Soluciones a las actividades de cada epígrafeSoluciones a las actividades de cada epígrafe1

Unidad 1. Divisibilidad y números enteros

PÁGINA 27

1 Calcula mentalmente.

a) 5 – 7 b) 2 – 9 c) 3 – 4 d) 6 – 10 e) 5 – 12 f ) 9 – 15

g) –12 + 17 h) –22 + 10 i) –21 + 15 j) –3 – 6 k) –1 – 9 l) –12 – 13

a) –2 b) –7 c) –1 d) –4 e) –7 f) –6

g) 5 h) –12 i) –6 j) –9 k) –10 l) –25

2 Resuelve.

a) 10 – 3 + 5 b) 5 – 8 + 6 c) 2 – 9 + 1 d) 7 – 15 + 2

e) 16 – 4 – 6 f ) 22 – 7 – 8 g) 9 – 8 – 7 h) 15 – 12 + 6

a) 12 b) 3 c) –6 d) –6

e) 6 f) 7 g) –6 h) 9

3 Calcula.

a) –3 + 10 – 1 b) –8 + 2 – 3 c) –5 + 6 + 4 d) –12 + 2 + 6

e) –18 + 3 + 6 f ) –20 + 12 + 5 g) –7 – 3 – 4 h) –2 – 13 – 5

a) 6 b) –9 c) 5 d) – 4

e) –9 f) –3 g) –14 h) –20

4 Copia y completa como en el ejemplo.

• 7 – 4 – 6 – 2 + 5 + 3 – 4 = 15 – 16 = –1

a) 3 – 9 + 4 – 8 – 2 + 13 = 20 – 19 = 1

b) –15 – 4 + 12 – 3 – 11 – 2 = 12 – 35 = –23

5 Calcula.

a) 3 – 7 + 2 – 5 b) 2 – 6 + 9 – 3 + 4

c) 7 – 10 – 5 + 4 + 6 – 1 d) –6 + 4 – 3 – 2 – 8 + 5

e) 12 + 5 – 17 – 11 + 20 – 13 f ) 16 – 22 + 24 – 31 + 12 – 15

a) –7 b) 6 c) 1 d) –10 e) –4 f) –16

6 Quita paréntesis y calcula.

a) (–3) – (+4) – (–8) b) –(–5) + (–6) – (–3)

c) (+8) – (+6) + (–7) – (–4) d) –(–3) – (+2) + (–9) + (+7)

a) (–3) – (+4) – (–8) = –3 – 4 + 8 = 1

b) –(–5) + (–6) – (–3) = 5 – 6 + 3 = 2

c) (+8) – (+6) + (–7) – (–4) = 8 – 6 – 7 + 4 = –1

d) –(–3) – (+2) + (–9) + (+7) = 3 – 2 – 9 + 7 = –1

Pág. 1

Soluciones a las actividades de cada epígrafeSoluciones a las actividades de cada epígrafe1

Unidad 1. Divisibilidad y números enteros

7 Resuelve de dos formas, como en el ejemplo.

• a) 10 – (13 – 7) = 10 – (+6) = 10 – 6 = 4

b) 10 – (13 – 7) = 10 – 13 + 7 = 17 – 13 = 4

a) 15 – (12 – 8) b) 9 – (20 – 6) c) 8 – (15 – 12)

d) 6 – (13 – 2) e) 15 – (6 – 9 + 5) f ) 21 – (3 – 10 + 11 + 6)

a) 15 – (12 – 8) = 15 – (+4) = 15 – 4 = 11 15 – (12 – 8) = 15 – 12 + 8 = 23 – 12 = 11b) 9 – (20 – 6) = 9 – (+14) = 9 – 14 = –5 9 – (20 – 6) = 9 – 20 + 6 = 15 – 20 = –5c) 8 – (15 – 12) = 8 – (+3) = 8 – 3 = 5 8 – (15 – 12) = 8 – 15 + 12 = 20 – 15 = 5d) 6 – (13 – 2) = 6 – (+11) = 6 – 11 = –5 6 – (13 – 2) = 6 – 13 + 2 = 8 – 13 = –5e) 15 – (6 – 9 + 5) = 15 – (11 – 9) = 15 – (+2) = 15 – 2 = 13 15 – (6 – 9 + 5) = 15 – 6 + 9 – 5 = 24 – 11 = 13f) 21 – (3 – 10 + 11 + 6) = 21 – (20 – 10) = 21 – (+10) = 21 – 10 = 11 21 – (3 – 10 + 11 + 6) = 21 – 3 + 10 – 11 – 6 = 31 – 20 = 11

8 Resuelve de una de las formas que ofrece el ejemplo:

• a) (8 – 13) – (5 – 4 – 7) = (8 – 13) – (5 – 11) = (–5) – (–6) = –5 + 6 = 1

b) (8 – 13) – (5 – 4 – 7) = 8 – 13 – 5 + 4 + 7 = 19 – 18 = 1

a) (4 – 9) – (5 – 8) b) –(1 – 6) + (4 – 7)

c) 4 – (8 + 2) – (3 – 13) d) 12 + (8 – 15) – (5 + 8)

e) (8 – 6) – (3 – 7 – 2) + (1 – 8 + 2) f ) (5 – 16) – (7 – 3 – 6) – (9 – 13 – 5)

En cada caso, de cualquiera de las dos formas:a) (4 – 9) – (5 – 8) = (–5) – (–3) = –5 + 3 = –2 (4 – 9) – (5 – 8) = 4 – 9 – 5 + 8 = 12 – 14 = –2b) –(1 – 6) + (4 – 7) = –(–5) + (–3) = 5 – 3 = 2 –(1 – 6) + (4 – 7) = –1 + 6 + 4 – 7 = 10 – 8 = 2c) 4 – (8 + 2) – (3 – 13) = 4 – (+10) – (–10) = 4 – 10 + 10 = 14 – 10 = 4 4 – (8 + 2) – (3 – 13) = 4 – 8 – 2 – 3 + 13 = 17 – 13 = 4d) 12 + (8 – 15) – (5 + 8) = 12 + (–7) – (13) = 12 – 7 – 13 = 12 – 20 = –8 12 + (8 – 15) – (5 + 8) = 12 + 8 – 15 – 5 – 8 = 20 – 28 = –8e) (+2) – (3 – 9) + (3 – 8) = (+2) – (–6) + (–5) = +2 + 6 – 5 = 8 – 5 = 3 (8 – 6) – (3 – 7 – 2) + (1 – 8 + 2) = 8 – 6 – 3 + 7 + 2 + 1 – 8 + 2 = 20 – 17 = 3f) (–11) – (7 – 9) – (9 – 18) = (–11) – (–2) – (–9) = –11 + 2 + 9 = 11 – 11 = 0 (5 – 16) – (7 – 3 – 6) – (9 – 13 – 5) = 5 – 16 – 7 + 3 + 6 – 9 + 13 + 5 = 32 – 32 = 0

Pág. 2

Soluciones a las actividades de cada epígrafeSoluciones a las actividades de cada epígrafe1

Unidad 1. Divisibilidad y números enteros

9 Resuelto en el libro de texto.

10 Calcula.

a) 7 – [1 + (9 – 13)] b) –9 + [8 – (13 – 4)] c) 12 – [6 – (15 – 8)]

d) –17 + [9 – (3 – 10)] e) 2 + [6 – (4 – 2 + 9)] f ) 15 – [9 – (5 – 11 + 7)]

a) 7 – [1 + (9 – 13)] = 7 – [1 + 9 – 13] = 7 – 1 – 9 + 13 = 20 – 10 = 10

b) –9 + [8 – (13 – 4)] = –9 + [8 – (9)] = –9 + [8 – 9] = –9 + [–1] = –9 – 1 = –10

c) 12 – [6 – (15 – 8)] = 12 – [6 – 15 + 8] = 12 – 6 + 15 – 8 = 27 – 14 = 13

d) –17 + [9 – (3 – 10)] = –17 + [9 – (–7)] = –17 + [9 + 7] = –17 + 16 = –1

e) 2 + [6 – (4 – 2 + 9)] = 2 + [6 – 4 + 2 – 9] = 2 + 6 – 4 + 2 – 9 = 10 – 13 = –3

f) 15 – [9 – (5 – 11 + 7)] = 15 – [9 – (12 – 11)] = 15 – [9 – (+1)] = 15 – [9 – 1] =

= 15 – [+8] = 15 – 8 = 7

11 Resuelve.

a) (2 – 9) – [5 + (8 – 12) – 7] b) 13 – [15 – (6 – 8) + (5 – 9)]

c) 8 – [(6 – 11) + (2 – 5) – (7 – 10)] d) (13 – 21) – [12 + (6 – 9 + 2) – 15]

e) [4 + (6 – 9 – 13)] – [5 – (8 + 2 – 18)] f ) [10 – (21 – 14)] – [5 + (17 – 11 + 6)]

a) (2 – 9) – [5 + (8 – 12) – 7] = (2 – 9) – [5 + (–4) – 7] = (2 – 9) – [5 – 4 – 7] =

= (–7) – [5 – 11] = –7 – [–6] = –7 + 6 = –1

b) 13 – [15 – (6 – 8) + (5 – 9)] = 13 – [15 – 6 + 8 + 5 – 9] =

= 13 – 15 + 6 – 8 – 5 + 9 = 28 – 28 = 0

c) 8 – [(6 – 11) + (2 – 5) – (7 – 10)] = 8 – [(–5) + (–3) – (–3)] = 8 – [–5 – 3 + 3] =

= 8 – [–8 + 3] = 8 – [–5] = 8 + 5 = 13

d) (13 – 21) – [12 + (6 – 9 + 2) – 15] = (13 – 21) – [12 + 6 – 9 + 2 – 15] =

= 13 – 21 – 12 – 6 + 9 – 2 + 15 = 37 – 41 = –4

e) [4 + (6 – 9 – 13)] – [5 – (8 + 2 – 18)] = [4 + (6 – 22)] – [5 – (10 – 18)] =

= [4 – 16] – [5 + 8] = –12 – 13 = –25

f) [10 – (21 – 14)] – [5 + (17 – 11 + 6)] = [10 – 21 + 14] – [5 + 17 – 11 + 6] =

= 10 – 21 + 14 – 5 – 17 + 11 – 6 = 35 – 49 = –14

Pág. 3