This document provides solutions to math problems involving operations with integers such as multiplication, division, addition, and subtraction. Some key points: - It works through 26 examples of calculating various integer operations step-by-step. - The examples involve multiplying, dividing, adding, and subtracting integers, as well as performing operations within parentheses first before the outer operations. - Observations are made about the non-associative property of division based on an example.

1. 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

2. Soluciones a las actividades de cada epígrafeSoluciones a las actividades de cada epígrafe1
Unidad 1. Divisibilidad y números enteros
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

3. Soluciones a las actividades de cada epígrafeSoluciones a las actividades de cada epígrafe1
Unidad 1. Divisibilidad y números enteros
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