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Bonsoir,
[tex]a)\ \dfrac{48}{78}=\dfrac{6\times8}{6\times13}=\dfrac{8}{13}\\\\b)\ \dfrac{90}{108}=\dfrac{18\times5}{18\times6}=\dfrac{5}{6}\\\\c)\ \dfrac{54}{72}=\dfrac{18\times3}{18\times4}=\dfrac{3}{4}\\\\d)\ \dfrac{162}{186}=\dfrac{6\times27}{6\times31}=\dfrac{27}{31}[/tex]
[tex]a)\ \dfrac{48}{78}=\dfrac{6\times8}{6\times13}=\dfrac{8}{13}\\\\b)\ \dfrac{90}{108}=\dfrac{18\times5}{18\times6}=\dfrac{5}{6}\\\\c)\ \dfrac{54}{72}=\dfrac{18\times3}{18\times4}=\dfrac{3}{4}\\\\d)\ \dfrac{162}{186}=\dfrac{6\times27}{6\times31}=\dfrac{27}{31}[/tex]
Je calcule le PGCD à l'aide de la méthode de la division euclidienne.
a) 78 = 48 x 1 + 30
48 = 30 x 1 + 18
30 = 18 x 1 + 12
18 = 12 x 1 + 6
12 = 6 x 2 + 0
PGCD ( 78 ; 48 ) = 6
[tex] \frac{48}{78} = \frac{6 * 48}{6*78}= \frac{8}{13} <== Simplifier[/tex]
b) 108 = 90 x 1 + 18
90 = 18 x 5 + 0
PGCD ( 108 : 90 ) = 18
[tex] \frac{90}{108}= \frac{18*90}{18*108} = \frac{5}{6} <==Simplifier [/tex]
c) 72 = 54 x 1 + 18
54 = 18 x 3 + 0
PGCD ( 72 ; 54 ) = 18
[tex] \frac{54}{72} = \frac{18*54}{18*72}= \frac{3}{4} <==Simplifier[/tex]
d) 186 = 162 x 1 + 24
162 = 24 x 6 + 18
24 = 18 x 1 + 6
18 = 6 x 3 + 0
PGCD ( 186 ; 162 ) = 6
[tex] \frac{162}{186} = \frac{6*162}{6*186}= \frac{27}{37} <==Simplifier [/tex]
a) 78 = 48 x 1 + 30
48 = 30 x 1 + 18
30 = 18 x 1 + 12
18 = 12 x 1 + 6
12 = 6 x 2 + 0
PGCD ( 78 ; 48 ) = 6
[tex] \frac{48}{78} = \frac{6 * 48}{6*78}= \frac{8}{13} <== Simplifier[/tex]
b) 108 = 90 x 1 + 18
90 = 18 x 5 + 0
PGCD ( 108 : 90 ) = 18
[tex] \frac{90}{108}= \frac{18*90}{18*108} = \frac{5}{6} <==Simplifier [/tex]
c) 72 = 54 x 1 + 18
54 = 18 x 3 + 0
PGCD ( 72 ; 54 ) = 18
[tex] \frac{54}{72} = \frac{18*54}{18*72}= \frac{3}{4} <==Simplifier[/tex]
d) 186 = 162 x 1 + 24
162 = 24 x 6 + 18
24 = 18 x 1 + 6
18 = 6 x 3 + 0
PGCD ( 186 ; 162 ) = 6
[tex] \frac{162}{186} = \frac{6*162}{6*186}= \frac{27}{37} <==Simplifier [/tex]