euclid's division lemma
DESCRIPTION
ACTIVITY ON REAL NUMBERS FOR CLASS XTRANSCRIPT
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ACTIVITY 01
CLASS X
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OBJECTIVE
TO FIND THE HCF OF TWONUMBERS EXPERIMENTALLYBASED ON EUCLID’SDIVISION LEMMA
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MATERIALS REQUIRED
CARD BOARD SHEETSGLAZED PAPERS OF DIFFERENT COLOURSSCISSORSRULERSKETCH PEN GLUE ETC.,
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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.
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METHOD OF CONSTRUCTION
COVER THESE STRIPS IN DIFFERENT COLOURS USING GLAZED PAPERS AS SHOWN INFIG 1 AND FIG 2.
ab
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FIGURES 3,4 & 5
C C
d
e e
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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
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d FIG 7.
FIG . 8 FIG. 9
bc
c
c d
d e e
FIG CONTINUED…
d
e
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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
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FIG.7 DEPICTS b = c X 2 + d
Here, q = 2 , r= d
bc
c
d
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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
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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.
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OBSERVATIONOn actual measurement [ in mm ]a = _____________, b = ________________
c = ______________, d = _________________
e = _______________
So, HCF of _________ and ________ = ________
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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.
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