TEMA3_HOJA1_OPERACIONES_FRACCIONES_SOLUCIONES

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(1)IES Juan García Valdemora Departamento de Matemáticas. TEMA 3. HOJA 1. OPERACIONES COMBINADAS CON FRACCIONES 2º ESO. OPERACIONES CON FRACCIONES 1. Calcula y simplifica: 18 105 18 ⋅ 105 2 ⋅ 3 2 ⋅ 3 ⋅ 5 ⋅ 7 2 ⋅ 33 ⋅ 5 ⋅ 7 3 = = 2 2 ⋅ = = a) 2 2 35 36 35 ⋅ 36 5⋅7 ⋅ 2 ⋅3 2 ⋅3 ⋅5⋅7 2 6 6 2  105   192  105 ⋅ 192 3 ⋅ 5 ⋅ 7 ⋅ 2 ⋅ 3 2 ⋅ 3 ⋅ 5 ⋅ 7 2 ⋅ 3 ⋅ 7 b)  − = 4 = = = 42 ⋅− = 1 2 ⋅ 2⋅3⋅5 25 ⋅ 3 ⋅ 5  16   30  16 ⋅ 30. 64 ⋅ 27 2 6 ⋅ 33 2 6 ⋅ 33  64  32 c)  : = − = − = − = −1  54 ⋅ 32 2 ⋅ 33 ⋅ 2 5 2 6 ⋅ 33  − 54  27. d). 15 21 27 45 15 ⋅ 21 27 ⋅ 28 3 ⋅ 5 ⋅ 3 ⋅ 7 33 ⋅ 2 2 ⋅ 7 3 2 ⋅ 5 ⋅ 7 2 2 ⋅ 3 3 ⋅ 7 ⋅ − : = − = − = 2 − = 7 25 14 28 7 ⋅ 25 14 ⋅ 45 7 ⋅ 52 2 ⋅ 7 ⋅ 32 ⋅ 5 5 ⋅7 2 ⋅ 32 ⋅ 5 ⋅ 7 =. e). 32 2 ⋅ 3 9 6 3 − = − = 5 5 5 5 5. 9 35 4 7 21 9 ⋅ 35 ⋅ 4 7 ⋅ 45 32 ⋅ 5 ⋅ 7 ⋅ 2 2 7 ⋅ 32 ⋅ 5 − = ⋅ ⋅ − : = − = 14 18 15 15 45 14 ⋅ 18 ⋅ 15 15 ⋅ 21 2 ⋅ 7 ⋅ 2 ⋅ 3 2 ⋅ 3 ⋅ 5 3 ⋅ 5 ⋅ 3 ⋅ 7 =. 2 2 ⋅ 32 ⋅ 5 ⋅ 7 32 ⋅ 5 ⋅ 7 1 1− 3 2 − 2 = −1 = =− 2 3 3 3 2 ⋅3 ⋅5⋅7 3 ⋅5⋅7 3. 35 ⋅ 5 3  243 125   196 225  243 ⋅ 125  196 ⋅ 225  f)  ⋅ : ⋅ ⋅ = : − =      3 4  250 162   100 − 147  250 ⋅ 162  100 ⋅ 147  2 ⋅ 5 ⋅ 2 ⋅ 3 35 ⋅ 53 = 2 4 3 2 ⋅3 ⋅5.  2 2 ⋅ 32 ⋅ 52 ⋅ 7 2 :  − 2 2 2  2 ⋅3⋅5 ⋅7.  2 2 ⋅ 7 2 ⋅ 32 ⋅ 52 :  − 2 2 2  2 ⋅5 ⋅3⋅7.   = .  3 3 3 1  = 2 : (− 3) = : (−3) = − =− 4 4⋅3 4  2. 11 11 11 ⋅ 20 20 4  24 84  33  2 7  11  10 − 21  11 g)  −  : =  − : = =− : =− =− = − : simplifica r simplifica r (: 5) 15 20 11 ⋅ 15 15 3  36 60  60 las  3 5  20  15  20 fracciones. h). 4  15 21   − 6   100 125  4 15 ⋅ 21  − 6  100 ⋅ 35 4 ⋅ 49 ⋅ 45 6 ⋅ 98 ⋅ 125 : ⋅ + : : + = − = : = : 49  49 45   147   98 35  49 49 ⋅ 45  147  98 ⋅ 125 49 ⋅ 15 ⋅ 21 147 ⋅ 100 ⋅ 35 =. 2 2 ⋅ 49 ⋅ 3 2 ⋅ 5 2 ⋅ 3 ⋅ 2 ⋅ 7 2 ⋅ 53 2 2 ⋅ 32 ⋅ 5 2 2 ⋅ 3 ⋅ 53 ⋅ 7 2 2 2 1 4 1 3 − = − = − = − = 49 ⋅ 3 ⋅ 5 ⋅ 3 ⋅ 7 3 ⋅ 7 2 ⋅ 2 2 ⋅ 5 2 ⋅ 5 ⋅ 7 3 2 ⋅ 5 ⋅ 7 2 2 ⋅ 3 ⋅ 5 3 ⋅ 7 3 7 7 7 7 7.

(2) IES Juan García Valdemora Departamento de Matemáticas. TEMA 3. HOJA 1. OPERACIONES COMBINADAS CON FRACCIONES 2º ESO. 9 ⋅ 25 ⋅ 10 108 ⋅ 25 ⋅ 14  9   25   − 10   − 108   25   − 14  i)  − = ⋅ ⋅ + ⋅− ⋅ =  125   − 18   14   175   6   18  125 ⋅ 18 ⋅ 14 175 ⋅ 6 ⋅ 18 32 ⋅ 5 2 ⋅ 2 ⋅ 5 2 2 ⋅ 33 ⋅ 5 2 ⋅ 2 ⋅ 7 2 ⋅ 3 2 ⋅ 53 2 3 ⋅ 33 ⋅ 5 2 ⋅ 7 1 2 1 1 − 28 27 = 3 − 2 = 2 2 3 − 2 3 2 = − = −2= =− 2 2 14 14 5 ⋅ 2⋅3 ⋅ 2⋅7 5 ⋅7 ⋅ 2⋅3⋅ 2⋅3 2 ⋅ 3 ⋅ 5 ⋅ 7 2 ⋅ 3 ⋅ 5 ⋅ 7 2 ⋅ 7 1 14. 2. Calcula y simplifica: a). 4 1 2 3 : +  − 3 3 6 4 =. b). =. paréntesis. 4 2 2 3 4 4 3 4 2 3 : +  − = :  − = : − simplifica r 3 6 6 4 3 6 4 3 3 4. =. división. 12 3 3 − = 2− = simplifica r 6 4 4. 8−3 5 = 4 4. 5 1 1  3  4 5  5 1  3  11 + 4  5  4  3  15  ⋅  −  + ⋅ 1 +  = ⋅ −  + ⋅  = ⋅  + ⋅  = paréntesis 11  2 10  5  11  11  10 10  5  11  11  10  5  11  simplificar. =. 5 2 3 15 ⋅ + ⋅ 11 5 5 11. =. operar y simplificar. 5 ⋅ 2 3 ⋅ 3 ⋅ 5 2 9 11 + = + = =1 11 ⋅ 5 5 ⋅ 11 11 11 11. c). 4 2 4 2 5 1 3 12 8 5 5 36 − 32 + 100 − 25 79 : − ⋅ + − : = − + − = = 10 3 5 3 3 4 5 20 15 3 12 60 60. d). 2 1 3  1 1 2  2 3  1 2 2  1   1 20 1 :  −  +  −  = :  −  +  −  = : −  + −  = − − = 5  5 10   4 2  5  10 10   4 4  5  10   4  5 4 =. simplificar. −4−. 1 − 16 − 1 17 = =− 4 4 4. 2. 3 3 1 9 3 3 1 3 e) + ⋅  − = + ⋅ − 2 4 3 16 2 4 9 4. f). 6 2 4 4 1 3 3 : − ⋅ + − : 10 3 5 3 3 4 7 =−. g). =. operar y simplificar. =. operar y simplificar. 3 3 ⋅1 3 3 1 3 18 + 1 − 9 10 5 + − = + − = = = 2 4 ⋅ 3 ⋅ 3 4 2 12 4 12 12 simplificar 6. 2 ⋅ 3 ⋅ 3 16 1 3 ⋅ 7 9 16 1 7 54 − 64 + 20 − 105 − + − = − + − = = 2 ⋅ 5 ⋅ 2 15 3 4 ⋅ 3 10 15 3 4 60. 95 19 = − simplifica r 60 12. 4  2 1  2 5 1 3 2  10 3  2 5 5 2 7 2 5 5 2 ⋅ 3 ⋅ 5 2 5 5 : − ⋅ + − : = : − ⋅ + − = : ⋅ + − = ⋅ + − = 10  3 5  3 3 4 5 5  15 15  3 3 12 5 15 3 3 12 5 ⋅ 7 3 3 12.

(3) IES Juan García Valdemora Departamento de Matemáticas. =. TEMA 3. HOJA 1. OPERACIONES COMBINADAS CON FRACCIONES 2º ESO. 2 ⋅ 3 ⋅ 5 ⋅ 2 5 5 4 5 5 48 + 140 − 35 153 51 + − = + − = = = 5⋅7⋅3 3 12 7 3 12 84 84 28. 2 7 5 1  4 2 h)  − − +  +  − + − 3 2 6 4  3 3. 2. 1 (− 6)2. 2.   8 − 42 − 10 + 3   4 2 1   =  =  +  − + −   12 36    3 3 . 41  − 5  41 25 − 123 + 25  41   4 2 1   41   − 8 + 4 − 1  = −  + − + −  = −  +  = =  =− +  =− + 6 12  6  12 36 36  12   3 3 6   12    98 49 =− =− 36 18 2. i). 2. 3 2 7 2 3 14 2 3 4  2 1  2 5 1 3 2  10 3  6 ⋅ −  + : − ⋅ = ⋅ −  + − = ⋅ + − = + − = 10  3 5  3 3 4 5 5  15 15  15 20 5 15 5 20 75 5 20 =. j). 2. 56 + 120 − 45 131 = 300 300. 1  3  1  3 − 4  1  1  1 1 2 +1 3 −  − 1 − − −   + 3 7 3⋅ 4 3 2 4  2  4  2  4 2 4 = = = = 4 = 4= : = = 3 3+ 4 7 7 7 7 4 4 4⋅7 7 +1 4 4 4 4 4 4.  2 5   3 5   6 5   9 10   1   1  1 1 1  − ⋅ −   − ⋅ −    ⋅−  − − − 3 9   4 6   9 9   12 12   9   12  108 k)  = = == = 108 = 108 = 1 2 7 5 4 7 10 4 3 4 1 4          −  ⋅ +1  −  ⋅ +1 −  ⋅ +1 −  ⋅ +1 − +1 3 3  12 6  3  12 12  3  12  3  4 3 =−. 1 2 3 3 1 : =− − =− 108 3 108 ⋅ 2 3 ⋅ 36 ⋅ 2 72. 2 6 2 1 1 6 − 30 + 10 3+ 2 − 14 5 − + +  14 − 9   5 28  5 3 3 − 2 3 = 15 6 − = 15 − 6 =  − : − :  = 2 6 2 6 20 − 8 − 30 10 + 18 − 18 28 15 10   6 15   1− − + 5 4 3 5 20 15 20 15. l).  14 ⋅ 10   5 ⋅ 15   14 ⋅ 2 ⋅ 5   5 ⋅ 3 ⋅ 5  28 25 1568 − 675 893 = + = = − = − = 1512 1512  15 ⋅ 9   6 ⋅ 28   3 ⋅ 5 ⋅ 9   2 ⋅ 3 ⋅ 28  27 56. m). 5  1 3 2  3  4 3  5  1 9  3  16 − 15  5  4 + 9  3  16 − 15  ⋅ + :  − ⋅ −  = ⋅ +  − ⋅  = ⋅  − ⋅ = 3  2 4 3  7  5 4  3  2 8  7  20  3  8  7  20  =. 5 13 3 1 65 3 2275 − 18 2257 ⋅ − ⋅ = − = = 3 8 7 20 24 140 840 840.

(4) IES Juan García Valdemora Departamento de Matemáticas.  1  1 1 n) 1 +  ⋅ 1 −  +    2  3  2  =1+. 2. TEMA 3. HOJA 1. OPERACIONES COMBINADAS CON FRACCIONES 2º ESO.  16 3   2 + 1   3 − 1  1  4 3  3 2 1 1 ⋅  −  =  ⋅  + ⋅ −  = ⋅ + ⋅ = 25 5  2   3  4  5 5 2 3 4 5 . 1 20 + 1 21 = = 20 20 20. 3. Calcula y simplifica: a). 3  5 1  4  3 1  3  10 − 3  4  15 − 4  3  7  4  11  3 ⋅ 7 4 ⋅ 11 ⋅ −  − ⋅ −  = ⋅ − =  − ⋅  = ⋅  − ⋅  = 8  3 2  11  4 5  8  6  11  20  8  6  11  20  8 ⋅ 6 11 ⋅ 20 =. b). 3⋅7 4 ⋅ 11 7 1 35 − 16 19 = − = − = 8 ⋅ 2 ⋅ 3 11 ⋅ 4 ⋅ 5 16 5 80 80. 5  3 1   1 3  5  − 3 + 2   5 − 6  5  −1  −1 5 1 1 − − +  +  −  = −  = +  = − +  = + − 4  4 2   2 5  4  4   10  4  4   10  4 4 10 =. 25 + 5 − 2 28 7 = = 20 20 (:4) 5. 1 3. c) 1 − 2 ⋅  −. 1 1  5 − 4  1 1 1 2 2  1 1  1 1 1 ⋅  −  + 1 :  :  = 1 − 2 ⋅  − ⋅  +1:  =  + 1:  = 1 − 2 ⋅  − ⋅ 2  4 5 3 3  3 2   3 2 20  3 2  20 . 2 ⋅ 217 2 ⋅ 217 1 1 3   40 − 3 + 180   217  =1− 2⋅  − +  =1− 2⋅  =1− 2⋅  =1− =1− =   120 120 2 ⋅ 60  3 40 2     120 . =1−. 217 60 − 217 157 = =− 60 60 60. 1 3. 1 1 1  3   3 + 2   2 −1 5  5 1  5 − 3  ⋅  −  + 2 − 3 ⋅  1 : − 1 =  ⋅  + 2 − 3 ⋅  − 1 =   ⋅   + 2 − 3 ⋅  = 2 2 4  5   6   4  3  6 4  3 . d)  +. =. e). 5 2 5 5 + 2 − 3⋅ = +2−2= 24 3 24 24. 1 1  1 1     3   1 1  2 − 1     3 − 5   3 + 2 ⋅  2 − 4  + 2 − 3 ⋅ 1 :  5 − 1 =  3 + 2 ⋅  4  + 2 − 3 ⋅ 1 :  5  =                 2   1 1 1 1 1    5   8 + 3 + 48  15 59 15 =  + ⋅ + 2 − 3 ⋅ 1 :  −  =  + + 2 − 3 ⋅  −  =  + = + =  2   24  2 24 2 3 2 4     5   3 8 =. 59 + 180 239 = 24 24.

(5) IES Juan García Valdemora Departamento de Matemáticas. f). TEMA 3. HOJA 1. OPERACIONES COMBINADAS CON FRACCIONES 2º ESO.      2 3  1 1   1  8 1   2 3  2 + 3   1  16 − 1   3 − 5 ⋅  3 + 2  −  5 : (−2) +  3 − 6  =  3 − 5 ⋅  6  − − 10 +  6  =          1  424 3 15 5   = 6 2   3 ⋅ 5   − 1 + 25   2 1   24   4 − 3  12 2 3 5  1 5 2 =  − ⋅  − − +  =  − − = − −  = − = 10 6    5  3 5 6   10 2   3 5 ⋅ 2 ⋅ 3   10   3 2  1 23 24 12 = 10 (:2 ) 5. =. g). 1 12 5 − 72 67 =− − = 6 5 30 30. 5 9 3  1  1 3  5 5 9 1  1  1 3  5 +  −  : + − + ⋅ = +  −  : + − + ⋅ = r 12 12  4 36  2  4 10  2 simplifica  4 12  2  4 10  2 3 1 = 36 12. =. 5  27 − 1  1  − 5 + 6  5 5  27 − 1  1 1 5 5 13 1 1 5 + ⋅ = + : + ⋅ = : + ⋅ = + : + 12  12  2  20  2 12 1 412 24 3 2 20 2 12 6 2 20 2 26 13 = 12 6. =. 5 13 ⋅ 2 5 5 13 1 20 + 208 + 6 234 39 + + = + + = = = 12 2 ⋅ 3 5 ⋅ 4 ⋅ 2 12 3 8 48 48 (:6) 8. 4 1  4 3 6−4 1  24 − 15  2 1 3 1 3 2 − ⋅ − 2⋅ −   ⋅ − 2⋅  ⋅ − 2⋅ − 3 4 5 6 3 4 30         3 4 10 6 5 h) = = = = operar 3 8 operar 60 − 45 − 32 1 2 2 4 9 8 y y 1− : − ⋅ 1− − 1− − simplificar 4 15 simplificar 60 6 9 5 3 12 15 5 − 18 − 13  13   17  13 ⋅ 60 13 ⋅ 2 ⋅ 30 26 = 30 = 30 =  −  :  −  = = = − 17 − 17  30   60  30 ⋅ 17 30 ⋅ 17 17 60 60. i). 1  1 2  4 + 3  1⋅ 5 1 7 1 7 1 7 − 30 23  + − :  − − − −  15 20  5 5 =  60  5 ⋅ 2 = 60 2 = 60 2 = 60 = 60 =  − 23  : 14 =   4 5 8 5 4⋅5 8⋅3 4 2⋅4⋅3 4 2 20 − 6 14  60  15 ⋅ − : − − − 5 3 12 3 5 ⋅ 3 12 ⋅ 5 3 4⋅3⋅5 3 5 15 15 =−. 23 ⋅ 15 23 ⋅ 15 23 23 =− =− =− 60 ⋅ 14 15 ⋅ 4 ⋅ 14 4 ⋅ 14 56.

(6) IES Juan García Valdemora Departamento de Matemáticas. TEMA 3. HOJA 1. OPERACIONES COMBINADAS CON FRACCIONES 2º ESO. 4. Calcula y simplifica: 16  1  3  1 1 2  4 1− 2  3  1 3  4  −1 3  4 + 9  ⋅  − 1 + ⋅  + :  = − ⋅   + ⋅ +  = − ⋅  + ⋅ = 9 2  4 3 2 3 3  2  4 3 4 3  2  4  12 . a) − =. 4 3 13 4 39 2 13 32 + 39 71 + ⋅ = + = + = = 6 4 12 6 48 3 16 48 48. 2 1  3 2  3 6 2 9 3 2⋅3⋅3 3 3 3 ⋅  − 1 + ⋅ (− 2 ) = 3 − ⋅  −  − = 3 − ⋅ − = 3 − − = 3− − = 3 4  8 3  4 8 3 16 4 3⋅ 2⋅8 4 8 4 2. b) 3 − =. 2. 24 − 3 − 6 15 = 8 8. 1  5   5 5 2   1  3 + 5   5 5 1   1 8 5 5 2 1  c)  − + ⋅  : 2 − ⋅ 1 +   =  − +  :  2 − ⋅   =  − +  :  2 − ⋅  = 4  3   2 6 12   2  3   2 6 6   2 3 2 6 3 4  8  11  4  11 6 − 4 11 2 33 11  15 − 5 + 1   = : = =   : 2 −  = : 2 −  = : 6 6 6  3 6 3 6 3 12 4   . 2 3 1 1 1 5 2 3−2 1  2 −5 2 1 1  1 2 1 1 1 d) ⋅ −  − ⋅ −  = ⋅  − ⋅  = ⋅  − ⋅−  = ⋅ − ⋅ = 3 4 2 36  3 6  3  4  6  6  3 4 6  2 3 16 6 4 2. =. 2. 2. 2. 2. 2. 2 1 1 1 − = − =0 48 24 24 24 −2. −1. −2. −1. −2. −1. 1  1 1 1+ 2  1− 2  3  1 e) 5 :  + 1 + 3 :  −  = 5 :   + 3:  = 5:  + 3:−  = 2  4 2  2   4  2  4 2. 4 45 3 42 21 2 1 = 5 :   + 3 : (− 4 ) = 5 : + 3 : (− 4 ) = − = = 9 4 4 4 2 3. 3  3  17   1  f) − 3 − −  − 1 :  − 3  8  5  20   3 . −1. −1 −1  3  3  17 − 20   1 − 9   3  3  −3  −8  :   = − 3 − −  :  =  = − 3 − −  8  5  20   3   8  5  20   3   . 3  3  − 3   − 3  3  3 3⋅8  3  3 2 3 15 − 3 − 2  3 10 = − 3 − −  = − 3 − −  = −  =− ⋅ = :  = − 3 − −   8  5  20   8  8  5 3 ⋅ 20  8  5 5 8 5 8 5  3 6 3 = − ⋅2 = − = − 8 8 4.

(7) IES Juan García Valdemora Departamento de Matemáticas. TEMA 3. HOJA 1. OPERACIONES COMBINADAS CON FRACCIONES 2º ESO. −2 −1 −2 1  2 1   6 − 1  2 2    3  1    2   5  2  g)  −  + 13 :  − 1  :  −  =   + 13 :  −   :  −  =   + 13 : (− 3)  :  −  =  3    2   3    3   9    3  3 9   9 . 6 5   2   5 13   2  18  2   2 =  + 13 : 9 :  −  =  +  :  −  = :  −  = 2 :  −  = − = −3 2 9   3  9 9   3  9  3   3. 1 7 2 2−7 2  −5 2 15 − 15 + 16 1  −  : +1   : +1   : +1 − +1 + 1  5  4 8 3 8  3 8  3    16 16 16 h) = = = == == = : −  = 5 5 5 16  72  2 3 5 8−9 5  −1 5 − − −  − ⋅  ⋅  ⋅ 72 72 72 3 4 6  12  6  12  6 =. 1  5  72 8⋅9 9 : −  = − =− =− 16  72  16 ⋅ 5 8⋅ 2⋅5 10. 19−2 1 7  13 2  7 − 60 + 7 − 53 −1+  −  −1+   −1+   −1+ 4  5 15  4  15  4  15  60 = 60 i) = == = 60 = = −1 −1 −1 2 2 1 2  2 −3 2  −1 4 1 3 1 − : (− 4 ) 1+ 1+ 1− :  1− :   1− : −   5 20 10 25  2 4  5  4  5  4 . − 53 53 11 53 ⋅ 10 53 = 60 = − : =− =− 11 60 10 60 ⋅ 11 66 10. 1. 1 3  25 8  5  1 2 5 1 7 5 1    −1 − (− 2 ) 3 − :  : 3 −  : −  −  3 −  : + : + 4 8  16 12  4  2  3 4 2 3 4 2 j)  = = = = 7 ⋅ 24  3 1 1   19 1   9 − 6 + 4   38 − 3   7   35   − + : −   :   :  12 ⋅ 35  4 2 3   12 8   12   24   12   24 . 28 1 56 + 15 71 28 1 + + 15 2 = 15 2 = 30 = 30 = 71 : 2 = 71 ⋅ 5 = 71 ⋅ 5 = 71 7 ⋅ 2 ⋅ 12 7 ⋅ 2 ⋅ 12 2 2 30 5 30 ⋅ 2 5 ⋅ 6 ⋅ 2 12 5 5 12 ⋅ 5 ⋅ 7 12 ⋅ 5 ⋅ 7 1 1 5 4 5 16 − 15 1 (− 3) :  3 − 1  − 5  − 1  :  3 − 2  − 5 : − −  4 2  12 =  3   4  12 = 9 4 12 = 9 12 = 36 = 36 = 1 : 13 = k)  9 − 10  1 1  − 1  3 − 5 + 3 − 5 + 18 13 36 12 1 1 3 5 5⋅  + 5⋅ + : 5⋅ −  + : 12 2 12 12  12  2 3  12  2 4 3 4 6 −2. =. 12 12 1 = = 36 ⋅ 13 12 ⋅ 3 ⋅ 13 39. 2.

(8) IES Juan García Valdemora Departamento de Matemáticas. −1. l). TEMA 3. HOJA 1. OPERACIONES COMBINADAS CON FRACCIONES 2º ESO. −1. −1. 4 3 1 1 3 4 3−2 4 1   6 + 1 3 7 3 :  −  − 2 + ⋅ : :  − ⋅  − ⋅ 5 4 2 3 4 5  4  5 4   3  4 = 3 4 = =  1 2   1   1 2  5  1 − 4  :  − 1  +  1 − 2  ⋅ 5  − 3  :  − 1  +  5 − 8  ⋅ 5 − ⋅  −  : −  +   6 3   3   16 5  12  6   3   4 5  12  6   3   20  12. 4 7 4 7 1 7 4 − 35 − 31 :4− − − 4 = 20 4 = 5 4 = 20 = 20 = − 31 : 23 = − 31 ⋅ 16 = − 31 ⋅ 4 ⋅ 4 = − 31 ⋅ 4 = − 124 = 5 24 − 1 23 3 15 3 1 9  − 3 5 20 16 20 ⋅ 23 4 ⋅ 5 ⋅ 23 5 ⋅ 23 115 − − + ⋅ 16 16 6  20  12 2 240 2 16.

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