Digital Sum or Digit Sum or C9 method is an amazing technique of vedic mathematics that can be used for faster calculations. These tricks are beneficial for competitive exams like ssc cgl ibps po and clerks group d railway etc
Shakuntala Devi was asked to find the 23rd root of a 201 digit number. She found the answer in 50 seconds. After a lengthy program was written and 13,000 instructions were fed into a computer the machine gave the same answer, but it took a full minute.
Shakuntala Devi refers to her calculating powers as her "God-given gift". She lives in Calcutta and often travels, giving demonstrations of the talents.
Vedic mathematics is an ancient form of Hindu mathematics. Vedic techniques are designed to simplify multiplication, divisibility, finding squares, square roots, cubes, cube roots, and other aspects of mathematics, including working with recurring decimals and fractions.
This activity focuses on aspects of divisibility and multiples. For example, a number is divisible by 9 if the sum of its digits is a multiple of 9.
This is another checking device which can be very useful and which comes under the Vedic formula The Product of the Sum is the Sum of the Products.
Every number, no matter how long, can be reduced to a single figure, called its digit sum, by adding the digits in the number and then adding again if necessary.
So for 43 the digit sum is 7 since 4+3 = 7.
Also for 47: 47 = 11 = 2.
And 876 = 21 = 3.
To check a multiplication sum the above Vedic formula reads: The Product of the Digit Sums is the Digit Sum of the Products. So if we have the sum:
74 × 76 = 5624
we reduce 74, 76 and 5624 to their digit sums: 74 = 11 = 2,
76 = 13 = 4,
5624 = 17 = 8.
Then replacing the original sum with these digit sums we get 2×4 = 8, which is true, and therefore supports our answer, 5624.
This digit sum check does not detect certain errors however: if we wrote
88+77 = 156 the digit sum check would be the same as above even though the answer is wrong. However in this case The Last by the Last tells us that the answer certainly is wrong since it must end with 5.
27 × 87 = 23/49
The conditions are satisfied here as 2 + 8 = 10 and both numbers end in 7.
So we multiply the first figure of each number together and
add the last figure: 2 × 8 = 16, 16 + 7 = 23 which is the first part of the answer.
Multiplying the last figures together: 7×7 = 49: which is the last part of the answer.
Similarly 69 × 49 = 3381
in which 33 = 6×4 + 9, and 81 = 9×9.
Numbers such as 135 can be expressed in expanded form as 1 x 100 + 3 x 10 + 5. This tells us that 135 is not a multiple of 10 because the last digit, 5, is not a multiple of 10. We can also write the expanded form for 135 in a different way: (1 x 99 + 1) + (3 x 9 + 3) + 5.
Sometimes the digit sum has more than one digit. When this occurs, the students need to repeat this process until the digit sum is a single digit. We have called this digit the Vedic digit for the number. For example, 2 389 has the digit sum 2 + 3 + 8 + 9 = 22. The digit sum for 22 is 2 + 2 = 4. So the Vedic digit for 2 389 is 4, which indicates that 2 389 is not a multiple of 9.
The mathematics above is not included in the activity for the students, but it does provide a background to the activities in which the students use patterns in their completed Vedic grids to devise rules for identifying multiples of 9, 6, and 3 (see questions 1 and 2).
It may be useful to put the following questions to the students to develop their thinking about multiples and divisibility:
Question: Are all multiples of 6 and 9 also multiples of 3? Why or why not?
Answer: Yes. 6 and 9 are themselves multiples of 3, so the product formed when any (whole) number is multiplied by 6 or 9 will also be divisible by 3 and be a multiple of 3. For example, 12 (a multiple of 6) is also a multiple of 3, and 18 (a multiple of both 6 and 9) is also a multiple of 3.
Question: Are all multiples of 9 also multiples of 6? Why or why not?
Answer: No. A number such as 27 is a multiple of 9 but not of 6. Multiples of 9 are sometimes odd (as with 27) but multiples of 6 are always even.
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