Pagina 029

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

Unidad 1. Divisibilidad y números enteros

PÁGINA 29

12 Multiplica.

a) (+10) · (–2) b) (–4) · (–9) c) (–7) · (+5) d) (+11) · (+7)

a) –20 b) 36 c) –35 d) 77

13 Observa los ejemplos y calcula.

• (–3) · (+2) · (–5) = (–6) · (–5) = +30 14243

• (–3) · (+2) · (–5) = (–3) · (–10) = +30 14243

a) (–2) · (–3) · (+4) b) (–1) · (+2) · (–5)

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

a) (–2) · (–3) · (+4) = (+6) · (+4) = +24 (–2) · (–3) · (+4) = (–2) · (–12) = +24

b) (–1) · (+2) · (–5) = (–2) · (–5) = +10 (–1) · (+2) · (–5) = (–1) · (–10) = +10

c) (+4) · (–3) · (+2) = (–12) · (+2) = –24 (+4) · (–3) · (+2) = (+4) · (–6) = –24

d) (–6) · (–2) · (–5) = (+12) · (–5) = –60 (–6) · (–2) · (–5) = (–6) · (+10) = –60

14 Divide.

a) (–18) : (+3) b) (–15) : (–5) c) (+36) : (–9)

d) (–30) : (–10) e) (–52) : (+13) f ) (+22) : (+11)

a) –6 b) +3 c) –4 d) +3 e) –4 f) +2

15 Calcula el valor de x en cada caso:

a) (–18) : x = +6 b) (+4) · x = –36 c) x · (–13) = 91 d) x : (–11) = +5

a) x = –3 b) x = –9 c) x = –7 d) x = –55

16 Copia, completa y compara. ¿Qué observas?

(+60) : [(–30) : (–2)] = (+60) : [+15] = +4

[(+60) : (–30)] : (–2) = [ –2 ] : (–2) = +1

Se observa que la división no es asociativa.

17 Calcula.

a) (–28) : [(+12) : (–3)] b) [(–45) : (+3)] : (+5)

c) (–100) : [(–36) : (–9)] d) [(–72) : (+9)] : (–8)

a) (–28) : [(+12) : (–3)] = (–28) : [–4] = +7

b) [(–45) : (+3)] : (+5) = [–15] : (+5) = –3

c) (–100) : [(–36) : (–9)] = (–100) : [+4] = –25

d) [(–72) : (+9)] : (–8) = [–8] : (–8) = +1

Pág. 1



18 Calcula siguiendo el ejemplo.

• [(–8) · (+9)] : [(+6) · (–3)] = [–72] : [–18] = +4 –72 –18 +4

a) [(+5) · (–8)] : [(–2) · (–5)]

b) [(+28) : (–7)] · [(+20) : (–4)]

c) [(–10) : (+5)] : [(–28) : (+4)]

a) [(+5) · (–8)] : [(–2) · (–5)] = [–40] : [+10] = –4

b) [(+28) : (–7)] · [(+20) : (–4)] = [–4] · [–5] = +20

c) [(–10) : (+5)] : [(–28) : (+4)] = [–2] : [–7] = +2/7

19 Calcula como en el ejemplo.

• 15 – 8 · 3 = 15 – 24 = –9

a) 18 – 5 · 3 b) 6 – 4 · 2 c) 7 · 2 – 16

a) 18 – 5 · 3 = 18 – 15 = 3 b) 6 – 4 · 2 = 6 – 8 = –2 c) 7 · 2 – 16 = 14 – 16 = –2

20 Calcula.

a) 18 – 15 : 3 b) 3 – 30 : 6 c) 20 : 2 – 11

a) 18 – 5 = 13 b) 3 – 5 = –2 c) 10 – 11 = –1

21 Calcula como en el ejemplo.

• 21 – 4 · 6 + 12 : 3 = 21 – 24 + 4 = 25 – 24 = 1

a) 20 – 4 · 7 + 11 b) 12 – 6 · 5 + 4 · 2 c) 15 – 20 : 5 – 3

d) 6 – 10 : 2 – 14 : 7 e) 5 · 3 – 4 · 4 + 2 · 6 f ) 7 · 3 – 5 · 4 + 18 : 6

a) 20 – 4 · 7 + 11 = 20 – 28 + 11 = 31 – 28 = 3

b) 12 – 6 · 5 + 4 · 2 = 12 – 30 + 8 = 20 – 30 = –10

c) 15 – 20 : 5 – 3 = 15 – 4 – 3 = 15 – 7 = 8

d) 6 – 10 : 2 – 14 : 7 = 6 – 5 – 2 = 6 – 7 = –1

e) 5 · 3 – 4 · 4 + 2 · 6 = 15 – 16 + 12 = 27 – 16 = 11

f) 7 · 3 – 5 · 4 + 18 : 6 = 21 – 20 + 3 = 24 – 20 = 4

Pág. 2



22 Observa el ejemplo y calcula.

• (–3) · (– 4) + (– 6) · 3 = (+12) + (–18) = 12 – 18 = – 6

a) 5 · (–8) – (+9) · 4 b) 32 : (–8) – (–20) : 5

c) (–2) · (–9) + (–5) · (+4) d) (+25) : (–5) + (–16) : (+4)

e) (+6) · (–7) + (–50) : (–2) f ) (+56) : (–8) – (–12) · (+3)

a) 5 · (–8) – (+9) · 4 = (–40) – (+36) = –40 – 36 = –76

b) 32 : (–8) – (–20) : 5 = (–4) – (–4) = –4 + 4 = 0

c) (–2) · (–9) + (–5) · (+4) = (+18) + (–20) = 18 – 20 = –2

d) (+25) : (–5) + (–16) : (+4) = (–5) + (–4) = –5 – 4 = –9

e) (+6) · (–7) + (–50) : (–2) = (–42) + (+25) = –42 + 25 = –17

f) (+56) : (–8) – (–12) · (+3) = (–7) – (–36) = –7 + 36 = 29

23 Calcula.

a) 18 – 5 · (3 – 8) b) 11 – 40 : (–8)

c) 4 · (8 – 11) – 6 · (7 – 9) d) (4 – 5) · (–3) – (8 – 2) : (–3)

a) 18 – 5 · (3 – 8) = 18 – 5 · (–5) = 18 – (–25) = 18 + 25 = 43

b) 11 – 40 : (–8) = 11 – (–5) = 11 + 5 = 16

c) 4 · (8 – 11) – 6 · (7 – 9) = 4 · (–3) – 6 · (–2) = (–12) – (–12) = –12 + 12 = 0

d) (4 – 5) · (–3) – (8 – 2) : (–3) = (–1) · (–3) – (+6) : (–3) = (+3) – (–2) = 3 + 2 = 5

24 Resuelto en el libro de texto.

25 Calcula.

a) 15 + 2 · [8 – 3 · 5] b) (–3) · (+5) – 3 · [11 + 3 · (5 – 11)]

c) 28 : (–7) – (–6) · [23 – 5 · (9 – 4)] d) (–2) · (7 – 11) – [12 – (6 – 8)] : (–7)

e) [18 + 5 · (6 – 9)] – [3 – 16 : (5 + 3)]

a) 15 + 2 · [8 – 3 · 5] = 15 + 2 · [8 – 15] = 15 + 2 · [–7] = 15 – 14 = 1

b) (–3) · (+5) – 3 · [11 + 3 · (5 – 11)] = –15 – 3 · [11 + 3 · (–6)] =

= –15 – 3 · [11 – 18] = –15 – 3 · [–7] = –15 + 21 = 6

c) 28 : (–7) – (–6) · [23 – 5 · (9 – 4)] = (–4) – (–6) · [23 – 5 · (5)] =

= –4 + 6 · [23 – 25] = –4 + 6 · [–2] = –4 + (–12) = –16

d) (–2) · (7 – 11) – [12 – (6 – 8)] : (–7) = (–2) · (–4) – [12 – (–2)] : (–7) =

= 8 – [12 + 2] : (–7) = 8 – [14] : (–7) = 8 – (–2) = 8 + 2 = 10

e) [18 + 5 · (6 – 9)] – [3 – 16 : (5 + 3)] = [18 + 5 · (–3)] – [3 – 16 : 8] =

= [18 + (–15)] – [3 – 2] = [+3] – [+1] = 3 – 1 = 2

Pág. 3

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