Raspuns scurt :
Fractiile sunt :
9070/24,9170/24,9270/24,9370/24,9470/24,9570/24,9670/24,9770/24,9870/24,9970/24,9071/24,9171/24,9271/24,9371/24,9471/24,9571/24,9671/24,9771/24,9871/24,9971/24,9172/24,9272/24,9372/24,9472/24,9572/24,9772/24,9872/24,9972/24,9073/24,9173/24,9273/24,9373/24,9473/24,9573/24,9673/24,9773/24,9873/24,9973/24,9074/24,9174/24,9274/24,9374/24,9474/24,9574/24,9674/24,9774/24,9874/24,9974/24,9075/24,9175/24,9275/24,9375/24,9475/24,9575/24,9675/24,9775/24,9875/24,9975/24,9076/24,9176/24,9276/24,9376/24,9476/24,9676/24,9776/24,9876/24,9976/24,9077/24,9177/24,9277/24,9377/24,9477/24,9577/24,9677/24,9777/24,9877/24,9977/24,9078/24,9178/24,9278/24,9378/24,9478/24,9578/24,9678/24,9778/24,9878/24,9978/24,9079/24,9179/24,9279/24,9379/24,9479/24,9579/24,9679/24,9779/24,9879/24,9979/24
In total 97 de fractii.
Raspuns complet, matematic :
24 = 8*3
Presupunem ca 9y7xsupra 24 e reductibil.
Teorema : Daca a este divizibil cu m*n, atunci a este divizibil cu m si a este divizibil cu n.
Deci 9y7x e divizibil cu 8 si 9y7x e divizibil cu 3.
Criteriul de divizibilitate cu 3 :
9 + y + 7 + x divizibil cu 3
Deci avem urmatoarele perechi :
x = 0 si y = 2
x = 0 si y = 5
x = 0 si y = 8
x = 1 si y = 1
x = 1 si y = 4
x = 1 si y = 7
x = 2 si y = 0
x = 2 si y = 3
x = 2 si y = 6
x = 2 si y = 9
x = 3 si y = 2
x = 3 si y = 5
x = 3 si y = 8
x = 4 si y = 1
x = 4 si y = 4
x = 4 si y = 7
x = 5 si y = 0
x = 5 si y = 3
x = 5 si y = 6
x = 5 si y = 9
x = 6 si y = 2
x = 6 si y = 5
x = 6 si y = 8
x = 7 si y = 1
x = 7 si y = 4
x = 7 si y = 7
x = 8 si y = 0
x = 8 si y = 3
x = 8 si y = 6
x = 8 si y = 9
x = 9 si y = 2
x = 9 si y = 5
x = 9 si y = 8
Criteriul de divizibilitate cu 8 :
y7x e divizibil cu 8.
Verificam care din perechile de mai sus indeplinesc criteriul de divizibilitate cu 8 :
x = 2 si y = 0
x = 2 si y = 6
x = 6 si y = 5
(cazuri pentru 9y7xsupra 24 reductibil )
Avem 10 * 10 = 100 cazuri posibile. In trei dintre acestea 9y7xsupra 24 este reductibila. Deci in 100 - 3 = 97 cazuri fractia e ireductibila.
Raspuns final : 97 fractii