HOJA3_ENTEROS_SOLUCIONES
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(2) IES Juan García Valdemora Departamento de Matemáticas. TEMA 1. HOJA 3. OPERACIONES CON Nº ENTEROS 2º ESO. = 3 − 4 ⋅ [−2 + 6] + 9 − (− 3) = = 3 − 4 ⋅ (+4) + 9 − (− 3) = = 3 − (+16) + 9 − (− 3) = 3 − 16 + 9 + 3 = = +15 − 16 = = −1. g). (− 15) ⋅ (− 7 + 8) − (− 12) + 15: (− 2 − 3) = = (−15) ⋅ (+1) − ⋅(−12) + 15: (− 5) = = (−15) − (−12) + ( −3) = = −15 + 12 − 3 = = +12 − 18 = = −6. h) 23 − 3 ⋅ (22 − 25) + 2 ⋅ (12 − 10) ⋅ (15 − 19) = = 23 − 3 ⋅ (−3) + 2 ⋅ (+2) ⋅ (− 4) =. = 23 − (−9) + (−16) = = 23 + 9 − 16 = = +32 − 16 = = +16. i). (9 − 5) ⋅ (7 − 10): (6 − 9) − (− 3 − 9)⋅ (9 − 4) = = (+4) ⋅ (−3) : (−3) − ⋅(−12) ⋅ (+ 5) = = (+4) − (−60) = = +4 + 60 = = +64. j) 31 − 5 ⋅ [21 + 17 ⋅ (5 − 6)] = = 31 − 5 ⋅ [21 + 17 ⋅ (− 1)] =. = 31 − 5 ⋅ [21 + (− 17 )] = = 31 − 5 ⋅ [21 − 17] = = 31 − 5 ⋅ (+3) = = 31 − (−15) = = +31 + 15 = = +46. 2.
(3) IES Juan García Valdemora Departamento de Matemáticas. TEMA 1. HOJA 3. OPERACIONES CON Nº ENTEROS 2º ESO. k) (− 7 ) ⋅ (9 − 4) − 6 ⋅ [− 3 + (7 − 9) ⋅ 4] = = (− 7 ) ⋅ (+ 5) − 6 ⋅ [− 3 + (− 2) ⋅ 4] =. = (− 7 ) ⋅ (+ 5) − 6 ⋅ [− 3 + (− 8)] = = (− 7 ) ⋅ (+ 5) − 6 ⋅ [− 3 − 8] = = (− 35) − 6 ⋅ (−11) = = (− 35) − (− 66) =. = −35 + 66 = = +31 l) 3 ⋅ [− 12 − 3 ⋅ (4 − 2 ⋅ 5)] + 28 = = 3 ⋅ [− 12 − 3 ⋅ (4 − 10)] + 28 =. = 3 ⋅ [− 12 − 3 ⋅ (− 6)] + 28 = = 3 ⋅ [− 12 − (− 18)] + 28 = = 3 ⋅ [− 12 + 18] + 28 = = 3 ⋅ (+6) + 28 = = +18 + 28 = = +46. m) [− 6 + 3 ⋅ (4 − 35 : 5)] − [5 − 3 ⋅ (13 − 11)] = = [− 6 + 3 ⋅ (4 − 7 )] − [5 − 3 ⋅ (+ 2 )] =. = [− 6 + 3 ⋅ (− 3)] − [5 − (+ 6)] = = [− 6 + (− 9 )] − [5 − 6] = = [− 6 − 9] − (−1) = = (−15) − (−1) = = −15 + 1 = = −14. n) [3 + 5 ⋅ (18 − 19)] − (− 7 ) − [8 − 4 ⋅ (21 : 3 − 4)] = = [3 + 5 ⋅ (− 1)] − (− 7 ) − [8 − 4 ⋅ (7 − 4)] =. = [3 + (− 5)] − (− 7 ) − [8 − 4 ⋅ (+ 3)] = = [3 − 5] − (− 7 ) − [8 − (+ 12)] = = (−2) − (− 7 ) − [8 − 12] = = (−2) − (−7) − (−4) = = −2 + 7 + 4 = = −2 + 11 = = +9. 3.
(4) IES Juan García Valdemora Departamento de Matemáticas. TEMA 1. HOJA 3. OPERACIONES CON Nº ENTEROS 2º ESO. o) [− 3 + 2 ⋅ (3 − 5 ⋅ 2)] − 7 − [− 4 ⋅ (9 : (−3) − 4)] = = [− 3 + 2 ⋅ (3 − 10)] − 7 − [− 4 ⋅ (− 3 − 4 )] =. = [− 3 + 2 ⋅ (− 7 )] − 7 − [− 4 ⋅ (− 7 )] = = [− 3 + (− 14)] − 7 − (+28) = = [− 3 − 14] − 7 − (+28) = = (−17) − 7 − (+28) =. = −17 − 7 − 28 = = −52 p) 32 − 2 ⋅ (22 − 25 : 5) − (8 : (−2) − 10) ⋅ (5 − 9 ) = = 32 − 2 ⋅ (22 − 5) − (− 4 − 10) ⋅ (− 4) =. = 32 − 2 ⋅ (+ 17) − (− 14) ⋅ (− 4) = = 32 − (+ 34) − (+ 56) = = +32 − 34 − 56 = = +32 − 90 = = −58. q) [6 + 2 ⋅ (3 − 25 : 5)] − [4 − 3 ⋅ (8 − 6)] = = [6 + 2 ⋅ (3 − 5)] − [4 − 3 ⋅ 2] = = [6 + 2 ⋅ (− 2 )] − [4 − 6] = = [6 + (− 4 )] − (−2) = = [6 − 4] − (−2) =. = (+2) − (−2) = = +2 + 2 = = +4. r) 2 − (+ 3) − (−4)3 + (− 5) : (− 5) + 2 2 = = 2 − (+ 27 ) − (−64) + (+ 25) : (− 5) + 4 = = 2 − (+ 27 ) − (−64) + (− 5) + 4 = = 2 − 27 + 64 − 5 + 4 = 3. 2. = +70 − 32 = = +38. s). [. ]. 32 ⋅ (− 2 ) − (11 − 13) + ( −9) : (− 3) = 2. [. 3. ]. 1. = 9 ⋅ + 4 − (− 2 ) + ( −9) : (− 3) = 3. = 9 ⋅ [+ 4 − (− 8)] + ( +3) =. 4.
(5) IES Juan García Valdemora Departamento de Matemáticas. TEMA 1. HOJA 3. OPERACIONES CON Nº ENTEROS 2º ESO. = 9 ⋅ [+ 4 + 8] + ( +3) = = 9 ⋅ ( +12) + ( +3) = = +108 + 3 = = +111. t). [. ]. ( −2) 3 ⋅ (− 3) : (7 − 8) + ( −5) − ( −9) : (− 3) = = ( −8) ⋅ [(+ 9 ) : (− 1)] + ( −5) − ( −9) : (− 3) = 2. 3. 1. = ( −8) ⋅ ( −9) + ( −5) − ( +3) = = ( +72) + ( −5) − ( +3) = = +72 − 5 − 3 = = +72 − 8 = = +64. [. ]. u) (− 3) ⋅ (2 − 3) − 6 ⋅ − 32 + (6 − 8) ⋅ 4 = 2. 2. = (+ 9) ⋅ (− 1) − 6 ⋅ [− 9 + (− 2) ⋅ 4] = = (+ 9) ⋅ (+ 1) − 6 ⋅ [− 9 + (− 8)] = = (+ 9) − 6 ⋅ [− 9 − 8] = 2. = (+ 9) − 6 ⋅ (−17) = = (+ 9) − (−102) =. = +9 + 102 = = +111. [. ] = [(−3) + 5 ⋅ (− 3) ] + 7 − [8 − 4 ⋅ (− 4 + 4)] =. v) (−3)1 + 5 ⋅ (6 − 9) + 7 − [8 − 4 ⋅ (12 : (−3) + 4)] = 0. 0. = [(−3) + 5 ⋅ (+ 1)] + 7 − [8 − 4 ⋅ 0] = = [(−3) + (+ 5)] + 7 − [8 − 0] = = [− 3 + 5] + 7 − 8 = = 2+7−8 = = +9 − 8 = = +1. w) 2 2 ⋅ [(−3) 2 − (6 − 8) 3 ] + (−4) : (− 2 ) = 1. = 4 ⋅ [+9 − (−2) 3 ] + (−4) : (− 2 ) = = 4 ⋅ [+9 − (−8)] + (+2) = = 4 ⋅ [+9 + 8] + (+2) =. 5.
(6) IES Juan García Valdemora Departamento de Matemáticas. TEMA 1. HOJA 3. OPERACIONES CON Nº ENTEROS 2º ESO. = 4 ⋅ (+17) + (+2) = = (+68) + (+2) = = +68 + 2 = + 70. 2. Realiza las siguientes operaciones: a) − 5 + 4 ⋅ (− 2 + 1) − 6 ⋅ (5 − 6 ) − (−4) ⋅ (12 − 9 ) = 3. 4. 2. = −5 + 4 ⋅ (− 1) − 6 ⋅ (− 1) − (−4) ⋅ (+3) 2 = = −5 + 4 ⋅ (− 1) − 6 ⋅ (+ 1) − (−4) ⋅ (+9) = = −5 + (−4) − (+6) − (−36) = 3. 4. = −5 − 4 − 6 + 36 = = 21. b) (3 − 4 ) − (− 2 ) + 18 : (− 1 − 8) − (− 4 + 2 ) = 4. 3. 2. = (− 1) − (− 8) + 18: (− 9) − (− 2) = = +1 + 8 + (−2) − (+ 4) = = +1 + 8 − 2 − 4 = =3 4. 2. c) 12 − 8 ⋅ [−2 − 3 + (− 2 ) − 3 2 ] − (5 − 6 ) − 9 ⋅ (8 − 9 ) = 2. 5. = 12 − 8 ⋅ [− 2 − 3 + 4 − 9] − (− 1) − 3 ⋅ (− 1) = = 12 − 8 ⋅ (−10) − (− 1) − (−3) = 5. = 12 − (−80) + 1 + 3 = = 12 + 80 + 1 + 3 = = 96. d) 12 : (−6) + (−8 − 7) ⋅ (−3 − 2 + 6) − (−3) ⋅ (−4) = = −2 + (−15) ⋅ 1 − 12 = = −2 + (−15) − 2 = = −12 − 15 − 12 = = −29. e). (−40) : (− 2 ) + 36 ⋅ (6 − 2 ⋅ 5) + (− 15) : (− 3) = = (−40) : (−8) + 6 ⋅ (6 − 10) + 5 = 3. = 5 + 6 ⋅ (−4) + 5 = = 5 − 24 + 5 = = −14 6.
(7) IES Juan García Valdemora Departamento de Matemáticas. f). TEMA 1. HOJA 3. OPERACIONES CON Nº ENTEROS 2º ESO. (− 5)3 : [1 + (− 2 )3 ⋅ (− 3)] − 4 ⋅ (− 10)2 = = −125 : [1 + (−8) ⋅ (−3)] − 4 ⋅ 100 = = −125 : [1 + 24] − 400 = = −125 : 25 − 400 = = −5 − 400 = −405. g) 3 ⋅ [5 − 3 ⋅ (6 − 2 ⋅ 5 + 24 : 2 ) + (− 3) ] − (− 3 − 1) = 3. 1. = 3 ⋅ [5 − 3 ⋅ (6 − 10 + 12 ) + (− 27 )]− (− 4 ) = = 3 ⋅ [5 − 3 ⋅ 8 − 27] − (− 4 ) = 1. = 3 ⋅ [5 − 24 − 27] + 4 = = 3 ⋅ (−46) + 4 = = −138 + 4 = = −134. h). (− 3) ⋅ (− 5)2 − [4 + 2 5 − 3 2 ⋅ (− 2)2 ] − (− 1)10 = = (− 3) ⋅ (+ 25) − [4 + 32 − 9 ⋅ (+ 4 )]− (+ 1) = = (− 75) − [4 + 32 − 36]− 1 = = −75 − 0 − 1 = = −76. i). (− 3)2 ⋅ [4 − (− 6 + 8 ⋅ (− 5))]− 4 ⋅ (− 1 − 3)0 = 0 = (+ 9)⋅ [4 − (− 6 + (− 40))]− 4 ⋅ (− 4) = = 9 ⋅ [4 − (− 6 − 40)]− 4 ⋅1 = = 9 ⋅ [4 − (− 46 )]− 4 = = 9 ⋅ (4 + 46) − 4 = = 9 ⋅ 50 − 4 = = 450 − 4 = = 446. j) 5 − 3 ⋅ (12 − 7 ) − [24 : (2 − 36 )] = 2. = 5 − 3 ⋅ 5 2 − [24 : (2 − 6 )] = = 5 − 3 ⋅ 25 − (24 : (−4)) = = 5 − 75 − (−6) = = 5 − 75 + 6 = = −64. 7.
(8) IES Juan García Valdemora Departamento de Matemáticas. TEMA 1. HOJA 3. OPERACIONES CON Nº ENTEROS 2º ESO. k) − 12 : (− 7 + 3) − (−9 − 3) : (−3) + (−20) : (6 − 7)1 = = −12 : (− 4 ) − (−12) : (−3) + (−20) : (−1)1 = = −12 : (− 4 ) − (−12) : (−3) + (−20) : (−1)1 = = 3 − 4 + 20 = = 19. l). [ 144 − (− 2). 2. + (− 5). ] : [(− 7). 1 2. 2. ]. − (−1) − (+41) =. = [12 − 4 + (− 5)] : [49 + 1 − 41] = 2. = [12 − 4 − 5]2 : 9 = = 32 : 9 = = 9:9 = =1 m) (5 − 8) ⋅ (− 2 ) + (− 4 − 2 ) : (− 3) − [45 − (−8)] ⋅ (− 3 + 2 ) = 3. 2. 1. 7. = (−3) 3 ⋅ 4 + (− 6 ) : (− 3) − [45 + 8] ⋅ (− 1) = = −27 ⋅ 4 + 2 − 53 ⋅ (− 1) = 7. = −108 + 2 + 53 = = −108 + 55 = = −53. n). 25 − [34 + 55 : (−13 + 2)] − (13 − 9 ⋅ 2 ) ⋅ (− 2 + 1) = 3. = 5 − [34 + 55 : (−11)] − (13 − 18) ⋅ (− 1) = = 5 − [34 − 5] − (− 5) ⋅ (− 1) = 3. = 5 − 29 − 5 = = −29. (. ). o) 2 4 : (−2) 3 + (−12 − 18) : − 16 + 3 ⋅ 4 = = 16 : (−8) + (−30) : (− 16 + 3 ⋅ 2 ) = = −2 + (−30) : (−16 + 6) = = −2 + (−30) : (−10) =. = −2 + 3 = =1. 8.
(9) IES Juan García Valdemora Departamento de Matemáticas. p). TEMA 1. HOJA 3. OPERACIONES CON Nº ENTEROS 2º ESO. [(6 − 11) ⋅ (− 3)] : [− 25 : (2 − (− 3) ⋅ (− 9))] = = [(− 5) ⋅ (− 3)] : [− 25 : (2 − 27 )] = = 15 : [−25 : (−25)] = = 15 : 1 = = 15. q). (− 5)3 : (2 0 − 6) + 3 8 ⋅ [(−3 − 1) 2 + 3 − 8 ] − (−3)1 = = −125 : (1 − 6) + 2 ⋅ [(−4) 2 + (−2)] − (−3) = = −125 : (−5) + 2 ⋅ [16 − 2] + 3 = = 25 + 2 ⋅ 14 + 3 = = 25 + 28 + 3 = = 56. r). (2 − 5)4 : (1 − 4 ⋅ 7 ) − 2 ⋅ (. ). (. ). 64 : (− 4 ) + 1 − (−27) : 81 + 5 0 =. = (−3) : (1 − 28) − 2 ⋅ (8 : (−4) + 1) − (−27) : (8 + 1) = = 81 : (−27) − 2 ⋅ (−2 + 1) − (−27) : 9 = = −3 − 2 ⋅ (−1) − (−3) = = −3 + 2 + 3 = =2 4. s). (− 8 + 6)4 ⋅ [(− 9 + 4 + 13) : (− 5 + 3 ⋅ 2) − (− 2)3 ] − (− 9 + 6 ⋅ 3) ⋅ (− 6 + 8) = 4 = (− 2 ) ⋅ [8 : (− 5 + 6 ) − (− 8)] − (− 9 + 18) ⋅ 2 = = 16 ⋅ [8 : 1 + 8] − 9 ⋅ 2 = = 16 ⋅ (8 + 8) − 18 = = 16 ⋅ 16 − 18 = = 256 − 18 = = 238. t). (− 2)5 : [(−8) : (−4) − 9 ⋅ (−2)] − [(−18) : 9 + (−3 + 5) 0 ] = = −32 : [2 − 3 ⋅ (−2)] − [− 2 + (+2) 0 ] = = −32 : (2 + 6) − (−2 + 1) = = −32 : 8 − (−1) = = −4 + 1 = = −3. 9.
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