NÚMEROS ENTEROS: SUMA, RESTA, MULTIPLICACIÓN Y DIVISIÓN

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NÚMEROS
ENTEROS:
SUMA, RESTA,
MULTIPLICACIÓN
Y DIVISIÓN
NOMBRE:___________________
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SUMA Y RESTA DE NUMEROS ENTEROS:
1 Calcula.
a) 5 – 9
d)22 – 30
g) –8 – 14
j) –13 + 18
Soluciones:
a) –4 b) –6
j) 5 k) –13
b)5 – 11
e) 21 – 33
h)–21 – 15
k)–22 + 9
c) 4 d) –8 e) –12
l) –16
c) 13 – 9
f ) 46 – 52
i) –33 – 22
l) –37 + 21
f ) –6 g) –22
h) –36
i) –55
2 Calcula.
a) 5 – 8 – 4 + 3 – 6 + 9
c) 9 – 2 – 7 – 11 + 3 + 18 – 10
b) 10 – 11 + 7 – 13 + 15 – 6
d)–7 – 15 + 8 + 10 – 9 – 6 + 11
Soluciones:
a)
–1 b) 2 c) 0 d) –8
3 Quita paréntesis y calcula.
a) (+5) – (–3) – (+8) + (–4)
c) +(–9) – (+13) – (–11) + (+5)
b) –(–7) – (+5) + (–6) + (+4)
d)–(+8) + (–3) – (–15) – (+6) – (+2)
Soluciones:
a)
–4 b) 0 c) –6 d) –4
4 Calcula.
a) 3 – (5 + 7 – 10 – 9)
c) (7 – 11 – 4) – (9 – 6 – 13)
Soluciones:
a) 10 b) –4 c) 2 d) –2
b) 4 + (8 – 6 – 10) – (6 – 10 + 4)
d)–(6 – 3 – 5) – (– 4 – 7 + 15)
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5 Opera.
a) 16 + [3 – 9 – (11 – 4)]
c) (6 – 15) – [1 – (1 – 5 – 4)]
e) [9 – (5 – 17)] – [11 – (6 – 13)]
b) 8 – [(6 – 9) – (7 – 13)]
d)(2 – 12 + 7) – [(4 – 10) – (5 – 15)]
Soluciones:
a) 3 b) 5 c) –18 d) –7 e) 3
6 Quita paréntesis y calcula.
a) 6 – (5 – [4 – (3 – 2)])
c) 10 + (11 – [12 + (13 – 14)])
e) [(3 – 8) – 5] + (–11 + [7 – (3 – 4)])
b) 6 – (7 – [8 – (9 – 10)])
d)10 – (9 + [8 – (7 + 6)])
Soluciones:
a) 4 b) 8 c) 10 d) 6 e) –13
MULTIPLICACIÓN Y DIVISION DE NUMEROS ENTEROS
7 Opera aplicando la regla de los signos.
a) (–5) · (–6)
d)(+42) : (–6)
g) (+10) · (+5)
j) (+112) : (–14)
b) (–21) : (+3)
e) (–6) · (–8)
h)(–63) : (–9)
c) (–4) · (+7)
f ) (+30) : (+5)
i) (–9) · (–5)
Soluciones:
a) 30 b) –7 c) –28 d) –7 e) 48 f ) 6 g) 50 h) –8 i) 45 j) –8
8 Obtén el valor de x en cada caso:
a) x · (–9) = +9
d)x : (–4) = +3
b) (–5) : x = –1
e) x · (+6) = –42
Soluciones:
a) x = –1 b) x = 5 c) x = 9 d) x = –12 e) x = –7 f ) x = –4
c) (–5) · x = –45
f ) (+28) : x = –7
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9 Calcula.
a) (–2) · [(+3) · (–2)]
c) (+6) : [(–30) : (–15)]
e) (–5) · [(–18) : (–6)]
g) [(–21) : 7] · [8 : (–4)]
b) [(+5) · (–3)] · (+2)
d)[(+40) : (–4)] : (–5)
f ) [(–8) · (+3)] : (–4)
h)[6 · (–10)] : [(–5) · 6]
Soluciones:
a) 12 b) –30 c) 3 d) 2 e) –15 f ) 6 g) 6 h) 2
OPERACIONES COMBINADAS CON NUMEROS ENTEROS
10 Calcula.
a) 5 – 4 · 3
b) 2 · 9 – 7
d)2 · 8 – 4 · 5
e) 16 – 4 · 7 + 2 · 5 – 19
f ) 5 · 6 – 21 – 3 · 7 + 12
c) 4 · 5 – 6 · 3
Soluciones:
a) –7 b) 11 c) 2 d) –4 e) –21 f ) 0
O
M
11 Opera dentro del paréntesis y, después, multiplica.
a) 3 · (9 – 11)
b) –5 · (4 – 9)
c) 5 · (9 – 4) – 12
d)1 + 4 · (6 – 10)
e) 6 · (8 – 12) – 3 · (5 – 11)
f ) 4 · (13 – 8) + 3 · (9 – 15)
Soluciones:
a) 3 · (9 – 11) = 3 · (–2) = –6
b) –5 · (4 – 9) = –5 · (–5) = 25
c) 5 · (9 – 4) – 12 = 5 · 5 – 12 = 25 – 12 = 13
d) 1 + 4 · (6 – 10) = 1 + 4 · (–4) = 1 – 16 = –15
e) 6 · (8 – 12) – 3 · (5 – 11) = 6 · (– 4) – 3 · (–6) = –24 + 18 = –6
f ) 4 · (13 – 8) + 3 · (9 – 15) = 4 · 5 + 3 · (– 6) = 20 – 18 = 2
12 Calcula y observa que el resultado varía según la posición de los
paréntesis.
a) 17 – 6 · 2
c) (–10) – 2 · (–3)
e) (–3) · (+5) + (–2)
b) (17 – 6) · 2
d)[(–10) – 2] · (–3)
f ) (–3) · [(+5) + (–2)]
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Soluciones:
a)17 – 6 · 2 = 17 – 12 = 5
b) (17 – 6) · 2 = 11 · 2 = 22
c) (–10) – 2 · (–3) = –10 + 6 = –4
d) [(–10) – 2] · (–3) = (–12) · (–3) = 36
e) (–3) · (+5) + (–2) = –15 – 2 = –17
f ) (–3) · [(+5) + (–2)] = (–3) · (+3) = –9
13 Calcula paso a paso.
a) 5 · (– 4) – 2 · (–6) + 13
c) (–2) · (+8) – (–5) · (–6) + (–9) · (+4)
b)–6 · (+4) + (–3) · 7 + 38
d)–(–9) · (+5) · (–8) · (+7) – (+4) · (–6)
Soluciones:
a) 5 · (– 4) – 2 · (–6) + 13 = –20 + 12 + 13 = –20 + 25 = 5
b) –6 · (+4) + (–3) · 7 + 38 = –24 – 21 + 38 = –45 + 38 = –7
c) (–2) · (+8) – (–5) · (–6) + (–9) · (+4) = –16 – 30 – 36 = –82
d) –(–9) · (+5) · (–8) · (+7) – (+4) · (–6) = –2 496
14 Opera.
a) 5 · [11 – 4 · (11 – 7)]
b) (–4) · [12 + 3 · (5 – 8)]
c) 6 · [18 + (–4) · (9 – 4)] – 13
d)4 – (–2) · [–8 – 3 · (5 – 7)]
e) 24 – (–3) · [13 – 4 – (10 – 5)]
f ) 6 · (7 – 11) + (–5) · [5 · (8 – 2) – 4 · (9 – 4)]
Soluciones:
a) 5 · [11 – 4 · (11 – 7)] = 5 · [11 – 4 · 4] = 5 · [11 – 16] = 5 · (–5) = –25
b) (–4) · [12 + 3 · (5 – 8)] = (–4) · [12 + 3 · (–3)] = (–4) · [12 – 9] = (–4) · 3 = –12
c) 6 · [18 + (–4) · (9 – 4)] – 13 = 6 · [18 + (–4) · 5] – 13 = 6 · [18 – 20] – 13 =
= 6 · (–2) – 13 = –12 – 13 = –25
d) 4 – (–2) · [–8 – 3 · (5 – 7)] = 4 + 2 · [–8 – 3 · (–2)] = 4 + 2 · [–8 + 6] =
= 4 + 2 · [–2] = 4 – 4 = 0
e) 24 – (–3) · [13 – 4 – (10 – 5)] = 24 + 3 · [13 – 4 – 5] = 24 + 3 · 4 = 24 + 12 =
36
f ) 6 · (7 – 11) + (–5) · [5 · (8 – 2) – 4 · (9 – 4)] = 6 · (– 4) + (–5) · [5 · 6 – 4 · 5]
= –24 – 5 · [30 – 20] = –24 – 5 · 10 = –24 – 50 = –74
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15 Calcula paso a paso.
a) 10 : [8 – 12 : (11 – 9)]
b) 6 : (13 – 15) – [(8 – 4) : (–2) – 6 : (–3)]
Soluciones:
a) 10 : [8 – 12 : (11 – 9)] = 10 : [8 – 12 : 2] = 10 : [8 – 6] = 10 : 2 = 5
b) 6 : (13 – 15) – [(8 – 4) : (–2) – 6 : (–3)] = 6 : (–2) – [4 : (–2) + 2] =
= –3 – [–2 + 2] = –3