euclid's division lemma

15
ACTIVITY 01 CLASS X

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ACTIVITY ON REAL NUMBERS FOR CLASS X

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Page 1: EUCLID'S DIVISION LEMMA

ACTIVITY 01

CLASS X

Page 2: EUCLID'S DIVISION LEMMA

OBJECTIVE

TO FIND THE HCF OF TWONUMBERS EXPERIMENTALLYBASED ON EUCLID’SDIVISION LEMMA

Page 3: EUCLID'S DIVISION LEMMA

MATERIALS REQUIRED

CARD BOARD SHEETSGLAZED PAPERS OF DIFFERENT COLOURSSCISSORSRULERSKETCH PEN GLUE ETC.,

Page 4: EUCLID'S DIVISION LEMMA

METHOD OF CONSTRUCTIONCUT OUT ONE STRIP OF LENGTH a UNITS, ONESTRIP OF LENGTH b UNITS [ b<a], TWO STRIPS EACH OF LENGTH c UNITS [ c<b], ONE STRIP OF LENGTH d UNITS [ d<c] AND TWO STRIPS EACH OF LENGTH e UNITS [ e<d] FROM THE CARDBOARD.

Page 5: EUCLID'S DIVISION LEMMA

METHOD OF CONSTRUCTION

COVER THESE STRIPS IN DIFFERENT COLOURS USING GLAZED PAPERS AS SHOWN INFIG 1 AND FIG 2.

ab

Page 6: EUCLID'S DIVISION LEMMA

FIGURES 3,4 & 5

C C

d

e e

Page 7: EUCLID'S DIVISION LEMMA

Fig 6, 7, 8 and 9STICK THESE STRIPS ON THE OTHER CARDBOARD SHEET AS SHOWN IN THE FIG.6 TO FIG.9

c FIG.6

ab

c

Page 8: EUCLID'S DIVISION LEMMA

d FIG 7.

FIG . 8 FIG. 9

bc

c

c d

d e e

FIG CONTINUED…

d

e

Page 9: EUCLID'S DIVISION LEMMA

DEMONSTRATION

AS PER EUCLID’S DIVISION LEMMA, [ a= bq + r]

FIG. 6 DEPICTS a = b X 1 + c Here, q = 1, r = c

ab

c

Page 10: EUCLID'S DIVISION LEMMA

FIG.7 DEPICTS b = c X 2 + d

Here, q = 2 , r= d

bc

c

d

Page 11: EUCLID'S DIVISION LEMMA

FIG.8 DEPICTS C = d X 1 + eHere, q = 1 , r= e

FIG.8 DEPICTS d = e X 2 + 0Here, q = 2 , r= 0

c d e

d e e

Page 12: EUCLID'S DIVISION LEMMA

As per assumption in Euclid Division Algorithm,HCF of a and b = HCF of b and c = HCF of c and d = HCF of d and eThe HCF of d and e is equal to e.So, HCF of a and b = e.

Page 13: EUCLID'S DIVISION LEMMA

OBSERVATIONOn actual measurement [ in mm ]a = _____________, b = ________________

c = ______________, d = _________________

e = _______________

So, HCF of _________ and ________ = ________

Page 14: EUCLID'S DIVISION LEMMA

CONCLUSION

The process depicted can be used forFinding The HCF of two or morenumbers, which is Known as finding HCF of numbers by Division Method.

Page 15: EUCLID'S DIVISION LEMMA

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