=> 4 _ _ _ _ _ 2
=> 4 (4+8) (4+8+3) (4+8+3+2) (8+3+2) (3+2) 2
=> 4 (12) (15) (17) (13) (5) 2
=> 4 (12) (15) (17+1) 3 5 2
=>4 (12) (15+1) 8 3 5 2
=> 4 (12+1) 6 8 3 5 2
=> (4+1) 3 6 8 3 5 2
=>5 3 6 8 3 5 2
Therefore 4832 X 1111 is 5368352
Question: Multiply 1242 X 1111
Answer:
The solution is a 7-digit number: _ _ _ _ _ _ _
=> 1 _ _ _ _ _ 2
=> 1 (1+2) (1+2+4) (1+2+4+2) (2+4+2) (4+2) 2
=> 1 (3) (7) (9) (8) (6) 2
=> 1259862
Therefore 1242 X 1111 is 1379862
Question: Multiply 3254 X 1111
Answer:
The solution is a 7-digit number: _ _ _ _ _ _ _
=> 3 _ _ _ _ _ 4
=> 3 (3+2) (3+5+2) (3+2+5+4) (2+5+4) (5+4) 4
=> 3 5 (10) (14) (11) 9 4
=> 3 5 (10) (14+1) 1 9 4
=> 3 5 (10+1) 5 1 9 4
=> 3 (5+1) 1 5 1 9 4
=> 3 6 1 5 1 9 4
Therefore 3254 X 1111 is 3615194