Ejercicios enteros solucion

PÁGINA 35

EJERCICIOS DE LA UNIDAD

Suma y resta de enteros

1 Calcula:

a) 5 – 3 – 7 + 1 + 8

b) 2 – 3 + 4 + 1 – 8 + 2

c) 1 – 3 + 5 – 7 + 9 – 11

d) 2 + 4 – 6 – 8 + 10 – 12 + 14

a) 5 – 3 – 7 + 1 + 8 = (5 + 1 + 8) – (3 + 7) = 14 – 10 = 4

b) 2 – 3 + 4 + 1 – 8 + 2 = (2 + 4 + 1 + 2) – (3 + 8) = 9 – 11 = –2

c) 1 – 3 + 5 – 7 + 9 – 11 = (1 + 5 + 9) – (3 + 7 + 11) = 15 – 21 = –6

d) 2 + 4 – 6 – 8 + 10 – 12 + 14 = (2 + 4 + 10 + 14) – (6 + 8 + 12) = 30 – 26 = 4

2 Quita paréntesis:

a) a + (b + c) b) a – (b + c)

c) a + (b – c) d) a – (b – c)

a) a + (b + c) = a + b + c b) a – (b + c) = a – b – c

c) a + (b – c) = a + b – c d) a – (b – c) = a – b + c

3 Quita paréntesis y después opera:

a) 1 – (7 – 2 – 10) – (3 – 8) b) (8 – 4 – 3) – (5 – 8 – 1)

c) (3 – 5) – (1 – 4) + (5 – 8) d) 3 – (5 – 8) – (11 – 4) + (13 – 9)

a) 1 – (7 – 2 – 10) – (3 – 8) = 1 – 7 + 2 + 10 – 3 + 8 = (1 + 2 + 10 + 8) – (3 + 7) == 21 – 10 = 11

b) (8 – 4 – 3) – (5 – 8 – 1) = 8 – 4 – 3 – 5 + 8 + 1 = (8 + 8 + 1) – (4 + 3 + 5) == 17 – 12 = 5

c) (3 – 5) – (1 – 4) + (5 – 8) = 3 – 5 – 1 + 4 + 5 – 8 = (3 + 4 + 5) – (5 + 1 + 8) == 12 – 14 = –2

d) 3 – (5 – 8) – (11 – 4) + (13 – 9) = 3 – 5 + 8 – 11 + 4 + 13 – 9 == (3 + 8 + 4 + 13) – (5 + 11 + 9) = 28 – 25 = 3

Pág. 1

SOLUCIONES A LOS EJERCICIOS DE LA UNIDAD

Unidad 1. Números enteros y divisibilidad

1

Pág. 2

4 Calcula operando primero dentro de los paréntesis:

a) (2 – 6 – 3) + (5 – 3 – 1) – (2 – 4 – 6)

b) (8 – 11 – 5) – (12 – 13) + (11 + 4)

c) 15 + (6 – 18 + 11) – (7 + 15 – 19) + (1 – 3 – 6)

a) (2 – 6 – 3) + (5 – 3 – 1) – (2 – 4 – 6) = (–7) + (1) – (– 8) = –7 + 1 + 8 = 2

b) (8 – 11 – 5) – (12 – 13) + (11 + 4) = (– 8) – (–1) + (15) = –8 + 1 + 15 = 8

c) 15 + (6 – 18 + 11) – (7 + 15 – 19) + (1 – 3 – 6) = 15 + (–1) – (3) + (– 8) = = 15 – 1 – 3 – 8 = 3

5 Quita paréntesis y calcula:

a) 3 – [(5 – 8) – (3 – 6)]

b) 1 – (3 – [4 – (1 – 3)])

c) (2 + 7) – (5 – [6 – (10 – 4)])

a) 3 – [(5 – 8) – (3 – 6)] = 3 – [(–3) – (–3)] = 3 – [–3 + 3] = 3

b) 1 – (3 – [4 – (1 – 3)]) = 1 – (3 – [4 – (–2)]) = 1 – (3 – 6) = 1 + 3 = 4

c) (2 + 7) – (5 – [6 – (10 – 4)]) = 9 – (5 – [6 – 6]) = 9 – 5 = 4

6 Calcula:

a) (–7) · (+11) b) (–6) · (–8)

b) (+5) · (+7) · (–1) d) (–2) · (–3) · (–4)

a) (–7) · (+11) = –77 b) (–6) · (–8) = 48

c) (+5) · (+7) · (–1) = –35 d) (–2) · (–3) · (–4) = –24

7 Opera:

a) (–45) : (+3) b) (+85) : (+17)

b) (+36) : (–12) d) (–85) : (–5)

a) (–45) : (+3) = –15 b) (+85) : (+17) = 5

c) (+36) : (–12) = –3 d) (–85) : (–5) = 17

8 Opera las expresiones siguientes:

a) (+400) : (–40) : (–5) b) (+400) : [(–40) : (–5)]c) (+7) · (–20) : (+10) d) (+7) · [(–20) : (+10)]e) (+300) : (+30) · (–2) f) (+300) : [(+30) · (–2)]



1

a) (+400) : (–40) : (–5) = (–10) : (–5) = 2

b) (+400) : [(–40) : (–5)] = (+400) : (+8) = 50

c) (+7) · (–20) : (+10) = –140 : 10 = –14

d) (+7) · [(–20) : (+10)] = 7 · (–2) = –14

e) (+300) : (+30) · (–2) = 10 · (–2) = –20

f ) (+300) : [(+30) · (–2)] = 300 : (–60) = –5

Operaciones combinadas

9 Calcula:

a) 6 · 4 – 5 · 6 – 2 · 3

b) 15 – 6 · 3 + 2 · 5 – 4 · 3

c) 5 · (–4) + (–2) · 4 – 6 · (–5) – 3 · (–6)

d) 18 – 3 · 5 + 5 · (–4) – 3 · (–2)

a) 6 · 4 – 5 · 6 – 2 · 3 = 24 – 30 – 6 = –12

b) 15 – 6 · 3 + 2 · 5 – 4 · 3 = 15 – 18 + 10 – 12 = –5

c) 5 · (–4) + (–2) · 4 – 6 · (–5) – 3 · (–6) = –20 – 8 + 30 + 18 = 20

d) 18 – 3 · 5 + 5 · (–4) – 3 · (–2) = 18 – 15 – 20 + 6 = –11

10 Opera estas expresiones:

a) (–5) · (8 – 13)

b) (2 + 3 – 6) · (–2)

c) (+4) · (1 – 9 + 2) : (–3)

d) (–12 – 10) : (–2 – 6 – 3)

a) (–5) · (8 – 13) = (–5) · (–5) = 25

b) (2 + 3 – 6) · (–2) = (–1) · (–2) = 2

c) (+4) · (1 – 9 + 2) : (–3) = 4 · (–6) : (–3) = (–24) : (–3) = 8

d) (–12 – 10) : (–2 – 6 – 3) = (–22) : (–11) = 2

11 Calcula:

a) 13 – [8 – (6 – 3) – 4 · 3] : (–7)

b) 5 · (8 – 3) – 4 · (2 – 7) – 5 · (1 – 6)

c) 12 · (12 – 14) – 8 · (16 – 11) – 4 · (5 – 17)

Pág. 3



1

Pág. 4

a) 13 – [8 – (6 – 3) – 4 · 3] : (–7) = 13 – [8 – 3 – 12] : (–7) = 13 – (–7) : (–7) == 13 – 1 = 12

b) 5 · (8 – 3) – 4 · (2 – 7) – 5 · (1 – 6) = 5 · 5 – 4 · (–5) – 5 · (–5) == 25 + 20 + 25 = 70

c) 12 · (12 – 14) – 8 · (16 – 11) – 4 · (5 – 17) = 12 · (–2) – 8 · 5 – 4 · (–12) == –24 – 40 + 48 = –16

12 Realiza las operaciones siguientes:

a) 18 – 40 : (5 + 4 – 1) – 36 : 12

b) 4 + 36 : 9 – 50 : [12 + (17 – 4)]

c) 48 : [5 · 3 – 2 · (6 – 10) – 17]

d) 3 · 4 – 15 : [12 + 4 · (2 – 7) + 5]

a) 18 – 40 : (5 + 4 – 1) – 36 : 12 = 18 – 40 : 8 – 3 = 18 – 5 – 3 = 10

b) 4 + 36 : 9 – 50 : [12 + (17 – 4)] = 4 + 4 – 50 : 25 = 8 – 2 = 6

c) 48 : [5 · 3 – 2 · (6 – 10) – 17] = 48 : [15 + 8 – 17] = 48 : 6 = 8

d) 3 · 4 – 15 : [12 + 4 · (2 – 7) + 5] = 12 – 15 : [12 + 4 · (–5) + 5] == 12 – 15 : [12 – 20 + 5] = 12 – 15 : (–3) = 12 + 5 = 17

13 Calcula:

a) (–2)7 b) (–3)5 c) (–5)3

d) (–10)3 e) (–1)16 f) (–1)17

a) (–2)7 = –128 b) (–3)5 = –243 c) (–5)3 = –125

d) (–10)3 = –1 000 e) (–1)16 = +1 f ) (–1)17 = –1

14 Expresa como una única potencia:

a) (–2)4 · (–2)3 b) (+2)3 · (–2)3

c) (–3)5 : (–3)3 d) (–5)6 : (–5)3

a) (–2)4 · (–2)3 = (–2)7 b) (+2)3 · (–2)3 = (+2)3 · (–2)3 = –(23 · 23) = –26

c) (–3)5 : (–3)3 = (–3)2 d) (–5)6 : (–5)3 = (–5)3

15 Calcula:

a) (–2)3 + (–3)3 – (–4)3

b) (–5)2 · (–2)2 + (+3)2 · (–3)

c) (–2)2 · [(–5)2 – (+4)2]

d) (–6)3 : (–3)3 + (–8)2 : (–4)2



1

Documents

Ejercicios enteros solucion