Bonjour,

1)

A = 1/15 - 8/15 x 5/4

A = (1 x 4) / (15 x 4) - 40/60

A = 4/60 - 40/60

A = - 36/60

A = (12 x - 3) / (12 x 5)

A = - 3/5

B = (1/5 - 8/15) x 5/4

B = [(1 x 3) / (5 x 3) - 8/15] x 5/4

B = (3/15 - 8/15) x 5/4

B = - 5/15 x 5/4

B = - 25/60

B = (5 x - 5) / (5 x 12)

B = - 5/12.

C = - 4/7 : 5/14 + 5/6

C = - 4/7 x 14/5 + 5/6

C = - 56/35 + 5/6

C = (- 56 x 6) / (35 x 6) + (5 x 35) / (6 x 35)

C = - 336/210 + 175/210

C = - 161/210

C = (7 x - 23) / (7 x 30)

C = - 23/30

D = (- 3/4 + 1/2) : (2/5 - 5/2)

D = [- 3/4 + (1 x 2) / (2 x 2)] : [(2 x 2) / (5 x 2) - (5 x 5) / (2 x 5)]

D = (- 3/4 + 2/4) : (4/10 - 25/10)

D = - 1/4 : - 21/10

D = - 1/4 x - 10/21

D = 10/84

D = (2 x 5) / (2 x 42)

D = 5/42.

2)

1 - 1/5 = (1 x 5) / (1 x 5) - 1/5 = 5/5 - 1/5 = 4/5

Après que Tom ait dépensé 1/5 de son argent de poche il lui en reste 4/5.

4/5 x 3/4 = 12/20 = (4 x 3) / (4 x 5) = 3/5

Tom dépense 3/5 de son argent de poche pour acheter du pop corn

3/5 = 9 € donc 9 x 5 : 3 = 15 €

Tom avait initialement 15 € d'argent de poche.