The document provides a step-by-step guide to solving various math operations involving integers and natural numbers. It includes over 50 problems of varying difficulty ranging from easy to medium complexity. The problems cover adding, subtracting, multiplying, dividing, and combining multiple operations in single expressions.

1. SOLUCIÓN GUÍA N°1:
OPERACIONES COMBINADAS y APLICACIÓN DE N° NATURALES Y ENTEROS
I. PARTE I:Realiza las siguientes operaciones con limpieza y en orden en tu cuaderno, con
desarrollo paso a paso y con resultado final.
1. Tipo de dificultad: FÁCIL
a) -65 + 13 =-52 b) 6 - (-23) = 6 + 23 = 29 c) -2 + (-3) = -2 – 5 = -7
d) (-12) × (-3) × 5 = 36 x 5 = 180 e) 45 : (-5) =-9 f) 3 - 2 + 9 - 7 = (3 + 9) + (-2 - 7) = (12) + (-9) = 3
g) 3 - 2 × 5 + 7 × 4 = 3 – 10 + 28 = (28 + 3) - 10= 31 – 10 = 21
h) 7 + (4 - 5) - (-89) = 7 + (-1) + 89 = (89 + 7) + (-1) = 96 – 1 = 95
i) 4 - 3 + 7 - 2 = (4 + 7) + (-3 - 2) = (11) + (-5) = 11 – 5 = 6
j) (-3) × (-2) + 7 = 6 + 7 = 13 k) 3 + 4 × 5 = 3 + 20 = 23
l) 9 − 7 + 5 + 2 − 6 + 8 − 4 = (9 + 5 +2 +8) + (-7 - 6 - 4) = (24) + (-17) = 7
m) (-1) × 7 + (2 - 5) = -7 + (-3) = -10 n) 4 : 2 - (3 + 1) = 2 – (4) = -2
ñ) 13 - (4 + 8) - 3 × 5 = 13 – (12) – 15 = 13 – 27 = -14
o) [21 : (7 × 3)] + 4 × (5 - 1) = [21 : (21)] + 4 x (4) = [1] + 16 = 17
p) 7 - 7 - [(2 × 3) : (3 × 2)] = 0 – [(6) : (6)] = - [1] = -1
q) -3 - 2 × [-9 × (5 - 4) - (-6)] = -3 – 2 x [-9 x (1) + 6] = -3 – 2 x [-9 + 6] = -3 – 2 x [-3] = -3 + 6 = 3
r) -3 + 3 × (5 - (-4)) = -3 + 3 x (5 + 4) = -3 + 3 x (9) = -3 + 27 = 24
s) 11 × 5 - 6 × 11 = 55 – 66 = - 11

2. 2. Tipo de dificultad: FÁCIL - MEDIO
a)1 - 5 × 4 = 1 - 20= -19 b)3 + 4 : 2 = 3 + 2 = 5 c)1 + 4 × (3 + 2) = 1 + 4 X (5) = 1 + 20 = 21
d)5 × 4 - (1 + 2) = 20 – 3 = 17 e)18 - [(3 + 6 + 9) : (9 - 6)] = 18 – [(18) : (3)] = 18 – [6] = 12
f)[(55 - 10) - (3 × 6 × 9)] : (-3) =[(45) – (162)] : (-3) = [-117] : (-3) = 39
h)10 : 2 + 5 · 3 + 4 − 5 · 2 − 8 + 4 · 2 − 16 : 4= 5 + 15 + 4 – 10 – 8 + 8 – 4 = 20 – 10 = 10
i)*15 − (8 − 10 : 2 )+ · *5 + (3 ·2 − 4 )+ − 3 + (8 − 2 · 3 )= [15 – (8 - 5)]·[5 + (6 - 4)] – 3 + (8 - 6)
= [15 – (3)]·[5 + (2)] – 3 + (2) = [12]·[7] – 3 + (2) = 84 – 3 + 2 = 86 – 3 = 83
j)14 − ,7 + 4 · 3 - [4 · 2 - 6]} + (4 + 6 - 5 · 3) + 3 - (5 - 8 : 2)=
= 14 − ,7 + 12 - [8 - 6)]} + (4 + 6 - 15) + 3 - (5 - 4)= 14 − ,7 + 12 - [2]} + (10 - 15) + 3 - (1)
= 14 − ,19 - [2]} + (-5) + 2 = 14 − ,17-+ (-5) + 2 = (14 + 2) + (-17 - 5) = (16) + (-22) = -6
k)27 + 3 · 5 – 16 = 27 + 15 – 16 = 42 – 16 = 26
l)27 + 3 – 45 : 5 + 16 = 30 – 9 + 16 = (30 + 16) – 9 = 46 – 9 = 37
m) (2 · 4 + 12) (6 − 4) = (8 + 12)(2) = (20)(2) = 40
n)3 · 9 + (6 + 5 – 3) – 12 : 4 =27 + (8) – 3 = 35 – 3 = 32
ñ)2 + 5 · (2 · 3) = 2 + 5 · (6) = 2 + 30 = 32
o)440 − *30 + 6 (19 − 12)+= 440 – [30 + 6 (7)]= 440 – [30 + 42] = 440 – [72] = 368
p)2,4 *7 + 4 (5 · 3 − 9)+ − 3 (40 − 8)- = 2,4 *7 + 4 (6)+ − 3 (32)} = 2,4 *7 + 24+ − 92}
= 2,4 *31+ − 92} = 2,124− 92} = 2{32} = 64
r) 5 − *6 − 2 − (1 − 8) − 3 + 6+ + 5 = 5 − *4 − (-7) + 3] + 5 = 5 − *4 +7 + 3] + 5= 5 − *14] + 5
= 10 – 14 = -4

3. II. Realiza las siguientes operaciones con limpieza y en orden en tu cuaderno, con desarrollo paso a
paso y con resultado final.
Tipo de dificultad: FÁCIL – MEDIO
s)9 : *6 : (− 2)+ = 9 : [-3] = -3
t)8 + 10 : 2 + 5 • 3 + 4 − 5 • 2 − 8 + 4 • 4 − 16 : 4 = 8 + 5 + 15 + 4 − 10 − 8 + 16 − 4 =
= (8 + 5 + 15 + 4 +16) + (-10 -8 -4) = (48) + (-22) = 26
1) 3 + 5 – 5 + 3 – 9 + 12 = 18 – 9 = 9
2) 5 – 4 + 9 + 2 – 2 – 3 – 7 – 12 – 4 = 14 – 30 = -16
3) 3 + 2 + 7 – 12 – 6 – 3 + 5 = 17 – 21 = -4
4) – 3 + 4 + 7 + 6 - 4 – 1 = 17 – 8 = 9
5) [- (3 + 2) – (5 + 4 - 3)] = [- (5) – (6)] = [- 5 - 6] = - 11
6) – 4 + [(3 – 9) – (-4 – 2) + 3] = - 4 + [(-6) – (-6) + 3] = -4 + [-6 + 6 + 3] = -4 + [3] = -1
7) – 5 – [(-5 – 4) – (-5 + 2)] = -5 – [(-9) – (-3)] = -5 – [-9 + 3] = -5 – [-6] = -5 + 6 = 1
8) -4 + [-(-4 + 9) + (-4 – 2)] = -4 + [-(5) + (-6)] = -4 + [-5 - 6] = -4 + [-11] = -4 – 11 = -15
9) -4 – {5 + [4 – (7 + 4 - 4)]} = -4 – {5 + [4 – (7)]} = - 4 – {5 + [-3]} = - 4 – {3} = -7
10) 3 + {3 – 6 – [9 + 12 – (4 + 9)]} = 3 + {- 3 – [21 – (13)]} = 3 + {- 3 – [8]} = 3 + {-11} = -8
11) 4 + {4 – 9 – [9 + 4 – (3 + 6) - 5] + 3} =4 + { – 5 – [13 – (9) - 5] + 3} =4 + {- 5 - [-1] + 3}
= 4 + {- 5 + 1 + 3} = 4 + {-1} = 3

4. 12) 3 – {5 – [-9 – 7 – (5 – 4 – 3)]} = 3 – {5 – [ -16 – (-2)]} = 3 – {5 – [-16 + 2]} = 3 – {5 – [-14]} = = 3 – {5 + 14} = 3 – {19} = -16
13) 4 – {-12 : 4 + [4 – (4 : -2 + 12 – 2) – 6]} =4 – {-3 + [4 – (-2 + 10) – 6]} = 4 – {-3 + [4 – (8) – 6]} == 4 – {-3 + [-10]}
= 4 – {-13} = 4 + 13 = 17
14) – 8 – {5 – [6 – (4 x -3 : - 6 + 5 – 2)] + 7} – 6 : - 3 = – 8 – {5 – [6 – (-12 : - 6 + 3)] + 7} + 3 = – 8 – {5 – [6 – (2 + 3)] + 7} + 3
= – 8 – {5 – [6 – (5)] + 7} + 3 = – 8 – {5 – [1] + 7} + 3 = – 8 – {11} + 3 = -16
15) 5 – 9 – {4 + [4 – (12 : -6 x 2 + 4 - 3) – 5 : -5]} = – 4 – {4 [4 – (-2 x 2 + 1) + 1]} = – 4 – {4 + [4 – (-3) + 1]}
= – 4 – {4 + [8]} = – 4 – {12} = -16
16) 2 – {1 – [0 – (3 x 3 : - 9 – 4 – 4) – 6 : 2 x – 2] + 7 – 4} = 2 – {1 – [0 – (9 : - 9 – 8) – 3 x – 2] + 3} = 2 – {1 – [0 – (- 1 – 8) + 6] + 3}
= 2 – {1 – [0 – (- 9) + 6] + 3} = 2 – {1 – [15] + 3} = 2 – {- 11} = 2 + 11 = 14
17) 6 – {4 – [3 x -2 + 3 x 6 – (4 : -2 + 4 -2) – 9 : -3] + 4} = 6 – {4 – [- 6 + 18 – (-2 + 2) + 3] + 4} =6 – {4 – [15 – (0)] + 4}
= 6 – {4 – [15] + 4} = 6 – {- 7} = 6 + 7 = 13
18) 4 – {-5 – 9 – [- (-5 x – 4 + 6 : -3) – 9 x – 30 : - 6 + 7] - 3} – 3 : - 3 = 4 – {-14 – [- (20- 2) + 270 : - 6 + 7] - 3} + 1
=5 – {-14 – [- (18) – 45 + 7] - 3} = 5 – {-14 – [- 56] - 3} = 5 – {- 14 + 56 – 3} = 5 – {39} = - 34

5. III. Realiza las operaciones, paso a paso, con limpieza y destaca el resultado, en tu cuaderno:
Tipo de dificultad: FÁCIL
a)252724
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b)10(386)•(5) = 50
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c)(4835)42•4 + 2 = 56 + 2 = 58
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d)(68):218:(54)
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e)8(1015:3)346
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f)63(252)(538)1
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IV. Calculaelresultadodelassiguientesoperaciones combinadas en tu cuaderno.
Tipo de dificultad: FÁCIL
a)83:4:(10:24)20
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b)(1634)(1515:3)(20:28)
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c)425:10(1253)65•5  10 + (12 + 15) – 30 = 40  10 + (27) = 4 + 27 = 31
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d)(3445)(12:320:4)256
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e)4(93)5(127)•(6) + 5•(5) = 24 + 25 = 49
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f)173(84)54:2•(4) + 27 = 44 – 12 = 32
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6. V. Calcula teniendo mucho cuidado con los paréntesis en tu cuaderno:
Tipo de dificultad: FÁCIL - MEDIO
a) 532(253)102:4•*3 + 2•(4)+ –204 = 5•*3 + 8+ – 5 = 5•*11+ – 5
= 55 – 5 = 50
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b) (3125):242(421)•(5) = [5 – 2]•5 = [3]•5 = 15
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c) (173)(32)30:(523)(5)(5) – 30:(6) = 25 – 5 = 20
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d) 436(536)3(5(12))436(2)3(5(3))43123(2) 
      4156