Question

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Answer 1

6.
a+b=(24x8+3)/8=195/8 
a=b+(3x6+5)/6=b+23/6
b+23/6 +b=195/8
Numitorul comun este 48.
48b+23x8+48b=195x6
96b=1170-192
96b=978 =>b=978/96=489/48=10 intregi 9/48

7.
a+b=(32x12+5)/12=389/12
a=b-(9x18+7)/18=b-169/18
b- 169/18 + b=389/12
Numitorul comun este 36.
36b-169x2+36b=389x3
72b=389x3+169x2
72b=1167+338
72b=1505 =>b=1505/72=20 intregi 65/72

8.
a+b=(36x4+3)/4=147/4
a-b=(24x6+5)/6=149/6 
Adunam cele doua expresii si avem
2a=147/4 + 149/6
Numitorul comun este 12.
24a=147x3+149x2
24a=441+298
24a=739 =>a=739/24 =>a=30 intregi 19/24
739/24 + b=147/4
Numitorul comun este 24.
739+24b=147x6
739+24b=882
24b=143 =>b=143/24 =>b=5 intregi 23/24