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. 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

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

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

III. Realiza las operaciones, paso a paso, con limpieza y destaca el resultado, en tu cuaderno:

Tipo de dificultad: FÁCIL

a)252724

b)10(386)•(5) = 50

c)(4835)42•4 + 2 = 56 + 2 = 58

d)(68):218:(54)

e)8(1015:3)346

f)63(252)(538)1

IV. Calculaelresultadodelassiguientesoperaciones combinadas en tu cuaderno.

Tipo de dificultad: FÁCIL

a)83:4:(10:24)20

b)(1634)(1515:3)(20:28)

c)425:10(1253)65•5 10 + (12 + 15) – 30 = 40 10 + (27) = 4 + 27 = 31

d)(3445)(12:320:4)256

e)4(93)5(127)•(6) + 5•(5) = 24 + 25 = 49

f)173(84)54:2•(4) + 27 = 44 – 12 = 32

V. Calcula teniendo mucho cuidado con los paréntesis en tu cuaderno:

Tipo de dificultad: FÁCIL - MEDIO

a) 532(253)102:4•*3 + 2•(4)+ –204 = 5•*3 + 8+ – 5 = 5•*11+ – 5

= 55 – 5 = 50

b) (3125):242 (421)•(5) = [5 – 2]•5 = [3]•5 = 15

c) (173)(32)30:(523)(5)(5) – 30:(6) = 25 – 5 = 20

d) 436(536)3(5(12))436(2)3(5(3))43123(2)

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