Matemática 5to Grado Unidad 6 Sr Vic

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Competencias •  Actúa y piensa

matemátic matemáticament amentee en situaciones situaciones de cantidad. cantidad. •  Actúa y piensa

matemáticamente en situaciones situaciones de regularidad regularidad,, equivalencia equivalencia y cambi cambio. o.

246

Capacidades •   Matematiza

situaciones. y representa ideas matemáticas.

•   Comunica

Indicador Indica dores es de des desem empeñ peño o •  Emplea un model modelo o

de solu soluci ción ón aditiv aditivo o o multipli multiplica cativ tivo o con con fracciones. la compa omparració ación n y el orden den de las las frac fracci cion ones es prop propia iass y núme númerros mixtos.

•   Describe

dato datoss y relac relacione ioness en proble problemas mas de equiva equivalenc lencia ia o equilib equilibrio rio,, expresá xpresándol ndolos os en ecuacio ecuaciones nes simples simples..

•   Interpreta

 .    l   a    i   r   o    t    i    d    E   a    l   e    d   o   s   e   r   p   x   e   o   s    i   m   r   e   p   n    i   s   o    t   n   e    i   m    i    d   e   c   o   r   p   o   o    i    d   e   m   r   e    i   u   q    l   a   u   c   r   o   p   o   r    b    i    l   e    t   s   e   e    d    l   a    i   c   r   a   p   o    l   a    t   o    t   n    ó    i   c   c   u    d   o   r   p   e   r   a    l   a    d    i    b    i    h   o   r    P

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Recordando... 1) Une cada cada fracci fracción ón con su repr represe esent ntación ación gráfic gráfica. a. 1 4

3 10

3 4

•

•

•

•

•

•

2) Escribe la fracción fracción que repres represent entaa cada gráfico. gráfico.

 .    l   a    i   r   o    t    i    d    E   a    l   e    d   o   s   e   r   p   x   e   o   s    i   m   r   e   p   n    i   s   o    t   n   e    i   m    i    d   e   c   o   r   p   o   o    i    d   e   m   r   e    i   u   q    l   a   u   c   r   o   p   o   r    b    i    l   e    t   s   e   e    d    l   a    i   c   r   a   p   o

•

=

1 4

•

=

7 12

•

=

3 6

•

=

4 8

3) Pinta adecuadam adecuadamen ente te los gráfic gráficos os para para repr represe esent ntar ar cada cada fracción.

Una de las características de la con convive vivenc ncia ia es sabe saberr compar mparttir con los demá demás. s. Par Para ello, ello, es necesa necesario rio serequ ser equit itat ativ ivos os y justo justos. s. Repartir en partes iguales es la mejo mejorr mane manerra de que que todo todoss est estemos emos

•

2 = 6

•

5 = 9

•

7 = 8

•

10 = 12

4) Encierra la fracción que representa la cantidad de regiones regiones no color coloreada eadass de la figur figura. a.

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Números y op opera eracio ciones nes

Unidad

6

 

Nivel 1 Niv

 

Fracciones

Ficha de tr trab abaj ajo o

Nombres y apellidos:

Fecha:

1) Escribe las fracciones fracciones correspondient correspondientes es y las clases a las las que pertenecen. pertenecen. 3 5

a) Tres quintos: quintos: Clase:

d) Dos sextos:

propia pro pia e irr irreduc eductibl tiblee

b) Nueve Nueve octavos: octavos:

Clase:

9 8

Clase:

•

Clase:

9 11

Clase: c) 2 5

8 10

propia pr opia y re reducti ductible ble

f) Siete Siete novenos: novenos:

propia pro pia e irr irreduc eductibl tiblee

2) Observa las fraccio fracciones nes y responde. a) 5 b) 8 3 9

propia pro pia y re reducti ductible ble

e) Ocho décimos:

Clase: impr impropia opia e irr irreduc eductibl tiblee c) Nueve Nueve onceavos: onceavos:

2 6

7 9

propia pr opia e irr irreduct eductible ible d) 9 11

e) 3 9

¿Qué fraccio fracciones nes tienen tienen el mismo denominad denominador? or? Las letras b y e

3) Marca con un aspa (X) para para indicar indicar si las fracci fracciones ones son reducti reductibles bles o irreduct irreductible ibles. s. Fracción 2 3 3 4 6 8

Reductible

3 9

X

12 9 8 9 7

X

Irreductible X X

X

X X

 .    l   a    i   r   o    t    i    d    E   a    l   e    d   o   s   e   r   p   x   e   o   s    i   m   r   e   p   n    i   s   o    t   n   e    i   m    i    d   e   c   o   r   p   o   o    i    d   e   m   r   e    i   u   q    l   a   u   c   r   o   p   o   r    b    i    l   e    t   s   e   e    d    l   a    i   c   r   a   p   o

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Números y op opera eracio ciones nes

Unidad

6

Nivel 2 Ni

RelacióFnraec nctririe nc e onceosnjuntos

Ficha de tr trab abaj ajo o

Nombres y apellidos:

Fecha:

Escribe un grupo de cinco cinco fracci fracciones ones homogéne homogéneas as con denomina denominador dor

1)

15. Respuest Respuestaa libre li bre Escribe un grupo grupo de cinco cinco fracci fracciones ones hete hetero rogén géneas eas con nume numerrador

2)

15. Respuest Respuestaa libre li bre

3) Colorea adecuadam adecuadament entee el gráfic gráfico o para para repr represe esent ntar ar a cada cada fracció fracción n y luego luego escribe las letras letras correspondien correspondientes. tes.

 .    l   a    i   r   o    t    i    d    E   a    l   e    d   o   s   e   r   p   x   e   o   s    i   m   r   e   p   n    i   s   o    t   n   e    i   m    i    d   e   c   o   r   p   o   o    i    d   e   m   r   e    i   u   q    l   a   u   c   r   o   p   o   r    b    i    l   e    t   s   e   e    d    l   a    i   c   r   a   p   o

a)

3 =

b) 2 =

c) 8 =

4

10

4

d) 5 8

•

Fracciones Fracciones propias: propias: a , b , c y d

•

Fracciones Fracciones irreductibles: irreductibles: a y d

•

Fracciones Fracciones decimales: decimales: c

•

Fracciones Fracciones reductibles: reductibles: b y c

=

4) Escribe en cada caso caso la fracci fracción ón que repr represe esent ntaa a cada cada uno de de los grá gráfico ficos. s.

a)

=

8 9

b)

4 9

=

c)

=

5 8

d)

=

5) Une cada gráfic gráfico o con la fracció fracción n que le corre correspond sponde. e.

•

•

•

•

3 6

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Números y op opera eracio ciones nes

Unidad

6

 

Nive Niv el 3

 

Fracciones

Ficha de tr trab abaj ajo o

Nombres y apellidos:

Fecha:

1) Marca con un aspa (X) para para indicar indicar a qué tipo perten pertenece ecen n las siguien siguiente tess fracci fracciones ones:: Tipos de fracción

8 7

16 10

X

X

Fracción Fracción propia propia Fracción Fracción impropia impropia Fracción Fracción reductib reductible le Fracción irreductible irreductible Fracción Fracción decimal decimal

X

2 8 X

6 28 X

5 100 X

X

X

X

X

X X

X

2) Encierra con un círculo círculo aquellos gráficos gráficos que represen representan tan la fracción fracción 1 . 4

3) Observa las figur figuras as y colorea 1 de cada ada una una de ella ellas. s. 2

4) Escribe y representa gráficam gráficament entee las siguientes fracciones: fracciones:

a) Cuatro séptimos 4 7 b) Seis octavos 6

2 15 X

d) Seis sextos 6 6 e) Ocho doceavos 8

 .    l   a    i   r   o    t    i    d    E   a    l   e    d   o   s   e   r   p   x   e   o   s    i   m   r   e   p   n    i   s   o    t   n   e    i   m    i    d   e   c   o   r   p   o   o    i    d   e   m   r   e    i   u   q    l   a   u   c   r   o   p   o   r    b    i    l   e    t   s   e   e    d    l   a    i   c   r   a   p   o

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ReC laíc íc rció un loem ntare tec m oántjiucnoto tos Fracciones

Números y op opera eracio ciones nes

Unidad

6

Ficha de tr trab abaj ajo o

Nombres y apellidos:

Fecha:

1) Escribe la fracci fracción ón corres correspondi pondient entee al enunciado enunciado y marca con con un aspa aspa (X) (X) indi indica cand ndo o la clas clasee a la que que pert perten enec ece. e. Fracción

Propia

Se divi divide den n dos tart tartas as en 8 troz trozos os iguales iguales cada una y se comen comen 10.

10 8

De un folio olio divid ividiido en 6 part partees iguale igualess se marc marcan an 2.

2 6

X

De las las 9 pági página nass de la lecc lecció ión, n, se han leído 5.

5 9

X

Impropia

Irreductible

Reductible

X

X X X

2) Observa la figura y completa cada cada enunciado enunciado con la fracció fracción n que corres corresponda ponda..  .    l   a    i   r   o    t    i    d    E   a    l   e    d   o   s   e   r   p   x   e   o   s    i   m   r   e   p   n    i   s   o    t   n   e    i   m    i    d   e   c   o   r   p   o   o    i    d   e   m   r   e    i   u   q    l   a   u   c   r   o   p   o   r    b    i    l   e    t   s   e   e    d    l   a    i   c   r   a   p   o

E

A

D C

B

•

A re representa

1

del total.

•

E representa

•

B re representa

1 8

del total.

•

E y D re representan

•

C re representa

3 8

del total.

•

A, B y C representan

•

D re representa

1 del total. 16

•

A, B, C y D representan

3

del total. 1 4

del to total. 3 4

del total. 13 del total. 16

3) Lee los problemas y resuélvelos.

a) Los 25 estudi tudiaantes de una secci cción del 5.o grado de prima primari riaa tienen tienen activ activida idade dess extr extraa esco escolar lares es.. Se sabe que 10 juegan fútbol, 7 practican natación, 5 danza y el resto va al taller de música.   Escribe la fracció cción n que representa la cant cantida idad d de estud estudian iante tess por cada cada activi actividad dad.. Total: 25 estudiantes Fútbol: 10  Fracción: 10 25

b) Un grup grupo o de mon montañer ñeros lleg llegaa a un refugi fugio o que que est está casi casi llen lleno. o. En la entr entrad adaa se encu encuen entr tran an con con el siguien siguiente te cartel cartel:: Núme Númerro de plaz plazas: 20 Plaza Plazass ocupa ocupadas das:: 17 Plazas Plazas libres: libres: 3 Halla las fracciones fracciones que represen representan tan el número número

de plaz plazas ocupad ocupadas as y plaza plazass libre libres. s. Plaza Pla zass ocu ocupad padas: as: 17  Fracción: 17

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Fracciones

Números y op opera eracio ciones nes

6

Unidad

Fic ich ha de ev eval alua uaci ción ón

Nombres y apellidos:

Fecha:

1) Relaciona mediant mediantee flechas flechas cada gráfic gráfico o con su respec respectiv tivaa fracción. fracción.

1

•

•

•

•

•

•

•

•

6 9

3 6

9 12

7 9

2) Colorea adecuadame adecuadament ntee el gráfic gráfico o para para represe represent ntar ar a cada cada fracci fracción. ón. a) 9 = 24

b) 12 = 24

c) 4 = 24

3) Escribe V si es verda erdade derro o F si es falso also segú según n corr corres espo pond nda. a. •

La fracción 8 es propia. propia. 3

( F )

•

La fracción 3 es propia. propia.

(V )

 .    l   a    i   r   o    t    i    d    E   a    l   e    d   o   s   e   r   p   x   e   o   s    i   m   r   e   p   n    i   s   o    t   n   e    i   m    i    d   e   c   o   r   p   o   o

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PRre relp aa criá óndeonntroesc scpoanra junPtIo SA s Fracciones

Números y op opera eracio ciones nes

Unidad

6

Nombres y apellidos:

Fecha:

1) Lee y resuelve los siguiente siguientess problemas problemas de fracciones. fracciones. Don Don Jav Javier ier es un expert perto o maes maestr tro o pana panade derro con 20 años años de exper perienc iencia ia.. Tiene iene una una pana panade derí ríaa que que se llam llamaa El Pan de Oro, dond dondee cocin ocinaa varia ariado doss y ric ricos pane paness y sus sus clie clien ntes sale salen n muy muy sati satissfecho echoss por por la calid alidad ad y limp limpie iezza de sus prod produc ucttos. os. El día día de hoy hoy se ha prop propue uessto vender der much muchos os pane paness y, a esta hor hora del del día, día, solo olo le queda ueda par para vende venderr lo siguien siguiente: te:

 .    l   a    i   r   o    t    i    d    E   a    l   e    d   o   s   e   r   p   x   e   o   s    i   m   r   e   p   n    i   s   o    t   n   e    i   m    i    d   e   c   o   r   p   o   o

Tipo de pan

Cantidad

pan francés

50

pan de yema

23

ciabatta

12

pan de maíz

15

croissant

8

pan de camote

18

pan árabe

6

a) ¿Cuántos ¿Cuántos panes le quedan en total? Sumando: 50 + 23 + 12 + 15 + 8 + 18 + 6 = 132 Rpta.: Rpt a.: En tot total al le quedan quedan 132 pane panes. s. b) ¿Qu ¿Quéé part partee del del total otal repres presen entta el tipo tipo de pan pan que más más le queda? queda? Total: 132 panes Cant Ca ntid idad ad de dell ti tipo po de pa pan n qu quee má máss le qu qued edaa: 50

e) ¿Qué parte parte del total repre represent sentaa cada tipo de pan? Total: 132 panes Pan fr fran ancé cés: s: 50  Fracción: 50 132 Pan de yema ma:: 23  Fracción: 23 132 Ciabat Ciab atta ta:: 12  Fracción: 12 132

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Números y op opera eracio ciones nes

Unidad

6

Nivel 1 Niv

Número Núm eross mixt mixtos os

Ficha de tr trab abaj ajo o

Nombres y apellidos:

Fecha:

1) Relaciona mediant mediantee flechas flechas cada repr represe esent ntación ación gráfic gráficaa con la fracción fracción y el númer número o mixto mixto corres correspondi pondien ente. te.

•

• 5 •

•12

•

•

• 7 •

•22

•

•

•

•

2

5

5

8

18 • 8

•2

2) Convierte cada fracci fracción ón impropia impropia en un númer número o mixto. mixto. •

10 = 3

31 3

•

5 = 3

12 3

•

8 = 3

22 3

•

7 = 2

31 2

•

8 = 5

13 5

•

16 = 5

31 5

•

9 = 4

21 4

•

21 = 5

41 5

•

32 = 3

11 3

•

41 = 2

9 2

3) Convierte cada cada núme númerro mixto mixto en una fracci fracción ón impr impropia. opia. •

25 = 7

19 7

•

11 = 6

7 6

1 2  .    l   a    i   r   o    t    i    d    E   a    l   e    d   o   s   e   r   p   x   e   o   s    i   m   r   e   p   n    i   s   o    t   n   e    i   m    i    d   e   c   o   r   p   o   o

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Números y op opera eracio ciones nes

Unidad

6

Nivel 2 Ni

RelacNió úm n en rotrsem cioxn tojusntos

Ficha de tr trab abaj ajo o

Nombres y apellidos:

Fecha:

1) Colorea cada cada gráf gráfic ico o para para repr repres esen enta tarr la fracc fracción ión que se indic indica, a, luego luego convierte dich dichaa frac fracci ción ón en un núme númerro mixto.

 .    l   a    i   r   o    t    i    d    E   a    l   e    d   o   s   e   r   p   x   e   o   s    i   m   r   e   p   n    i   s   o    t   n   e    i   m    i    d   e   c   o   r   p   o   o

a) 5 3





12 3

b) 13 5





23 5

c) 15 4





33 4

d) 13 2





61 2

2) Convierte cada cada núme númerro mixto mixto en una fracc fracción ión impr impropia. opia. •

80 2 = 322 4 4

•

70 3 = 353 5 5

•

60 7 = 10

607 10

•

50 1 = 8

401 8

•

90 1 = 4

361 4

•

30 8 = 9

278 9

•

112 10 2 =

•

40 5 = 6

245

•

20 7 = 5

107

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Números y op opera eracio ciones nes

6

Unidad

Nive Niv el 3

Número Núm eross mixt mixtos os

Ficha de tr trab abaj ajo o

Nombres y apellidos:

Fecha:

1) Completa la siguiente siguiente recta recta numérica numérica y luego responde. 1 4

2 4

11 4

3 4

0

13 4

22 4

23 4

1

3 2

•

¿En cuántas cuántas parte partess iguales iguales se ha dividido dividido la distan distancia cia entre entre dos números números naturales naturales consecu consecutiv tivos? os? En 4 pa part rtes es ig igua uale less

2) Convierte cada fracció fracción n impropia impropia en un número número mixto. mixto. •

41 4

= 10 1 4

•

87 5

= 16 7 5

•

61 3

= 20 1 3

•

76 5

= 15 1 5

•

91 4

= 22 3 4

•

43 2

= 21 1 2

•

93 10

3 = 9 10

•

211 = 35 1 6 6

•

153 = 19 1 8 8

•

61 7

=

•

146 = 29 1 5 5

•

147 = 13 4 11 11

85 7

3) Completa la siguiente siguiente tabla: R

ió

áfi

F

ió

Nú

i

 .    l   a    i   r   o    t    i    d    E   a    l   e    d   o   s   e   r   p   x   e   o   s    i   m   r   e   p   n    i   s   o    t   n   e    i   m    i    d   e   c   o   r   p   o   o

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ReC laíc íc rció un loem ntare tec m oántjiucnoto tos Número Núm eross mixt mixtos os

Números y op opera eracio ciones nes

Unidad

6

Ficha de tr trab abaj ajo o

Nombres y apellidos:

Fecha:

1) Escribe el númer número o mixto mixto que repr represe esent ntaa cada gráfic gráfico. o. •

•

=

12 3

•

•

31 2

=

33 6

•

=  .    l   a    i   r   o    t    i    d    E   a    l   e

=

24 6

•

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Número Núm eross mixt mixtos os

Números y op opera eracio ciones nes

Unidad

6

Fic ich ha de ev eval alua uaci ción ón

Nombres y apellidos:

Fecha:

1) Convierte cada cada fracció fracción n impropia impropia en un número número mixto. mixto. •

33 = 4

8 1

•

55 = 9

61 9

•

37 = 9

41 9

•

43 = 6

71 6

•

23 = 7

32 7

•

17 = 5

32 5

4

2) Convierte cada cada núme númerro mixto mixto en una fracci fracción ón impr impropia. opia. •

21 = 3

7 3

•

76 = 8

62 8

•

45 = 8

37 8

•

53 = 4

23 4

•

95 = 6

59 6

•

63 = 9

57 9

3) Escribe la fracción fracción que repre represen senta ta cada gráfico gráfico,, luego conviértelo a un número número mixto.

 .    l   a    i   r   o    t    i    d    E   a    l   e

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PRre relp aa criá óndeonntroesc scpoanra junPtIo SA s Número Núm eross mixt mixtos os

Números y op opera eracio ciones nes

Unidad

6

Nombres y apellidos:

Fecha:

1) Lee el proble problema ma y responde las pregun preguntas tas expre expresando sando cada result resultado ado como un número número mixto. mixto. El señor Luis es un agricultor y tiene un terreno de 100 hm 2, dond dondee prod produc ucee gran gran varie arieda dad d de frut frutas as.. Est Esta temp tempor orada ada cose cosechó chó muchas muchas de esta estass (como (como indic indicaa el cuadr cuadro), o), y como como es un buen buen admini administ strrador ador de sus sus recu recurrsos, sos, toda oda su cosec osecha ha la empac pacó en cajas ajas de made maderra de dif diferent entes tamañ amaños os par para vende enderl rlas as en los los supe upermer mercados ados de Lima Lima.. Cosecha

 .    l   a    i   r   o    t    i    d    E   a    l   e

Fruta

Cantidad

Manzana

500 kg

Pera

800 kg

Palta

200 kg

Fresa

700 kg

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Números y op opera eracio ciones nes

Unidad

6

 

Nivel 1 Niv

Fracciones Fraccion es equivalentes

Ficha de tr trab abaj ajo o

Nombres y apellidos:

Fecha:

1) Divide cada ada regió egión n de la figu figurra segú según n la indi indiccació ación, n, lueg luego o  escribe la fracc fracción ión equiv equivale alent ntee que repr repres esen enta ta el

gráfico gráfico obtenido. a) Cada región en en do dos

1 4

=

b) Cada región en en tr tres

2 8

3 3

=

9 9

2) Escribe V si es verda erdade derro o F si es falso also segú según n corr orrespo espond nda. a. 4 = 2 1 = 3 • • ( F ) ( V) 5 10 5 15 •

3 = 6 4 8

( V )

•

2 = 7 7 5

c) Cada región en en ci cinco

( F )

1 2

• •

3) Marca con un aspa aspa (X) los gráficos gráficos que repre represent senten en fracciones fracciones equivalente equivalentess a:

2 = 3 10 15 2 = 3 6 9

=

5 10

( V) ( V )

 .    l   a    i   r   o    t    i    d    E   a    l   e

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Números y op opera eracio ciones nes

Unidad

6

Nivel 2 Ni

RFera laccciiiióonnesntere qucio io va nlu lje unto es

Ficha de tr trab abaj ajo o

Nombres y apellidos:

Fecha:

1) Determina, utili utilizzando ando la multipli multiplica cació ción n en cruz, cruz, si las siguie siguient ntes es pareja parejass de fracc fraccion iones es son equiv equivale alent ntes es o no. a) 5 y 15 7 21

b) 15 y 21 30 42

5 × 21 = 15 × 7 105 10 5 = 105 105 Rpta.: Son equivalentes.

c) 4 y 20 11 55

15 × 42 = 21 × 30 630 63 0 = 630 630 Rpta.: Son equivalentes.

d) 4 y 5 12 20

4 × 55 = 20 × 11 220 22 0 = 220 220 Rpta.: Son equivalentes.

4 × 20 = 5 × 12 80 = 60 Rpta.: Rpt a.: No No son equivalentes.

2) Completa cada proceso proceso de amplifica amplificación. ción. a) × 3  .    l   a    i   r   o    t    i    d    E   a    l   e

4 7

=

b) 12 21

×

4 5

c)

4 =

16 20

×

1 6

d)

3 =

3 18

×

6 7

e)

2 =

12 14

×

2 3

4 = 8 12

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Números y op opera eracio ciones nes

Unidad

6

 

Nive Niv el 3

Fracciones Fraccion es equivalentes

Ficha de tr trab abaj ajo o

Nombres y apellidos:

1) Lee los probl problema emass y resuelve utilizando utilizando fracciones fracciones

equivalentes. a) La capa capaci cida dad d de un bibe biberrón es de 25 cent centililit itrros. os. Si Lisa Lisa toma oma cada ada día día un bibe biberrón compl ompleeto y las las 3 part es de otro otro,, ¿cuán ¿cuánto toss cent centili ilitr tros os de lech lechee 5 partes toma Lisa al al día?

Fecha:

d) ¿Cuál ¿Cuál es es la fracci fracción ón equiva equivalen lente te a 12 tal que 15 la suma uma de sus términ rminos os sea el mayor número posible de dos cifras? cifras? Simplificando: 12 = 4 15 5 Fracción Fracci ón equivale equivalente nte:: 4n 5n

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ReC laíc íc rció un loem ntare tec m oántjiucnoto tos Fraccioness equivalente Fraccione equivalentess

Números y op opera eracio ciones nes

Unidad

6

Ficha de tr trab abaj ajo o

Nombres y apellidos:

1)   Observa el gráfico y   encierra la fracción que es equi equivvale alente a la frac fracci ción ón que que repre presen senta la part partee sombreada.

Fecha:

5) Lee y responde. ¿Cuánt ¿Cuántas as fracci fracciones ones equivalen equivalente tess a 7 con con denomin denominad ador or entr entree 300 y 900 existe xisten? n? 30 7 7n Fracción: Fracción Fracci ón equivale equivalente nte:: 30 30n Por la con ondi dici ción ón:: 30 300 0 < 30 30n n < 90 900 0  1 0 < n < 3 0  val alor ores espa parra «n «n»: »: 11 11;; 12 12;; .. .... ; 29

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Fracciones Fraccion es equivalentes

Números y op opera eracio ciones nes

Unidad

6

Fic ich ha de ev eval alua uaci ción ón

Nombres y apellidos:

Fecha:

1) Colorea las fracciones fracciones equivalente equivalentess a la fracción fracción indicada. a) 3 7

9 21

12 28

2) Completa los espacios espacios en blanco. blanco. 6 2 a) = 15

15 35

6 7

c)

1 9 = 7

b) 5 6

10 18

30 36

e)

30 3 = 80 8

24 20

40 48

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PRre relp aa criá óndeonntroesc scpoanra junPtIo SA s Fracciones Fraccion es equivalentes

Números y op opera eracio ciones nes

Unidad

6

Nombres y apellidos:

Fecha:

1) Lee el problema y  resuelve. Carol, ol, Carlos rlos,, Mig Miguel, Rosa y José compra praron barras de chocolate del mismo

tamañ tamaño o, per pero de dif diferen erente tess sabor sabores. es. Cada Cada uno uno de ellos ellos divi dividió dió su barr barraa en un núme númerro distin distinto to de part partes es igual iguales, es, como como se mues muestr traa a cont continu inuaci ación: ón: Carol

Carlos Rosa

Miguel José

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Números y op opera eracio ciones nes

Unidad

6

 

Nivel 1 Niv

Comp Co mpar arac ació ión n y ord orden en de fra fracc ccion iones es

Ficha de tr trab abaj ajo o

Nombres y apellidos:

Fecha:

1) Ordena las siguient siguientes es fraccio fracciones nes en forma forma ascenden ascendente. te. diez diez doce doceaavos - cinc cinco o doce doceaavos - ocho ocho doce doceaavos - once once doce doceaavos 5 12

<

8 12

<

10 12

<

11 12

2) Escribe las fracci fracciones ones que represen representan tan los siguient siguientes es gráficos, gráficos, luego  ordénalas de forma forma descenden descendente te..

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Números y op opera eracio ciones nes

Unidad

6

Nombres y apellidos:

 

Nivel 2 Ni

Comp Co mpar arac ació ión n y ord orden en de fra fracc ccion iones es

Ficha de tr trab abaj ajo o Fecha:

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Números y op opera eracio ciones nes

Unidad

6

Nombres y apellidos:

 

Nive Niv el 3

 

Compara Compa raci ción ón y ord orden en de fra fracc ccion iones es

Ficha de tr trab abaj ajo o Fecha:

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Números y op opera eracio ciones nes

Unidad

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Nombres y apellidos:

Círculo mate Círculo matemát mático ico Comp Co mpar arac ació ión n y ord orden en de fra fracc ccion iones es

Ficha de tr trab abaj ajo o Fecha:

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Números y op opera eracio ciones nes

Unidad

6

Nombres y apellidos:

Comp Co mpar arac ació ión n y ord orden en de fra fracc ccion iones es

Fic ich ha de ev eval alua uaci ción ón Fecha:

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Números y op opera eracio ciones nes

Unidad

Preparándono Preparánd onoss para PIS PISA A Comp Co mpar arac ació ión n y ord orden en de fra fracc ccion iones es

6

Nombres y apellidos:

Fecha:

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Números y op opera eracio ciones nes

Unidad

6

Nivel 2 Ni

Divisió Divi sión n de fra fracc ccion iones es

Ficha de tr trab abaj ajo o

Nombres y apellidos:

Fecha:

1) Completa cada recua recuadr dro o en blanco blanco y   halla el result resultado ado de cada división división en forma forma simplifi simplificad cada. a. a) 3 ÷ 2 = 5 3

3 5

b) 1 ÷ 7 7 5

=

c) 3 ÷ 5 = 2 12

×

3 2

=

1 7

×

5 7

5 = 49

•

2 4 ÷ • 9 11

•

77 45

3 2

12 × = 18 5 5

•

7 12 ÷ • 13 15

•

15 8

•

7 ÷ 5 • 9 11

•

35 52

4 × d) 4 ÷ 4 = 11 3 11  .    l   a    i   r   o    t    i    d    E   a    l   e    d   o   s   e   r   p   x   e   o   s    i   m   r   e   p   n    i   s   o    t   n   e    i   m    i    d   e   c   o   r   p   o   o    i    d   e   m   r   e    i   u   q    l   a   u   c   r   o   p   o   r    b    i    l   e    t   s   e   e    d    l   a    i   c   r   a   p   o    l   a

3 4

=

9 10

3 11

e) 2 ÷ 1 3 8

=

2 3

×

8 1

=

16 3

f) 5 ÷ 5 3 3

=

5 3

×

3 5

=

1

g) 3 ÷ 1 4 8

=

3 4

×

8 1

=

6

h) 6 ÷ 3 7 5

=

6 7

×

5 3

=

10 7

2) Resuelve cada cada oper operaci ación ón y encierra con con un cír círculo culo las respuest respuestas as halladas. d) 3 ÷ 5 = 21 4 ÷ 2 = 10 a) 9 5 9 10 7 50 6 ÷ 4 = ÷ 1 = 3 1 15 e) b) 18 3 20 2 2 c)

3) Relaciona median mediante te flecha flechass cada cada oper operaci ación ón con con su resultado. 11 5 ÷ 3 • • • 8 9 18

5 ÷ 8 = 45 14 9 112

f) 7 ÷ 6 = 49 12 7 72

4) Escribe V si si es verd verdade adero ro o F si si es falso falso según según corresponda. 1 ÷ 1 = 1 • ( F ) 3 4 12 1 ÷ 1 = 1 • ( F ) 5 2 20 2 3 4 3 1 7 2 5 6

÷ 4 = 5

( V ) 5 6 ÷ 6 = 10 • ( V ) 5 9 ÷ 14 = 7 • ( F ) 2 4 ÷ 8 = 3 • ( V ) 3 20 • ÷ 3 =4 ( V ) 7 1 4 =3 ( V ) 2 ÷ 6 • 9 81 5) Resuelve el problema y  responde. Matías tiene a con 1 L de agua agua.. Si deci decide de repar eparti tirl rlo o una 2 botell equit equ itat ativ ivam amen ente te entr entree sus 3 amigo amigos, s, ¿cuán ¿cuánto to le •

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Números y op opera eracio ciones nes

6

Unidad

Nive Niv el 3

Divisió Divi sión n de fra fracc ccion iones es

Ficha de tr trab abaj ajo o

Nombres y apellidos:

Fecha:

1) Completa el cuadr cuadro o de doble doble entr entrada ada.. ÷

1 2

1 2

1

4 5 23 7

8 5 46 7

3 4 2 3

2 2 1 2

3 2 1 3

16 15 92 21

4 5 23 7

8 15 46 21

2) Completa escribiendo los signos > o < según corresponda. corresponda. •

1 ÷ 2 2 3

<

5 6

• 2 1

<

2 ÷ 1 3 4

•

1 ÷ 1 9 8

>

1 7

• 3 1

>

3 ÷ 5 5 6

•

2 ÷ 2 9 5

>

5 12

• 11 1

>

1 ÷ 2 3 9

4 3

6

3) Resuelve las siguientes siguientes divisiones: divisiones: a) 18 ÷ 6 21 7

=

18 × 7 = 1 21 6

d) 13 ÷ 17 12 19

=

13 × 19 = 247 12 17 204

b) 450 ÷ 90 10 120

=

450 × 120 = 54 000 = 60 10 90 900

e) 2 3 ÷ 1 3 5 5

=

13 × 5 = 13 5 8 8

1000 × 10 000 = 1000 100 100

f) 12 7 ÷ 3 2 8 5

=

103 × 5 = 515 8 17 136

c) 1000 ÷ 100 = 100 10 000

4) Resuelve el problema y  responde. Marcela compró 9 1 m de lana lana para para cort cortarl arlas as poste posteri rior orme ment ntee en tiras tiras 3 ñas de 1 de lar ¿Cuán ¿Cuánta ta tir obt o?

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Números y op opera eracio ciones nes

6

Unidad

Círculo mate Círculo matemát mático ico División Divi sión de fra fracc ccion iones es

Ficha de tr trab abaj ajo o

Nombres y apellidos:

Fecha:

1) Agrupa las fracci fracciones ones 2 ; 1 ; 2 ; 5 ; 4 y 3 por por par parejas ejas par para que que al divi dividi dirl rlas as se obt obteng enga como como resul esulta tado do 5 1 11 9 7 10 7 10 27 ; y . 4 22 50 7 = 1 ÷ 4 4 1 7

10 = 2 ÷ 2 22 11 5

27 = 3 ÷ 5 50 10 9

2) Resuelve los siguientes siguientes problemas: problemas:

Si se reparten 14 kg de hari harina na en bols bolsit itas as en las las que que cabe cabe 1 kg de harin harina, a, ¿cuán ¿cuánttas bolsit bolsitas as se han llenado? 15 15

a) Operación:  .    l   a    i   r   o    t    i    d    E   a    l   e    d   o   s   e   r   p   x   e   o   s    i   m   r   e   p   n    i   s   o    t   n   e    i   m    i    d   e   c   o   r   p   o   o    i    d   e   m   r   e    i   u   q    l   a   u   c   r   o   p   o   r    b    i    l   e    t   s   e   e    d    l   a    i   c   r   a   p   o    l   a

14 ÷ 1 = 14 × 15 = 14 15 15 15 1 Rpta.: Rpt a.: Se han llenado llenado 14 bols bolsita itas. s. b) El cole colegi gio o ha org organiz anizad ado o una una camp campañ añaa de higi higien enee dent dental al.. Si en la clas clasee de Dani Daniel elaa han han repar eparti tido do una una bote botellllaa de 3 L de flúo flúorr en vasit asitos os de 1 L, ¿cuánt ¿cuántos os vasit vasitos os se han llenado? llenado? 4 32 Operación: 3 ÷ 1 = 3 × 32 = 24 4 32 4 1 Rpta.: Rpt a.: Se han llenado llenado 24 va vasit sitos. os. c) Si Isab Isabel el ha repar eparti tido do una una bote botellllaa de lech lechee de 3 L en pomos de 1 L, ¿hab ¿habrrá llen llenad ado o un núme númerro exact acto de 4 10 pomos? Operación: 3 ÷ 1 = 3 × 10 = 30 = 15 El re result sultado ado no es un núme número ro ex exact acto. o. 4 10 10 4 1 4 2 Rpta Rp ta.: .: No ha llenado llenado un númer número o exac acto to de pom pomos. os. 3) Halla el result resultado ado de las sigui siguient entes es opera operacione ciones: s: 1 b) 3 ÷ 2 1 5

a) 3 ÷ 1 ÷ 5 ÷ 9 4 9 6 5 3

1

5

9

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Números y op opera eracio ciones nes

Unidad

6

Divisió Divi sión n de fra fracc ccion iones es

Fic ich ha de ev eval alua uaci ción ón

Nombres y apellidos:

Fecha:

1) Completa el sigu siguie ient ntee cuad cuadrro de dobl doblee entr entrad ada, a, lueg luego o  encierra con con un cír círculo culo la alte altern rnaativ tiva que que pres presen entte el mayo mayorr result resultado ado obtenid obtenido. o. ÷

3 2

1 2

5 3

1 2

1 3

1

3 10

3 5

2 5

6 5

9 25

a) 2 5

c) 3 10

b) 9 25

d) 6 5

2) Completa los recua recuadr dros os en blanco blanco para para que cada oper operación sea corre correct cta. a. •

3 5 9 ÷ = 2 3 10

•

1 5 = 3 ÷ 3 35 7

•

1 ÷ 1 = 5 7 7 5

•

3 15 3 ÷ = 5 24 8

•

3 ÷ 4 = 21 2 8 7

•

1 ÷ 9 = 11 3 11 27

3) Halla el result resultado ado de las siguien siguiente tess division divisiones: es: • 1 2 ÷ 1 3

7

•

5

3 ÷ 2 4 7 5

• 1 3 ÷ 1 5

4

6

=

45 56

=

15 98

• 2

=

21 22

• 2 1 ÷ 2 2

•

1 11 ÷ 5 14 2

1 ÷ 2 2 = 7

3

4) Halla la suma suma de términos términos del result resultado ado de: 1 ÷ 1 ÷ 1 5 3 4

=

3

5

=

5 7

• 2 2 ÷ 6

45 56

•

35 36

=

4 9

1 = 3 ÷ 2 8 4

1 6

3

• 3 1 ÷

5

8 = 15

5) Si A = 5 y B = 6, halla el valor alor de: de: A÷ B B A

6

 .    l   a    i   r   o    t    i    d    E   a    l   e    d   o   s   e   r   p   x   e   o   s    i   m   r   e   p   n    i   s   o    t   n   e    i   m    i    d   e   c   o   r   p   o   o    i    d   e   m   r   e    i   u   q    l   a   u   c   r   o   p   o   r    b    i    l   e    t   s   e   e    d    l   a    i   c   r   a   p   o    l   a

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Números y op opera eracio ciones nes

Unidad

Preparándon Preparán donos os para PIS PISA A División Divis ión de fra fracc ccion iones es

6

Nombres y apellidos:

 .    l   a    i   r   o    t    i    d    E   a    l   e    d   o   s   e   r   p   x   e   o   s    i   m   r   e   p   n    i   s   o    t   n   e    i   m    i    d   e   c   o   r   p   o   o    i    d   e   m   r   e    i   u   q    l   a   u   c   r   o   p   o   r    b    i    l   e    t   s   e   e    d    l   a    i   c   r   a   p   o    l   a

Fecha:

1) Lee el proble problema ma y resuelve. Don Don Luch Lucho o aca acaba ba de de lleg llegar ar de su via viaje je por por el el int interio eriorr del del paí paíss y ha tr traído aído alg algun unos os prod produc ucttos que que piensa repartir entre sus familiares. Estos productos son arroz ( 8 1 kg), azúcar (5 1 kg), sal 3 4 (2 1 kg), kg), harin harina (8 1 kg), fideos (6 1 kg), entre entre otros. otros. 2 2 4 a) Si los los 2 hijo hijoss de don don Luc Lucho se reparten el arr arroz d) Si los 3 nietos de don Lucho se reparten los en part partes es iguale iguales, s, ¿cuán ¿cuánto to le toca toca a cada cada uno? uno? fide fideos os en par partes igua iguale les, s, ¿cuá ¿cuán nto le toca oca a cada ada uno? Operación: Operación: 8 1 ÷ 2 = 25 ÷ 2 = 25 × 1 3 3 3 2 6 1 ÷ 3 = 25 ÷ 3 = 25 × 1 4 4 4 3 = 25 = 4 1 kg 6 6 = 25 = 2 1 kg 1 12 12 Rpta.: A cada uno le toca 4 kg. 6 Rpta.: Rpt a.: A cad cadaa uno le le toca toca 2 1 kg. 12 b) Si 3 sobr sobrin inos os se repar eparte ten n el azúc azúcar ar en part partes es iguales, iguales, ¿cuánto ¿cuánto le corre correspond spondee a cada cada uno? e) Si se quie quierre repar eparti tirr 1 kg de sal por persona, 2 Operación: ¿para cuántas personas personas alcanzaría? 1 21 21 1 5 ÷ 3 = ÷3= × 4 4 4 3 Operación: = 21 = 7 = 1 3 kg 5 × 2 12 4 4 2 1 ÷ 1 = 5 ÷ 1 = 2 2 2 2 2 1 Rpta.: A cada uno le corresponde 1 3 kg. 4 = 10 = 5 2 c) Si 4 hermanos de don Lucho se reparten la hari harina na en part partes es igua iguale les, s, ¿cuá ¿cuánt nto o le toca oca a cada cada uno? Operación: 8 1 ÷ 4 = 17 ÷ 4 = 17 × 1 2 2 2 4

Rpta.: Alcanz Alcanzaría aría para 5 per personas. sonas. f) Sise Si se quiererepar quiererepartir tir 1 kg deazú de azúca carr porpe por perrsona, sona, 4 ¿para cuántas personas personas alcanzaría? Operación:

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Números y op opera eracio ciones nes

Unidad

6

 

Nivel 1 Niv

Operacioness comb Operacione combinadas inadas

Ficha de tr trab abaj ajo o

Nombres y apellidos:

Fecha:

1) Completa los recuadr recuadros os efectuando efectuando las operaciones operaciones de manera manera secuencial. ÷ 1 × 2  – 1 + 3 2 3 3 2 1 a) 1 4 2 2  – 1 × + 4 ÷3 5 5 6 3 3 7 b) 2 6 2 6 × 7  – 2 ÷ + 1 1 4 11 3 11 12 3 c) 7 28 12 4

1 3 3 7 5 3

5 6 1 2 9 20

2) Relaciona mediant mediantee flechas flechas cada opera operación ción combinad combinadaa con con su desarr desarrollo ollo,, y este este con su result resultado. ado. 11 24

•

5 × 2 + 1 2 3 4

•

•

5  – 2 • 2 12

•

•

5  – 2 × 1 2 3 4

•

•

11 × 1 • 6 4

• 23

•

5 × 2 + 1 2 3 4

•

•

5 × 11 • 2 12

•

7 3

5  – 2 × 1 • 2 3 4

•

10 + 1 • 6 4

•

55 24

•

3) Completa los recuadros y halla el resul resulta tado do de cada cada oper operaci ación ón combi combina nada da.. 1 1  – 1 × 1 ÷ a) b) 5 ÷ 2  – 1 × 18 c) 5 4 4 6 3 3 3 9

12

5 × 1 ÷ 1  – 1 + 3 6 7 3 7 8

 .    l   a    i   r   o    t    i    d    E   a    l   e    d   o   s   e   r   p   x   e   o   s    i   m   r   e   p   n    i   s   o    t   n   e    i   m    i    d   e   c   o   r   p   o   o    i    d

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Números y op opera eracio ciones nes

Unidad

6

Nivel 2 Ni

Operaciones Operacio nes comb combinadas inadas

Ficha de tr trab abaj ajo o

Nombres y apellidos:

Fecha:

1) Resuelve las siguientes siguientes operaciones operaciones combinadas: combinadas: a) 1 2 + 1 ÷ 5  – 3 3 6 6 8 5  – 3 1 2 + 1 ÷ 3

6

6

8

5 + 1 ÷ 5  – 3 = 11 ÷ 11 = 4 3 6 6 8 6 24 24

9 ÷ 10 9 × 10

5 + 1 2 8 3 8 + 5 = 36 + 5 = 233 5 3 25 3 75

d) 5 1 ÷ 8 – 2 × 3 4 3 4

b) 4 5 ÷ 13 – 7 × 9 12 8 8 13 4 5 ÷ 13 – 7 × 9  .    l   a    i   r   o    t    i    d    E   a    l   e    d   o   s   e   r   p   x   e   o   s    i   m   r   e   p   n    i   s   o    t   n   e    i   m    i    d   e   c   o   r   p   o   o    i    d

c) 9 ÷ 5 + 1 2 10 8 3

12 8 8 13 53 × 8  – 7 × 9 = 106  – 63 = 659 12 13 8 13 39 104 312

2 × 3 3 4 4 21 × 1  – 1 = 21 – 1 = 5 4 8 2 32 2 32

5 1 ÷ 8 –

2) Calcula el área área sombr sombrea eada da de cada cada figur figura, a, toman tomando do en cuent cuentaa que las medida medidass está están n en cent centím ímet etrros. a) b) 2 3 5 5 2 2 1 4 3 1 6 A = 1 + 1 × 2  – 2 6 4 3 5

1 4

1 6 A = 1 + 1 × 2 1  – 3 6 3 4 5

1 3

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Números y op opera eracio ciones nes

Unidad

6

Nive Niv el 3

Operacioness comb Operacione combinadas inadas

Ficha de tr trab abaj ajo o

Nombres y apellidos:

Fecha:

1) Lee y resuelve los siguientes siguientes problemas: problemas:

a) Llenando con 18 L de gasolina el tanque de un carr arro, el indi indiccador ador de niv nivel de gasol asolin inaa de este pasa pasa de 1 a 5 . ¿Cuá ¿Cuáll es la capac apacid idad ad total otal del del 4 8 tanque? Fracción Fracci ón que repre represen senta ta los 18 L: 58 – 14 Luego: 85  – 41 × (ca (capacid pacidad ad tot total) al) = 18 Así,, capaci Así capacidad dad tot total al = 18 ÷ 5  – 1 8 4 Resol esolvien viendo: do: 18 ÷ 5  – 1 = 18 ÷ 3 = 48 L 8 4 8 Rptta. Rp a.:: La cap apac acid idad ad to tottal de dell ta tanq nque ue es de 48 L.

(

)

(

( )

)

b) Luis gasta gasta 1 desu de su suel sueldo do enr en ropa; opa; 1 , enco en comi mida da;; 5 4 1 , en el alqu alquililer er;; y 1 , en otr otros gast astos. os. Si al fina finall 3 6 le qued quedaa S/.1 S/.120 20,, ¿cuá ¿cuáll es el suel sueldo do de Luis Luis?? Ropa: 1 Comida: 1 Alquiler: 1 Otros: 1 5 4 3 6 Qued Qu eda: a: 1 – 1 + 1 + 1 + 1 = 1 – 19 = 1 20 20 5 4 3 6 Así, 1 × (sueldo) = 120 20 1

(

)

d) Una Una pisc piscin inaa vacía acía se llen llenaa con el agua agua deun gri grifo en 2 h y, una vez llena, puede vaciarse en 3 h por un desagüe ubicado en el fondo. Si con la pisc piscin inaa vacía acía y el desa desagü güee abie abiert rto o, algu alguie ien n abr abre el grif grifo o, ¿al ¿al cabo abo de cuán cuántto tiem tiempo po empe empezzará ará a desb desbor orda darrse el agua agua de la pisc piscin ina? a? El gri griffo lle llena na 1 de la piscin piscinaa en 1 h y el 2 desagüe desa güe vacía 1 de la pisci piscina na en 1 h. 3 Así, con el desagüe desagüe y grifo grifo abiertos, en 1 h se lle llena na 1  – 1 = 1 de la piscin piscina. a. 2 3 6 Luego, para llenarla Luego, llenarla por completo completo tendr tendrán án que pas pasar ar 6 h. Rpta.: Rpt a.: Al Al cabo de 6 h.

e) Juan Juan compr ompraa una una sand sandíía. Si el prim primeer día día come ome 1 de la sand sandía ía;; el segu segund ndo o día, día, 1 de lo que que 5 2 quedaba, y el te tercer día, 2 del nu nuevo re resto, 3

 .    l   a    i   r   o    t    i    d    E   a    l   e    d   o   s   e   r   p   x   e   o   s    i   m   r   e   p   n    i   s   o    t   n   e    i   m    i    d   e   c   o   r   p   o   o    i    d

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Números y op opera eracio ciones nes

Unidad

6

Círculo mate Círculo matemát mático ico Operaciones Operacio nes combi combinadas nadas

Ficha de tr trab abaj ajo o

Nombres y apellidos:

1) Lee los problemas y resuelve. a) Se tiene una botella botella cuya cuya capacidad es es 3 L y 4 7 contiene aceite en los del total. Si Amanda 15 gast asta 150 150 cm3 del contenido cuando prepara picar picaron ones es,, ¿cuán ¿cuánto to queda quedarrá en en la bot botell ella? a? (Considera 1 L = 1000 cm3) Cantida Can tidad d de acei aceite: te: 7 × 3 = 7 L 15 4 20 Como Co mo 1 L = 10 1000 00 cm3, en ento tonce nces: s:  .    l   a    i   r   o    t    i    d    E   a    l   e    d   o   s   e   r   p   x   e   o   s    i   m   r   e   p   n    i   s   o    t   n   e    i   m    i    d   e   c   o   r   p   o   o    i    d

7 L = 7 × 10 1000 00 = 350 350 cm3 20 20 Así, lo que Así, queque queda dade de ac acei eite tees es:: 350 35 0 – 150=200cm3 Rpta Rp ta.: .: Quedan Quedan 200 cm3. b) En una una mesa mesa hay hay cier ciertta cant cantid idad ad de cuad cuader erno nos, s, fólder ólderes es y borr borrador adores. es. Del total total de artícu artículos los que hay hay en la mesa mesa,, los los 3 son cuader cuadernos nos y los 7 del 4 8 res resto son fólder ólderes. es. Si la cant cantida idad d de borr borrador adores es eq equivalente a 1 de una do docena, ¿c ¿cuántos 4

Fecha:

c) Entre tre las ciud ciudad adees de de Lima Lima e Ica ha hay una una dis distanci anciaa de 720 720 km. Si la ciuda iudad d de Cañet ñete se encuentr encuentraa a 3 de dich dichaa dis distanci anciaa part partie iend ndo o de 4 Lima Lima,, y la ciud ciudad ad de Chin Chinch chaa se encu encuen entr traa a 11 20 de la dis distanc tancia ia entr entree Cañe Cañette e Ica Ica par parti tien endo do de Cañe Cañette, ¿a qué qué dis distanci anciaa se encu encuen entr tran an las las ciudad ciudades es de Chinch Chinchaa e Ica? Ica? Lima

Cañete 3 × 720 4

Chincha 1 × 720 4

Ica

11 × 1 × 720 9 × 1 × 720 20 4 20 4 La distan distancia cia de Chin Chincha cha a Ica Ica es: 9 × 1 × 72 720 0 = 81 81 km 20 4 Rpta.: Rpt a.: Se encuent encuentrran 81 km. 2) Si a y b son dos núme númerros natu naturrales ales tales tales que b  – a = 4 – 1 y a + b = 25; ad además a b 4 10 1 15 1

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Números y op opera eracio ciones nes

Unidad

6

Operacioness comb Operacione combinadas inadas

Fic ich ha de ev eval alua uaci ción ón

Nombres y apellidos:

Fecha:

1) Calcula el área área de la regi región ón somb sombrreada eada,, toman omando do en cuenta cuenta que que ttodas odas las las medidas medidas están están en metr metros. os. a) 6 7 1 3

d) Si Si un homb hombrre vende ende 2 de una una finc finca, a, y lueg luego o 1 5 2 de lo vendi endido do ante anteri rior orme ment nte, e, ¿qué ¿qué part partee de la

A= 3 + 6 × 1 = 3 + 2 8 7 3 8 7 A = 37 m2 56 2 m2 5

finca le queda? 3

2 2 3 5

A = 2 + 2 3 × 3 = 2 + 13 × 3 5 5 2 5 5 2 A = 2 + 39 = 43 m2 5 10 10 2) Lee los problemas y resuelve.

Opera Ope ración: ción: 324 – 7 × 32 324 4 = 324 324 – 12 126 6 = 198 198 18 Rpta.: Rpt a.: Ha Hayy 198 hombr hombres. es.

3 m2 8

b)

c) En un coleg colegio io hay hay 324es 324 estud tudian iante tes.Si s.Si lasmujere lasmujeress son son los los 7 del total, ¿cuántos ¿cuántos hombres hay? 18

Operac Ope ración: ión: 1 – 2  – 1 × 2 = 5  – 2  – 1 = 2 5 2 5 5 5 5 5 Rpta.: Rpt a.: Le queda 2 de la finc finca. a. 5 3) Resuelve los siguientes siguientes ejercicios: ejercicios: a) Reduce la expresión:

(12 × 43 × 182 × 19 )÷ (63 × 14 × 15 × 152 ) (12 × 43 × 182 × 19 )÷ (63 × 14 × 15 × 152 ) 2

3

8

 .    l   a    i   r   o    t    i    d    E   a    l   e    d   o   s   e   r   p   x   e   o   s    i   m   r   e   p   n    i   s   o    t   n   e    i   m    i    d   e   c   o   r   p   o   o    i    d

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Números y op opera eracio ciones nes

Unidad

Preparándon Preparán donos os para PIS PISA A Operaciones Operacio nes comb combinadas inadas

6

Nombres y apellidos:

Fecha:

1) Observa el mapa mapa con los los dat datos de algu alguna nass mon montañas añas del del mund mundo o y los los recor ecorri rido doss de cada ada esc escalad alador or. Lueg Luego o, realiza los cálculo cálculoss necesario necesarioss y completa.

 .    l   a    i   r   o    t    i    d    E   a    l   e    d

•

Miguel Miguel primer primero o subió subió 2 de la monta montaña ña más más baja, baja, y luego luego 1 de la misma. misma.

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Números y op opera eracio ciones nes

6

Unidad

Nivel 1 Niv

Potenciac Pote nciación ión y radic radicació ación n de frac fraccion ciones es

Ficha de tr trab abaj ajo o

Nombres y apellidos:

1) Efectúa las siguient siguientes es potencia potenciass de fraccio fracciones: nes: 2 3 a) 5 2 5 b)

3 5

1 2

3 = 23 = 2 × 2 × 2 = 8 5 5 × 5 × 5 125

c) 8 27 8 = 2 × 2 × 2 = 23 = 2 27 3 × 3 × 3 33 3

25 = 5 × 5 = 52 = 5 49 7 × 7 72 7 2

2 = 32 = 3 × 3 = 9 5 5 × 5 25

e)

2

1 64 1 = 1 × 1 × 1 × 1 × 1 × 1 = 16 = 1 64 2 × 2 × 2 × 2 × 2 × 2 26 2

5

1

3

d) 25 49

2

3 5 c)

3

Fecha:

5

5 = 15 = 1 × 1 × 1 × 1 × 1 = 1

6

3) Halla las raíces raíces de las siguientes siguientes fracciones: fracciones:

 .    l   a    i   r   o    t    i    d    E   a    l   e    d

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Números y op opera eracio ciones nes

6

Unidad

Nivel 2 Ni

Potencia Pote nciación ción y radic radicació ación n de frac fraccion ciones es

Ficha de tr trab abaj ajo o

Nombres y apellidos:

Fecha:

1) Relaciona cada potencia potencia con su result resultado. ado.

 .    l   a    i   r   o    t    i    d    E   a    l   e    d

•

1 5

2

•

2 3

3

•

4 7

0

•

3 8

2

b)

•

•

• 1

•

•

8 27

•

•

1 25

2) Escribe V si es verdadero o F si es falso convenientemente. •

64 = 8 81 9

1 6 cm 13

9 64

•

( V )

2 2 2 A = 1 6 = 19 = 192 = 361 = 2 23 cm2 13 13 13 169 169 Rpta.: 2 23 cm2 169

4) Resuelve las siguientes siguientes potencias: potencias: a) 1 2 5

2

1 2

5

2

2 2 = 7 = 72 = 49 = 1 24 5 5 25 25

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Números y op opera eracio ciones nes

Unidad

6

Nive Niv el 3

Potenciac Pote nciación ión y radic radicació ación n de frac fraccion ciones es

Ficha de tr trab abaj ajo o

Nombres y apellidos:

Fecha:

1) Halla las siguientes siguientes raíces: raíces:

a)

27 125

a)

3

3

b)

3) Calcula el volumen volumen de los siguie siguient ntes es cubos: cubos:

27 = 27 = 125 3 125

3

3

3×3×3 = 3 5×5×5

3

3

3

33 = 3 53 5

Se sa sabe be que que:: V = l3. Re Reemplaz emplazando: ando: 3 3 V = 3 = 33 = 27 cm3 7 343 7 Rpta.: 27 cm3 343

64 343

3

3

64 = 343

3

64 = 3 343

4×4×4 = 3 7×7×7

2) Resuelve los siguient ejercicios

3

43 = 4 73 7

3 cm 7

b) 3 1 cm 5

 .    l   a    i   r   o    t    i    d    E   a    l   e    d

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Números y op opera eracio ciones nes

Unidad

6

Ficha de tr trab abaj ajo o

Nombres y apellidos:

Fecha:

1) Calcula el valor alor de a + b + c, c, en las las sig sigui uien enttes expresiones: c a) a = 125 b 8 3 c Se tiene: a = 125 = 5 2 b 8 Igualando térm términos: inos: a=5 b=2 c=3 Suma Su mand ndo o: a + b + c = 5 + 2 + 3 = 10 Rpta.: 10

 .    l   a    i   r   o    t    i    d    E   a    l   e    d

c b) 1 a = 343 b 216 c 3 Se ti tieene ne:: 1 a = 343 = 7 = 1 1 b 216 6 6 Igualando térm términos: inos:

Círculo mate Círculo matemát mático ico Potencia Pote nciación ción y radic radicació ación n de frac fraccion ciones es

3

b) El cubo de una fracción impropia cuyos términos son dos números cuya suma es 29 y su dif diferen erenci ciaa es 1. Analizando los datos: Números Analizando Números cuyya sum cu sumaa es es 29 y su differen di enci ciaa es 1: 15 y 14 Fracción impropia impropia:: 15 14 3 Operando: 15 = 3375 14 2744 Rpta.: 3375 2744 3) Lee el prob proble lema ma y  resuelve. Un terr erreno de form orma 9 2 cuadrada tiene 232 m de área área.. ¿Cuá ¿Cuán nto mide mide 16 el lado del terre terreno? no?

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Números y op opera eracio ciones nes

6

Unidad

Potenciac Pote nciación ión y radic radicació ación n de frac fraccion ciones es

Fic ich ha de ev eval alua uaci ción ón

Nombres y apellidos:

1) Resuelve las siguient siguientes es potencia potenciass de fracci fracciones ones:: 2 4 a) 4 2 4 b) 6 7

3

4

4 = 24 = 16 = 1 4 256 16

Fecha:

d)

1 9  – 64 2

3

9  – 1 3 = 64 2

9  – 13 = 3  – 1 = 2 = 1 3 8 8 8 4 64 2

3) Calcula el área área del siguien siguiente te cuadrado: cuadrado:

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Números y op opera eracio ciones nes

Unidad

Preparándon Preparán donos os para PIS PISA A Potencia Pote nciación ción y radic radicació ación n de frac fraccion ciones es

6

Nombres y apellidos:

Fecha:

1) Lee el proble problema ma y responde las preguntas. El prof profes esor or de Cie Ciencia nciass habl hablaa sobr sobree las las bact bacter eria ias. s. Dice ice: «Las «Las bact bacteerias rias son micr microo oorrganis anismo moss que que no pose poseeen un núcl núcleo eo defi defini nido do y pued pueden en pres presen enttar dis distint tintas as forma ormass como como fila filame ment ntos os,, esf esferas eras,, héli hélice ces, s, etc. Sin Sin emba embarrgo, go, se reproduce ducen n de forma rápi ápida y en cant antidade dadess asombr ombro osas sas». El prof profeesor menciona que que la velocidad de creci crecimie mient nto o de una poblac población ión espec específi ífica ca de bacte bacteria riass está está dete determi rminad nadaa por una una regla regla,, y se puede puede sabe saberr cuánt cuántas as bacte bacteri rias as aprox aproxima imadam damen ente te habr habrá luego luego de un tiempo tiempo dete determi rminad nado. o. Dicha Dicha regla regla es: es: N = 100 × 16

t

donde donde «t» es el tiempo tiempo en horas horas..