# Special Contribution by. Indian Institute of Vedic Mathematics & Abacus New Delhi

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1 Special Contribution by Indian Institute of Vedic Mathematics & Abacus New Delhi 1 VEDAS TO VINCULUM 2 ABACUS Office of the State Project Office (SSA/RMSA) Himachal Pradesh, Shimla

2 Introduction It gives me an immense pleasure to share that Indian Institute of Vedic Maths and Abacus (IIVA) New Delhi, imparted 5 days training to 43 teachers of Government Schools of Himachal Pradesh in Abacus & Vedic Mathematics under RMSA. It is an eye opener experience & we look forward to inculcate this methodology in regular teaching pattern in our schools especially during readiness Programme in the beginning of session in all the secondary classes beginning from 6th to 10th. I therefore pass on my best wishes to Indian Institute of Vedic math and Abacus (IIVA) and TGT (Non Medical) of Himachal Pradesh and strongly recommend that these tactics may be propagated nationally and in the State for the benefits of students. State Project Director (RMSA) Shimla-1, Himachal Pradesh.

3 1

4 JOURNEY THROUGH TEMPUS Vedic Mathematics is a book written by the Indian Hindu priest jagadguru swami sri bharti krishna tirtha ji (rediscovered from vedas between 1911 and 1918) first published in It contains a list of mental calulation techniques based on the vedas. The mental calculation system mentioned in the book is also known by the same name or as "Vedic Maths 2

5 Vedic mathematics comprises 16 Sutras(formulae) & their subsutras(corollaries) At doer s end: doer has to identify and spot certain characteristics, patterns and then apply the sutra ( formula) which is applicable there to 3

6 Reduces silly mistakes Fastens the calculations Intelligent guessing Reduces burden Makes mathematics a bit of fun game for pupils 4

7 MULTIPLICATION BY 11 & ITS MULTIPLES 5

8 Put single 0 in extreme left and extreme right of the multiplicand (Single naught sandwich) Add the digits in pair starting from right to left 6

9 = (4+0=4) (1+4=5) (3+1=4) (2+3=5) (0+2=2)

10

11 IF SUM OF 2 DIGITS OF MULTIPLICAND EXCEEDS 9 When the sum exceeds 9 then carry the tens place digit & add to the preceding digit Single naught sandwich= =4 4+2=6 2+8=10=10 8+2=10=10+1=11=11 2+0=2=2+1=3 Product=

12 MULTIPLICATION BY MULTIPLES OF 11 (22,33, ) Multiply the multiplicand by the number of rank of the multiple (e.g. 44 is 4th and 99 is 9th multiple so multiply the multiplicand by 4 or 9 in case we are multiplying by 44 or 99) Then apply the rule of multiplication by 11 to the product obtained (single naught sandwich) 10

13 (2 11) 245 2=

14 MULTIPLICATION BY (Add 2 zeroes to the extreme right and extreme left of the multiplicand) Double Naught Sandwich Sandwiched Number=

15 (Double naught sandwich) Add 3 digits at a time starting from right to left 13

16

17 MULTIPLICATION BY MULTIPLES OF 111 (222 TO 999) Find the rank of the multiple (for 555 the rank is 5, for 777 the rank is 7 and so on) Multiply the multiplicand by the number of rank Apply the multiplication of 111 the product obtained (Double Naught Sandwich Method) 15

18 WORKING (2 111) (2 1348) (Double Naught Sandwich) 16

19

20 MULTIPLICATION BY 12 TO 19 (sutra sopantyadvayamantyam) sandwich the multiplicand between single zero Multiply each digit of the multiplicand by first digit of the multiplier from right to left and add to the immediate right digit following it one by one 18

21 WORKING (2 0)+1=1 1 (2 1)+2=4 4 (2 2)+3=7 7+1 (2 3)+5= (2 5)+0=

22 AME METHOD FOR TO Practice the method for

23 MULTIPLICATION OF SPECIAL NUMBERS Antyayordasake pi

24 Multiply the unit digit & write the product in two digits on one s & ten s place Multiply the ten s place digit with its successor 63 (7 3=21) (6 7=42)

25 22 82 Multiply the unit digits & write the product in two digits, one s & ten s place Multiply the ten s place digits & add one unit digit then put in hundred's & thousand s place (2 2=04) [(8 2)+2]

26 PRACTICE THE METHOD.. 24

27 NDEAVOUR Gaurav Raj (TGT N/M) GHS Dakahal Edu. Block: Kotkhai Distt. Shimla Yogesh Kumar (TGT N/M) GHS Samleu Edu. Block Banikhet Distt. Chamba Sunita Bindra (TGT N/M) GSSS Tutu Distt Shimla 25

28 26

29

30 GENERAL OBJECTIVES TO IMPROVE CONCENTRATION. TO IMPROVE MEMORY. TO GENERATES SELF CONFIDENCE AND IMPROVES PROFICIENCY. TO IMPROVE BRAIN DEVELOPMENT.

31 INTRODUCTION Abacus is a latin word that has its origin from greek word ABAX or ABAKON, meaning table or tablets. The abacus also called a counting frame, is a calculating tool that was in use in Japan, China and Russia. ABACUS is used for multiplication, division, addition, subtraction, square root and cube root operations at high speed. ABACUS is used for visual articulation and teach maths.

32 ABACUS DEVICE

33

34

35

36 Abacus based on 4 Topics :1. Without Compliments s compliments s compliments. 4. Mixed compliments.

37 Without compliments : Without compliments means direct sums. We can calculate the sum without using any formula.

38 Steps for without compliments:-

39 Step -1 To clear abacus i.e. to show zero on abacus with pinch. When all beads are on their respective position, the value shown is zero.

40 Zero value on ABACUS

41 Left hand s thumb and index finger to operate the abacus tool.

44 Practice Sums ( without compliments) (a) (b) (c) (d)

45 Subtraction: For subtraction take the beads away from value bar. (When beads are available)

46 5 s compliments. 5 s compliments are used when beads are not available for addition or subtraction of digits 1,2,3 & 4. For example if we want to add 1 in 4 beads that is not possible without complication method for that we have to use 5 s compliments.

47 Compliments of 5 s (+) For making 5 1 is friend of 4 Compliments +1 = is friend of 3 +2 = is friend of 2 +3= is friend of 1 +4 = +5-1

48 Compliments of 5 s (-) For making 5 1 is friend of 4 Compliments -1 = is friend of 3-2 = is friend of 2-3= is friend of 1-4 = +1-5

49 Step :- 1 Take 4 beads towards the value bar.

50 Step :- 2 For adding 1 use compliments +5-4 brings bead down with index finger and remove four lower beads with index finger. The rod represents 5 as answers ( so answer to question 4+1 = 5).

51 Practice Sums ( with 5 s compliments) (a) (b) (c) (d) 4 2-2

52 10 s compliments 10 s compliments are used when beads are not available for adding directly then we use 5 s compliments and if beads are not available to use 5 compliments even then we use 10 s compliments For example if we want to add 1 in 9 beads that is not possible without complication method and five compliments method for that we have to use 10 s compliments.

53 Compliments of 10 s (+) For making 10 1 is friend of 9 2 is friend of 8 3 is friend of 7 4 is friend of 6 5 is friend of 5 6 is friend of 4 7 is friend of 3 8 is friend of 2 9 is friend of 1 Compliments +1 = = = = = = = = =

54 Compliments of 10 s (-) For making 10 1 is friend of 9 2 is friend of 8 3 is friend of 7 4 is friend of 6 5 is friend of 5 6 is friend of 4 7 is friend of 3 8 is friend of 2 9 is friend of 1 Compliments -1 = = = = = = = = =

55 Step :- 1 Take 9 beads towards the value bar with pinch in method.

56 Step :- 2 For adding 1, 10 s compliments will be used. First remove 9 ( as 9 is a friend of 1) rod with pinch out method and bring 1 bead up with thumb on rod B (10 s). The rod represents 10 as answers ( so answer to question 9+1 = 10).

57 Practice Sums ( with 10 s compliments) (a) (b) (c) (d) 6 3 3

58 Mixed compliments. Mixed compliments are used specially for adding and subtracting numbers 6,7,8 and 9. In case where these number cannot be added or subtracted directly and with the 10 s compliments, then the mixed compliments will be used. For Appling mixed compliments for addition 5 should be on value bar.

59 For example if we want to add 6 in 5 beads that is not possible without compliment method, 5 s compliments method and 10 s compliments method for that we have to use mixed compliments method = 11

60 Take 5 beads towards the value bar.

61 Remove or subtract 5 with left index finger and add 1 with left hand thumb in unit rod. Add 1 bead on rod with the help of left thumb.

62 The rod represents 11 as answer( so answer to question 5+6 = 11).

63 Presented by: Sh. Jai Singh TGT (N.M) GMS Grahana u/c GSSS Dalash (kullu) Sh. Jeet Lect. In mathematics GSSS Bajaura(kullu) Sh. Sandeep TGT (N.M) GMS Narogi u/c GSSS Bhunter (kullu) Sh. Govind Thakur TGT (N.M) GHS Sari (kullu) Sh. Jag jeevan Pal TGT (N.M.) GSSS Nirmand (kullu)

64

65 List of Resource Persons Abacus and Vedic Maths Sr. No Name Designation Adress Tehsil District Ph. No. 1 YOGESH KUMAR TGT(N.M) GHS Samleu Dalhougi Chamba RAKESH KUMAR TGT(N.M) GHS Guniala Dalhogi Chamba LUDDAR DUTT TGT(N.M) GHS Sathwin Hamirpur Hamirpur SANJEEV KUMAR TGT(N.M) GMS Nara Badsar Hamirpur SANDEEP KUMAR Lec( Maths) GHS Bhali Kangra Kangra SUDERSHAN KUMAR Lec Maths GSSS B Garli Rakkar Kangra PANKAJ ANAND Lec (Maths) GSSS Dheera Kangra Kangra KEWAL SINGH TGT(N.M) GSSS Khanni Kangra Kangra ATUL SHARMA TGT(N.M) GSSS Kanam Pooh Kinnaur MANOJ KUMAR TGT(N.M) GHS Chansu Sangla Kinnaur NAROTAM KASWAL TGT(N.M) GHS Panvi Nichar Kinnaur ASHWANI KUMAR TGT(N.M) GSSS Urni Nichar Kinnaur HARISH KUMAR TGT(N.M) GSSS Sangla Sanla Kinnaur GOVIND THAKUR TGT(N.M) GHS Sari Banjar Kullu JEET Lec Maths GSSS Bajaura Bhunter Kullu SANDEEP TGT(N.M) GMS Narogi Bhunter Kullu JAI SINGH TGT(N.M) GMS Grahana Anni Kullu JAGJEEVAN PAL TGT(N.M) GSSS Nirmand Nirmand Kullu VISHAL GUPTA PGT(Maths) GSSS Jhahlman Udiapur L&S KULDIP DOGRA TGT(N.M) Kalong L&S JAI PAL PGT(Maths) GSSS Malang Keylong L&S HAKAM CHAND RANA TGT(N.M) GSSS paplog Sarkaghat Mandi SATISH KUMAR TGT(N.M) GMS Nagrota Baldwara Mandi LALIT KUMAR TGT(N.M) GSSS Dehar Sun Ngr Mandi DILA RAM VERMA TGT(N.M) GSSS Kapahi Sun Ngr Mandi SHILPI THAKUR TGT(N.M) GHS Nandi Chachi Mandi SUNITA BINDRA TGT(N.M) GSSS Totu Shimla Shimla GAURAV RAJ TGT(N.M) GHS Dakahal Kotkhai Shimla NIRUPAMA DHANJAL TGT(N.M) Shimla Shimla BALBIR SHARMA TGT(N.M) DIET Shimla GSSS Bandhi Dhadar Shilai Sirmour DEEP RAM SHARMA TGT(N.M) GSSS Haripurdhar Sirmaur Sirmour DEVRAJ THAKUR TGT(N.M) GHS Nihog Sirmaur Sirmour TGT(N.M) GMS Rugra Solan Solan Dr. ANJEEV KUMAR GMS Khangsar

66 34 KANHIYA LAL SHARMA Lec(Maths) 35 VINOD KUMAR SOOD 36 SANDEEP VASUDEV DIET Solan Solan Solan PGT(Maths) GSSS Chandi(Ark) TGT(N.M) GSSS Baliwal Arki Haroli Solan Una NEERAJ SAINI TGT(N.M) GSS Bhadsali Haroli Una ANUJ KUMAR TGT(N.M) GMS Barsara Una Una RAJ KUMAR TGT(N.M) GMS sapouri Una Una SATISH KUMAR TGT(N.M) GSSS Saroh Bangana Una

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