toán lớp 5 q2

hai
1 2 e m . 56
ae u c h o h QC
T6 m¢t c6 1
to hai n h�n dlfQ'C n h i e u hon 0 t6 m9t li:f 1 4 v i e n . Hoi moi to n h � n duqc bao n h i e u
1

vien kE;o?

5 -

I.

A . N HAN

-

1.

�

SO TH P PHAN

so

vO'i

n h ien

1 : 1 ,2

- Lam tlnh n h lf I a n h a n cac so t V n h i en .

- f) � t dau p h ay d tkh cu ng v! tri v6'i dau
phay a so th�p phan.

Bai 1 60.. M <) t khoi

h 9c si n h t h a m gia dong dien. N eu xe p 1 2 e m m ¢ t ha n g thl t h ua
Neu xep 1 4 em m¢t ha n g thl ding th U'a 6 em n h un g ft· cfi 2 h a n g . Hoi c6
bao n h i e u hqc si n h tham g ia don g dien?

6 em.

2. Nhan so th�p phan vai 1 0; 1 00; 1 000;
N ha n so t h � p p h a n voi 1 0; 1 00; 1 000;
chG' so ttio'ng ung .

Vi d ':J 2: 3,1 871

X

4

•.•

. ..

tuc

Ia

d ai dau p hay sang phai 1 ; 2; 3; . . .

1 00 = 3 1 8, 7 1

N han so th� p phan v6i so th� p ph an

- N han n h ll n h a n cac so

----- ------

1 ,2

4=?

4,8 _

3.

---···

X

X

1

Vi d �;�

tl! nhit�n.

- sa hang th� p p h a n Ci tkh bang ton g so
hang th� p p h a n d cac thua so.

3: 1 ,24
X

X

3,6 = ?

1 ,24

3,6

+ 744

3 72

4,464
4.

N ha n so th�p phan v6'i 0,1 ; 0,0 1 ; o,oo 1 ; .. ..
N ha n so thc}p p h a n voi 0 , 1 ; 0,0 1 ; 0,00 1 ;

chu so t uong ling.
Vi d l.} 4: 5 62,2

s . Tinh

X

- Tfnh chat g i a o hoan: a
X

5

=

5

X

- Tfnh chat ket hqp: (a
Vi d �;�

6: (0,8

X

75)

x

X

x

b=b xa

2,3

b)

1 25

=

x
.=

1 1 ,5

c=a

7, 5

X

x

(b

(0,8

x

X

c)

125) = 7 15

- Tfn h chat phan p h oi cua phep n han a6i voi

R i s e a bove o n es elf

a n d g ras p the w o r l d

7:

tuc Ia doi d au ph a y sa n g trai 1 ; 2; 3; . . .

0,1 = 5 6,22

chat

Vi d� 5: 2,3

...

2,5 X 613 + 2,5 X 3,7 = 215

X

X

1 00 = 750

p h e p cc)n g : (a + b)

(6,3 + 3,7) = 2,5 X 1 0 = 25

X c

=a

X

c +b

X c

Arch i m ed e s School
Asc h oo l .e d u .vn


ARCHIMEDES SCHOOL
B.

Bai 1 56.

(HIA SO TH�P PHAN

1 . C hia

so th� p phan cho so ty' n hh�n

.- Tn..toc .het c h ia ph�n ng uyen ch o so do. ­
-: Viet dau p hay vao ben p h a i t h u'on g

s,28 : 4 = !
5J28 �
1 2 f 1',3 2 .

- Tiep tttc chia . ph a n th�p phan cho
so d6.
2.

- Viet t h e m mqt ch u s o 0 vao b e n p h a i so
du va ti �l? tvc chia.

Chia so t l! n h ien cho so th�p ph an

- f)em chu so hang t h � p phan cua so c h ia
roi viet vao ben phai so b! chia cung m ¢t
c h u so o.

- 86

hai

4.
�

dau p hay 0
so ttj n h it�n.

so

Vf d y 2:

Bern xem

co

baa n h ieu cha

so (1 ph�n

th� p p ha n c u a s6 c h i a thl c huyen dau
phay (j so bi chia sang ben p h a i bay

nhiE�u ch u so.

- Bo

dau p h ay (J

sO ch ia

roi thlfc hi � n

p h e p chi a n h u chia cho so tV n hien.
5. Chia
. . .

n h6m b � n ru n h a u di hai qua hong. Neu moi b�h 5 q ua thl thua 11 q ual
neu moi b�n 6 qua thl m¢t b9 n khong ha i duc;;c qua nao. Hoi n h6m c6 bao n h i e u b �Hi
Va hai OU(JC bao nhieu q u a hong?

=

0

VI d fJ 3: 38: 9,5 = ?
380

�
1

00 4

Vf d y 4:

Bfd 1 58. M¢t to xe c6 m¢t so xe ta i, neu moi xe cho 1 5 bao 9 9 0 thl con th ieu 1 xe,
neu moi xe chO' 10 bao 990 th1 f9i th ua 1 xe. Hoi to co may xe ta i va dt,t d�nh ch6' bao

19,72 : 5�8 :::: ?
1 972 �
2320 1 3,4
0

nh ieu bao g?o?

so th�p phan cho 1 0; 1 00; 1 000; . . ..

so th � p p h an cho 1 O; 1
chu so.

Ch i a

Bai i 57. M¢t

19 :4 ?
19 �
30 1 4175
20

chia roi chia n h li c h ia

Ch i a so th�p ph a n cho so th�p phan

"Vi dl:I S�

41 ,84 : 1 0 = 4, 1 84

00; 1 ooo;

. .

15

0

- Neu p hep c h ia van co n dv thl viet them
m¢t ch a so 0 vao ben phai so du' va tiep
t y c chi a.
3.

Q uyen 2.1

08

Chi a so tl! nhh�n cho so tl! nhien (thu'dng Ia so th�p phan)

- Viet dau phay vao ben phai so thuong .

-

M9t ddn Vi b¢ d9i can sang $6ng. N�u moi thuyen ch d
n g V6'i thl thlta
40 nguoi chua duqc sang song. Neu moi thuyen ch6 20 n g uoi thl con t h ua 1 th uyen .
Hoi c6 bao nh!eu thuyef} va dan vi b9 d9i d6 co bao n h i e u n g uai?

vr d 'J 1:

tr�oc khi lay chu so aau tiE�n (J pha n th�p
p h a n ct}a s6 b j chia�

Toah s

. ta chi vi�c ch uyen dau phay san g tn§i

Rise a bove oneself
and g rasp the world

1 ; 2; 3;

A rch i m edes School

Aschoo l . ed u .v n

· .


pha i

m nhau
d a dj n h S a u kh i th ljc h i � n du ng s 6 n g a y da dj n h t hl n h o m 1
moi
1 40
II
t h i e u 1 00
v1
n g ay chi d?t dVQ'C 1 45 c 3 i . Hoi'
ngay va so ao aa d!n h theo ke h O<;!Ch c u a
moi n h 6 m .
,.... ,...,. .,. __. ....

.

•

a) 1 ,2

f)�t t[n h roi tfn h :
X

b) 5 1

0,6

X

4, 5

c) 7,92 : 6

·d) 5 76 : 45

Bai 2 . Tfn h:

0 m()t phong h Q p, n eu moi bim ngoi 3 n g uoi thl 1 7 n g uoi c h ua c6 cho ng6i,
neu m o i ba n ngoi 4 n g uai thl 2 nguoi chua c6 cho ngoi . Hoi c6 bao n h ieu n g uai dlf
hQp va bao nhh�u ban?
B a i 1 54

a ) 45,1 78 x 1 00 - 90, 32

b) 0, 1 862 1 x 1 000 + 3 1 8, 02

c) 2,5 x 81 4 + 1 6, 27

d) 1 880, 8 : 8 - 1 92, 8

..

f) 61 9 x 0, 1 + 23 1, 82 : 1 000

0 m()t l&p h QC, neu x�p _moi bim } b�n thi con thua 8 b9n c h u'a co cho ngoil
n eu xep moi bzm 5 b�n thl thlia 2 ban. Hoi lop c6 bao nhi<�u hQC sin h va bao nhh�u ba n ?
Bfd 1 5 5

..

Bai 3.

llm y, b h:?t:

a) 0,4 X Y

=

c) y + 1 ,59

I

R i se a bove o n e se lf

a n d g ra s p th e wo r l d

0,6

=

12

X

x

10

b) 1 05 : y = 7,46 - 3,26

2,5

d) 3,75 : y = 3 : 4

Archi medes Sch o o l

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Toa n s - Quyen 2. 1

ARCHIMEDES SCHOOL
Bai 4. Tfn h ban g each hqp ly:

c) 1, 07 x 7, 1 + 1, 07 x 2,9

·

d) 20,5 x 4,7 -20� 5 x 4,6

Bai 1 5 1 . Trong m 9t d<;tt t h u ho�ch th6c, neu chia moi bao 35kg thl co n thua 7 7 kg,

con neu chia m o i bao 40kg thl con thua 22kg. Hoi dQt <16 thu hoc;lch alJQ'C baa nhh?u
ki-lo-ga m th6c?

e) 1, 98 : 1 2 + 41 02 : 1 2

g) 2, 37 x 57, 8 +23, 7 x 4, 22

Bai 1 SO. Bac Tan t h u hoc;lch xoai va cho vao hqp dem di ban. Neu m o i h<)p chua
9 qua thl con thua 8 q ua, con moi h(>p 1 2 q ua thl th ieu 4 qua. Hoi bac Ta n thu hor?ch
au'<;lc bao n hieu qua xoai?

h) 1 2, 4 x 52 - 1 24 x 4� 2
B�ti 1 52. Hai c6 m{>t so bi va mqt so tu i. Neu Hai bo vao moi tui S vie n bi thl thua
1 2 vh�n, neu b6 vao m6i tui 1 1 vien bi thl vua au . Hoi Hai c6 bao nhieu vien bt, c6 ba o
n h i eu tui?

i) 0, 6 x 2�, 1 7 x 6 + 3 x 26, 83 x 1,2.

61

Ri se a bove oneself

a nd g rasp the world

j) 0, 8 x 23, 6 x 3 - 4, 8 x 1, 8

Arch i me des School

Aschool.edu.vn

_

Lop

Neu

m ua 4 q

90

q uyen1 neu moi b9-n 6 q uyen t hl vl.ra het. Hoi so va l ap SA au<;Jc m ua I a bao n h ieu
m ua

quyen ?

.:!2 :(3 -� ]= 2,5
12

5

y

1

1 48.. An h c h ia tao cho cac ems n eu c h i a moi em 6 q u a thi thua 7 qua, neu c hia
moi em 9 qua thl con th ieu 2 q u a. Hoi c6 bao nhieu q u a tao va bao n h ieu em dU'Q'c

c ) 1 - ( 1 , 1 + y ) : a10

1

.

=

7

b) 1, 5 x y : 2 = 2 -

0

.

2

2

d) (y + 4 ) : 0, 5 + 1-:- = 1 3 3
3

Bai

chia tao?

Bid

6. Ti m Y� bh�t:

a ) y x 3, 6 + y x 6, 4 = 1 81 9

Bid 1 49 . M¢t oia ha n g ban 9 9 0.

Neu chia mo� tui 1 7kg thl t h i eu 20kg, n eu chia moi
c6 b a o n h ieu ki-l o-gam g�o va dU'Q'C chia vao
bao n h i t� u t u i ? (moi tui co so 9 9 0 b a n g nhau)

tui 20kg thl th ieu 80kg .

Hoi cua

b) 9,4 : Y. + 5, 3 : y = 1 4

d) y : 0, 4 - y : 0, 5 = 1, 2

hang

Bai

7 . Tfnh n h a n h :

a) 3 x (36, 2 -6, 5�) + 7 x 36, 2 + 3 x 0, 52

Rise a bove o n eself

g ra s p the wo rld

A rchi medes School
AschooLed u .v n


Toa n s - Quyen 2. 1

ARCH IM EDES SCHOOL
b)

258,93 x (76; 1 -1 4, 3) � 1 58, 93 x (72 + 4, 1 ) + 258,93 x 1 4, 3

'

I. LY THUYET
1 . Cac bliO.c

giai d�ng

Buac T: Tofll tat bai

.

BAI 3 : HAl

.

�

-

H I EU
. SO

bai t�p hai hi�u so

toan.

Bciac 2: llm hi�u thanh ph an.
Buac 3: 1lm

· c) 1 5,2 x 34, 5 + 1 5, 2 x 471 5 + 84, 8 x 82

Buac 4: Tam

hi�u tong.

thanh p h an.

Butte 5: Ti m tong.

2. ca c: d�ng bai t�p

Co g iao chia VCJ c h o cac em hQC sinh. Neu moi em 3 quyen thi thua 4 q uyen.
Neu moi em 4 q uyen thl thiE�u 4 quyen. Tfnh so hQc sinh va so vo.

Vi dl}:

)

(

d ) 497,625 - 2 1 5;46 x 2 x 1 5, 9 - 6 + 2 1 5, 46 x 2 x 1 5, 9 - 2 1 5,46 x 6

Tom

Bai giai

tat:

3 q uy�n /em : thua 4 quyen

4 q uyen/em : thieu 4 quyen

Bid 8 . Trung b1n h moi p h ut 6 to di duqc t2km.

C h e n h l�ch so v& m¢t em g i ua 2 each chia Ia: 4 - 3

ca

2 1 4,5 1 ft

dau. Sau kh i do 1 0, 5 l it d a u tv t h u n g thu nhatsa ng

thu n g. thu hai thl .so dau (J th u ng thu n hat b�ng
dau moi thung c6 b a o n h i e u 1ft dau?

8 1·

Rise a bove oneself

and g rasp the world

�
3

so

dau b thu ng thu h a i. Hoi ltk

1 (qu y en)

Chenh l�ch tong so vo du chia g iua 2 each chia Ia: 4 + 4 = 8 (qu yen)

Hoi 6 to d6 di 45 km het "bao lau?

(c6 the sa dvng sa do de xac djnh hi�u tong)
56 hoc s i n h I a: 8 ; 1

=

8

(em)

Tong so vo co g i a o chia Ia: 8
Bai 9. Hai t h u n g c6 tat

=

·-

II.

LUY�N T�P

X

3 + 4 = 28 (quyen)

fla p so: 8 em, 28 q u ye n vC:J

-oai 1-46� -ch! ch ia k�o cho cac em, neu moi em 6 chiec thl thua 4 chiec, neu moi e m
8 chiec thi t hiE�u 6 chiec. H6i c 6 bao n h ieu chiec k�o va ba a n h ieu em duq2'chia ��o?

Archi medes School

Aschool.edu.vn


40%

kl I I,

them 1 b � n n a m va 4 b � n n v n e n so b � n n a m ba n g 60o/o s6 b� n n O'. Hoi da u n a m h9c
n hiE�u
l op
Ia n a m .

ti m

n6 cho n h a u thl g ia

11.
1

Bid 1 44..i M9t g ia

-

sa c h c6 3 n gan. So s a c h

& ngan

thu n hat

bang

66

�

_

so

sach b

so

cua so d6 ta n g l e n 1 0 i a n .

sao

Tln h :

a ) 1- -o
6

so t h � p

30

16
6 +I

b)

4
7
- + 1 - - 0, 8
30
15

n g a n thlt ba. 56 sach 6 nga n thd' h a i bang 75o/o so sach a ng a n thu n hat Hoi g i a c6
tat ca bao n h teu q uye n sac h ? Biet ran g ngan thu ba nhieu h an ngah th d' hai I a
45

quyen sach.

b uoi sang, 40% Ia hqc s i n h lop 61
36o/o Ia h QC sinh lop 7, so 'hQC sinh con 1<;1i I a h Q C s i n h l ap 8. Buoi chieu, so h Q C s i n h lo p
6 giam 75°/o, so h Q c sinh lop 1 tang 25%, so hQc s i n h l o p 8 tang 75%. Hoi so h9c sinh
tham gia lao d¢ng buoi chieu ta n g h ay g ia m bao- n hieu pha.n tra m so voi s o hQc. sinh
lao a¢ n g b u oi sang?

2

9

3

5

c)

2- : 2 + 1 8-5 .
1
4

d) 3 ' 1 2 x 9
4 .:... 3 6 x 2 +1 6x-

e)

.
1
1
1
1. 5 : ...:.. + 0, 4 x - + 1 6
3
2

f) l : 1 7, 5 x 24 + 1 3, 4 x 24 - 7, 9 x 24

1

.

1

I

Ba i 1 45 .. Trang s6 hQc sinh t h a m g ia lao a¢ n g

Rise a bove oneself

a n d g rasp the w o r l d

1 + 4 +7 + .. + 55 + 58 - 39 x 1 1

_

Arch i m ed es School

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·

Toan s - Quyen 2. 1

ARCHIMEDES SCHOOL
Bai 1 2 .. Cho day

a) Day s6 nay

Bid

1 40. Di�n tfch cua m¢t hlnh vu6ng se thay aoi n h lf the nao neu C9 n h hln h vu6ng
ta ng them 20%?

so; _1 , t ; 2, 2; 3r3; . � · ; 1 qs,9; 1 1 0,0.

c6 bao n hieu s6 h9ng?

.

b) So h�ng t h u 30 cua day Ia so nao?

Bai 1 3 . Cho day s6: o, 1 ; o,o-1 ; o,oo 1 ; � . .

a) So h�ng t hu 1 ooo c 6 bao nhiel.J chCrso o ph a n th�p phan?

b)

nhieu chu so 0?

Bai 1 4. Ch o day c6 quy lu�t sau: 1 ,2 1 ; 1 ,23 ; 1 ,25; 1 ,27;
Day tre n c6 b a a n hieu so th�p p ha n ?

b) Tfnh to ng cac so th� p p h a n cua day tren.

. ..

; 2,3 1 .

Bili 1 42 .

Khoi l ugng co n g vi$c tang l en 50% n h ung nang suat lao a¢ n g chi ta n g 25%.
nh�eu phan tram ae h o a n th� m h cong vi�c du n g

H o i phai ta n g s6 c6ng n h a n len bao

thai h � n ?

·

Bai 1 s. nm x 1 biE�t:

a)

1 5%

·

Be vi et tlt so h�ng th u n h at den so h(;lng thu 1 00 phai dung bao nhieu chu so 1 ;

bao

a)

B a i 1 41 . llm di¢n tlch hhih ch u n h�t, biet rang neu tang 20o/o chieu dai va g iam
chieu r¢ng thl di$n tkh ta n g them 20o/o dm2 •

(x +O�S) +(x +0,25) +(x + 0, 1 25) + (x + 0, 0625) = 1

Rise above oneself

a nd g rasp the world

Arch i m edes School

Aschoo Led u .vn


Do i : 3 2o/o

=

0,32; 1 Oo/o

=

0, 1 .

N eu c o i kho i l uqng c o n g vi?c.cu Ia i adn vi t hl khoi 'h iqng c6n g vi�c m 6' i so vdi

vi�c cG Ia: 1 + 0,3 2 = 1 ,3 2

N e u cof nang s u at l a o dqng c G I a 1 ddn vj

i(t
SUa

l.ao uqng
..=f "
, 1 + (\ 1
cu_ ,.a:
Vy

=

,

n a n g s u at

1 1
I

d() n g m cri so v6'i. nang

f)e th{jc h i�n dvqc khoi l vqng c6ng vi$c moi v oi nang suat lao d¢n g m�i t hl so cong
n ha n phai d9t toi muc la: 1 ,3 2 : 1 / 1

=

1 12

V�y ti so phan t r a m so c6n g n ha n p h a i ta ng t h e m so voi so cu Ia: 1 ,2 - 1 = 012

Bap so
Bai

t�p

=

20o/o

2o%

..

B a i 1 3 7 M(lt

so sa u k h i g ia m di 20o/o thl pha i ta ng them bao n h i e u phan tra m so m oi

de l�i au'Q'c so cu?

du'qc s o

c) x x 01 1 + x x 0, 3 + x x 0, 5 + �. + x x 21,7 = 2376, 2

B a i 1 38 . M
cu?

··

t h e m 259·6 th1 phai g iam d i bao nhieu p h an tra m so moi de l9i

..

.

cua m<)t hl n h chu n h�t se thay doi the n a o n eu t a n g chit�u dai cua
n6 l e n 20% va giam chieu r<)ng cua n 6 di 20%?

B a i 1 39 Di�n tfch

Rise above

oneself

a n d g rasp the worl d

(

23

3

d) 0 , 44 x x + x x 5 - - + - x 2, 24 = 1

Bai

55

J

14

1 6. T111h hqp I f:

a) 2, 3 + 2� 7 + 3, 1 + 3, 5 + ... + 24� 3 + 24, 7

Arch i m edes Schoo l

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Toan 5 - Quyen 2. 1

ARCH I MEDES SCHOOL
b) 1, 2 + 1, 7 + 2, 2 + 2, 7 + ... + 1 24, 7 + 1 25, 2

H. MQT s6 BAI TOAN KHAC

C h u y: Dol voi m Qt so h3i toa n ve ti so p h a n tram.. co th e h LJong dan hQc s i n h alia
ve cac dc�mg toa n q uen t h u9 c nt;lti tong - ti, hi$u - ti, . . . de· t1m ra_ da p so n ha n h han,
de hi�u hdn.

.

·

c) 1 0, 1 + 1 1, 2 + 1 2, 3 + 1 3, 4 + ... + 93,7 +94,8

Vf dl;l

l : To ng cua hai s6 bang 25% thucrng cua hai so d6 cung bang 25o/o. Tim hai so d6.

Ta c6

sa do:

Bili giai:

}0,25

so thu n hat:
so thu hai:

S6 thu nhat Ia: 0,25 : (1 + 4) = 0,05

so thu hai I a : o,25 - o,os = 0 ,2

Bai 1. 7 .. Tong cua hai so la 1 2,4. Biet so th u nhat bang � so th u haL llm hai s6 d6.
3

d� i: Gia g iay viet nam nay b an g 1 20% gia· g i ay n a m ngoaL Hoi val so tien mua
du<;1c 1 50 t� p g iay & th ai ctiem n a m ngoai thl n a m nay m u a du'<;1c ba o n hieu t�p g iay?

Vi

Bili giai:

n s6 gia g i ay n a m nay so vai nam ngoai
Vi cung m¢t so tien t h1

nay m u a avqc I a : 1 50

B�ti 1 8. _M9t h l n h ch G' rih�t co chit�u dai gap rllfli chie u r¢n g . Biet c;hieu dai lon hdn
chieu r(>n g Ia 2,4cm. Tfrih di�n tfch hl nh cha n h �t do.

£>ap so: o,o5; o,2.

Vi

x

1�: 1 2091:1

=

6

5

s6 g iay mua duqc ti I� n g h ! c h voi ti so g i a nen sO tien d6 nam
5 :6

=

1 25 (t� p)

f)ap s6: 1 25 t� p giay.

d�;� 3: Kh6i h.tqng cong vl�c ta n g 32°/o. Hoi phai tang so nguoi lao d¢n g them bao
n hieu phan tra m de n a ng SU!lt l a o d(>ng ta n g 1 0%?
Bai giai

ca�::: h 1 :

Neu coi khoi I VQ'ng cong vi$c cO Ia 1 00% t h l khoi luqng tof)g vi¢c mC1i so vC1i cong
vi�c c:u I a : 1 OOo/o + 32o/o = 1 32%.
Neu co i

d(>ng cu Ia 1 00% th1 n a ng suat lao d(>ng m6t so voi n a n g suat

tao d<) ng cu Ia: 1 OOo/o + 10% = 1 1 Oo/o
na ng suat lao

f)e thtjc hi�n avqc khoi h.tqn g co n g vi�c moi voi n a n g suat lao a(> n g mdi thl so cong
n h a n phai d<;1t t6'i m uc I a : 1 3 2% : 1 1 Oo/o = 1 20o/o
Vf?,y ti s6 phan tram so cong n han phai ta n g them

1 20o/o - 1 00% = 20%

Rise a bove oneself

a nd g ra s p the world

so

vai so cu I a :

Dap so: 20%

·

Schooi

Asch o o l .ed u.vn

Arch i medes


9 1 .3 3

S o/o

c6

so

hln h thoi a6.

Ia 1 1

2
9

hai.

Bai 1 34. Dan so cua m()t qu�n nam 201 6 1a 560 000 ngu'oi, tan g 1 2% so voi nam 20 1 5.
Neu tang 1 5% so Vdi nam 201 5 thl so dan cua qu�n a6 nam 20 1 6 1a bao n h i eu ngu'di ?

B a i 20. Tong c u a h a i so th�p p h a n
t h� p phan d6.

Ia 22,5 va

h i �u cua chung Ia 1 ,22. Tim h a i so

Bai 1 35. M9t tinh c6 2 tri�u dan, trung bl n h moi nam da n so c u a tin h d6 l�i tang 5°!0
so voi n a m tni6c. Hoi hai nam sau, tinh d6 c6 bao n hieu n g ucri?

B ili 2 1 . ll m h a i so c6 th llcmg Ia 2020 -va- hi¢u cua c h u n g Ia 201 ,9.
Bai 1 36. Mqt nha may c6 2 000 cong n h a n . Cu sau moi nam, n ha may lgi tuyen th em
1 0% so cong n han so voi nam tru6'c. Hoi sau ba n a mr n ha may c6 tat ca bao n h i e u
cong nhan?

Bai 22 Ti m h a i so c6 tong va thudng cua chung aeu ban g 0,25.
..

Rise above oneself
grasp

world

Archimed es Sch ool
Aschool.ed u. vn


ARCH I M EDES SCHOOL

·

Bid 23. Tt m· h a i

G.

so co thvang va hi�u cua ch ung deu bang o,s .

Toa n s - Quyen 2. 1

BAi TOAN LIEN QUAN £>EN DAN SO

1 . Ly thuyet

56 d a n nam· nay = so dan n a m tnJoc a6 + % s6 dan n a m tnJac d6.

Vi d�: Cuoi nam 2000 nvacta c6 78· tri�u n g uo i Hoi cuoi n a m 2002 da n so nuoc ta Ia
ba o n hieu neu moi nam dan so tang 2%?
.

Bai 24.

S o sanh: A = 2, 1 93 x21 9,9 va B = 21,96 x 21,96 .

So

Bai 9iai

dan nam nay = s6 dan ·na m tntac a6 + 2% so dan nam trvac d6.

Cuoi nam 2001 so d a n tang them Ia: 7 8 0 0 0 000

·

Bili 2S. Ti m

hai so th�p phan c6 h i<%u ba ng 36,84. Biet ran g neu lay so Ion chia. cho so

be thl duqc th udn g Ia 3,4 va du 0,024.
,-1_.,

�

X

2 : 1 00 = 1 560 000 (ng uoi)

Cuoi nam 2001 nuoc ta c6 so dan Ia: 78 000 000 + 1 5 60 000 = 79 560 000 (ngVQ'i)
Cu6i nam 2002 so dan nv6"c ta Ia:
79 560 ooo + (79 560 ooo x 2 : 1 OO) = 8 1 1 5 1 200 (nguoi)
f>ap so: 81 1 5 1 200 ng u'oL
'

2. Bai t�p
Ba i 1 3 1 .

f)au nam 201 8 da n so cua Vi�t N a m khoang 95 tri�u nglf<:ti. Dau na m 20 1 9
dan so cua Vi�t Nam khoan g 96,9 tri�u ngubi.

tu dau n am 20 1 8 den dau nam 201 9 d a n so cua
nh ieu phan tram?

a) Hoi

Vi�t

N a m ta n g them bao

Neu tu ctau n a m 201 9 den da u nam 2020 dan so cua Vi-�t Nam cGn g ta n g vai ti l�
tre n thl dau nam 2020 dan so cu a Vi�t N a m Ia bao n h ieu ngVai?
b)

Bili 26. B a o thu n hat

n hieu hdn bao th u hai 25,4kg g9o. N eu cho them vao moi bao
t.h1 s6 g�o 0 bao th u n hat gap bq lan so g�o (j bao thu hai. ll m so g�o a moi
bao luc aau.
1 ,7kg

Bai 2 7 .

Tfch cua hai so Ia 3 3,3 75. Neu tang t h ua s o tha n hat t h e m 1 ,2 ddn v j thl ta
dlioc tfch m6'i Ia 40,875. Tim hai so ban dau: ·
.

Rise a bove o n eself

and g rasp the world

.

.

Bid 1 32. Dan

da n

so cua m{>t xa cu o i nam 201 8 I a 1 0 000 nguai. Biet rang ti I� tang

s6 trung bin h moi nam cua xa d6 1a 3%. Hoi cuoi nam 201 9 xa a6 c6 bao· n hieu ng u'Oi?

.

Archi medes School
Asthool .�du.v n


trl n h p h a i

65%.
bay h ai I a bao n h ie u

say kh o n g

vi

ki- l o-g a m

c 6 s lj h a o h l:Jt n a o khac n g oa i n lfoc) .

h1 n h c h u

n h �t

n h�t

m 6'i

gap 5

di�n

lan

B a i 29 M9t h l n h chu n h�t c 6 ch u v i 26dm . B i et rang, n eu t a n g chiE�u dai l e n gap 2,5
lan t hi c h u vi se h a n g 38dm. Tfn h chieu dai va c h i e u n?ng hln h chu n h�t d6.
..

Nguoi ta p h oi 780 kg th6c tuail sa u kh i p hoi thl k h 6i higng th 6 c g i a m 1 30kg.
phan tram g i ua hiqng n u'oc va h Jqng t h u a n h � t c6 tro n g th6c da p h ai Biet
rang trong th6c tu'd'i n u'oc chiem 25o/o va trong q u a trl n h p h d'i kho n g c6 slf hao hl:lt
nao kh a c ngoai n u'6'c.

Bid 1 30.

Tfnh ty so

.

M(>t a(>i cong n ha n da l a m. xon g q uang duong AB trong 3 tu a n le. Ju� n .1�
aa u n g u'oi ta lam au'Q'C 0,5 quang au'O'n g . Tuan le th u h a i l a m d uqc 018 q u a n g dvang
con l � i. Tuan le t h u ba lam duqc 3,5km n ua thl xo n g to� m b9 qua n g aU'C1ng AB. Hoi
q u a n g duong AB dai bao n h i e u ki-16-met?

Bai 30

Rise a b ove o n eself

and g ra s p the wo rl d

..

Archimedes

Schoo l

As c h o o L e d u .v n


Toan s - Quyen 2. 1

ARCHI M EDES SCHOOL .

Bai 3 1 . Cho 56 20l 9. So nay se

a)

thay doi the nao neu

VH�t them dau phay vao gi U'a chii' so 1 va 9�

:

Bai 32. Cho m()t s6 .th�p p han
. c6 hai ch u s6 a phan th�p phan. So nay se ta n g g iam

bao nhieu lan neu:
a) Bo dau phay di:
b)

Bai 1 25� Lvc;tng ntt6'c trong h C;\t htoi chiem ty I � 48%, trong h�t kho chiem ti I� 1 0%._
Hoi phai 1 ,08 tan h9t tudi se duqc bao n h i e u ki-lo-gam h9t kho?

Bai 1 26.

H�t tvai co ti r� n tt6'c Ia 1-5%, h�t kho co ti 1� n uoc Ia 1 0°16. f)� c6 340kg h<;�t
kho thi can dem pho'i bao n hieu ki-lo-g a m h�t tuui?

Chuy�n dau p h ay sang ben trai m¢t hang:

c) C h uye n dau phay sang ben phai m¢t hang:
d) Chuyen dau phay sa n g ben phai hai hang:

Bai 1 21. N g uoi ta phai sookg h�t tU'O'i, sa u kh i phai thl khoi l uqng giam di 60kg .

tra m giua l u'Q'ng n uoc vii l lfqng th uan h�t co trong h 9t aa p h di kh6.
Biet di ng trong h9t tllO'i l uqn g nuoc ch iem ti l� Ia 20o/o?

Tinh ti so phan

Bid 33. Cho so 2 1,89. Hoi so nay se th a y doi t h e nao r:eu:
a) Xoa bo 2 chO so cr ph a n th� p p h a n :

b) Thay cac chu so 1

bang

Bid 34.

a) 1 3,52 ba ng bao n hieu

b) 2,0 1 9 bang

c h u so 9 :

lan t352? Bap s6:

Bai 1 28. Ti I� nude trong h9t ca phe tlfdi Ia 22o/o. C6 1 ,4 tan h�t ca phe tu'd'i dem p h di
kho. Hoi lliqng nVdc can bay h ai di Ia baa n h l e u ae lu'qng ca ph e kh6 th u .alfqc chi c6

_______________

bao n hieu l a n 0,020 1 9? f)ap so:

c) 0,362 b a ng bao nhieu la n o,00362? Bap so:

d) 216 bang bao n h ie u lan 260? 8a p so:

Rise a bove ones e lf

and g rasp the World

____
__________

______________
__

e) 0,1 045 ba ng bao nh h?u la n. l 04,5? Dap so:

16 1

ti l� nvoc Ia 4%?

______________

Aschool.ed u.vn

Arch imedes School

49


dau p h ay c u a
1 8, 1 7 1 don vi. Ti m sa t h � p p ha n d6.

Ta c6 sO' ao:
(1 OOo/o)

( 1 OOo/o)

P h oi

H9t tvai

Nvac A

so

N uoc B

Th u a n h 9t

Th u a n h9t

(= N uoc A - n voc ba y hoi)

Chu y: Lu't;tng thuan hqt trong hgt tUai va hQt kho la bang nhau. 0 dgng bai nay luon can
tim au'qcsolu'qng thuan hqt tn.tac. (Thuan h9t Ia phon hg t khong chua nuac).
.
.
. Vi d �: Phai 3,6 t� th6c tu'oi t hl avqc bao n h ieu t� th6c kho? B i et l uqng n uoc tro n g
th6c tuoi Ia 3 0o/o va trong th6c kho Ia 1 0%.

Bai 36. Kh i d �ch c h u yen dau phay c u a so th�p phtm S Q n g phai m <)t h a n g t hl so a6
t a n g them 469,683 ao'n vj. Ti m so th�p p h a n d6.

..

sai giai

Bai 3,6 t� = 36ok9
LVqng

h�t t h ua n I a : 3 6 0

x

( 1 oo - 30) : 1 oo = 252 (kg)

Trang t h 6c tho t h1 h.tqng h9t thw3n

chi em so ph an tra m I a :

LVQ'n g th6c kho thu duqc Ia: 252 : 90

x

1 oo = 280 (kg)

=

1 00°/o -

2,8 t9

1 0°/o = 90%

£>a p sO: 2,8 t?

Luqng n ttoc chua· trong h 9 t tuai Ia 55°/o. C6 3 00kg h 9t tttai s a u khi phai kh6
n h � di SO k g Tfn h ti so p h a n tram nttoc trong h�t da phoi kh6.

Bili 1 23

..

·

.

tuai I a

5 5%, t ro n g co kh6 I a 1 0°/o.

tutt i ta auqc bao n h i e u ki-lo-g a m co kho?
Bid 1 24. LVQ'ng n uac trong co

Rise a bove oneself
and g ra s p the world

Khi d ich ch uyen dau phay cu a so th� p phan sa n g trai hai h a n g thl. so d6
g i a m di 2 1 0, 1 77 adn vi . llm so th�p p h a n do.
Bid 3 7 .

Hoi p hdi

1 5 0 kg co

h a i so th�p p h a n c6 h i� u Ia 1 1 5,7. N e u dai dau phay c ua so be s a n g phai
m9t hang, ro i c 9 n g -voi so lon ta dugc 1 66,3 .

Bai 3 8. Ti m

Bai 39.. To n g cua h a i s o th�p p h a n ban g 1 1 6,55 4. Neu d j ch dau p h ay cua s o thu n hat
sang ben trai h a i c h O' so ta se avqc so thu haL Tt m h ai so d6.

Archimedes Sch ool
Aschoo l .ed u .vn

ARCH IMEDES SCHOOL

Bai 40. Hi�u cua hai s6 th�p ph an bang 1 23,75� Neu d!.ch d au p h ay cua so th U' nhat
.
sang ben .ph a i hai ch O' so ta se avqc so th u h a i. Tim hai so a6.

Bili 1 2 1 . c6 50 tan

Toan 5

Quyen 2. 1

- .

q u�ng sat chua 55°/o sat. Sau kh i trqn them vao 30 tan qu�ng sat
thl tat ca chua 35 tan sat. Tfnh tT so phan tra m cua s�t trong lo�i qu� n g au'Q'C them vao.

Biti 4 1 . Tong cua m9t so tv n h ien va mqt so th�p p han Ia 3 75,9. Khi c¢ng hai so nay
m9t bCJ n q uen mat dau p hay 0 so th�p phan va a�t tfnh c¢ng n h lf s6 til n h ien nen
ket q u a la 627. Tim s o tl/ n h ien va so th�p phan da cho.
Bai 1 22. C6 hai lo�i qu� ng sat, qu�ng lo�i I va 1 o� i I I, tong kh6i lvqng Ia 1 2 tan khoi
sat n g uyen chat trong qu� n g lo�i I I a 1 ,8 tan/ trong qu�ng lo�i I I Ia 1 ,6 tan. Biet ti I�
sat ng uyen chat trong q u � n g lo<;1i I hdn ti I� sat nguyen chat trong q u � n g lo�i II Ia
Bai 42. Tong cua mc?t so tv nhien va m¢t so th� p phan I a 534,3. Khi thtjc h i � n phep
c(>n g nay, m(>t b<;m da quen viet dau phay cua _so th�p pha n n e n da tien ha n h c (> n g
nh u' cqn g hai so tg n h ien va c6 ket qua I a 338 1 . Tim h ai so <16.

1 Oo/o. Tinh

khoi luqng moi lo�i qu� ng�

-----------------�--�

Bai 43. ll m ba so th�p phan c6 tong Ia 202,353. Biet ran g neu djch dau phay cua so
thu nhat s a n g trai mtrai m¢t c h u s 6 ta au'qc s o t h u ba.

18 1

Ris.e. a bove oneself

and grasp the world

Archimedes School

Aschoo Led u.vn


1

ba o n h ieu ki-1 6-g a m n voc I a de avqc m Ât loô? i d u n g d j c h c h ua 2% m u 6 i ?

n uoc

B a i 1 1 8 .. Mqt bl n h dljng SSOg d u n g d jc h nu'oc m u o i chua 2 0 % m uoi. H o i p h a i ao

them vao bln h d6 bao n hi eu gam n u'oc cat de. dvqc m¢t bl n h n uoc m uci i c h ua
1 0% muc>l?

· Bi d 1 1 9 .. Pha 650g d u n g d ich m 16'c cha nh chua 1 2°/o c ha n h ng uyen c h at va 3 50g

d u ng djch n u6'c_ c ha n h c h U'a 1 5% cha n h nguyen chat thl dvqc d u n g d j c h chva bao
n h ieu phan tram chanh n g u y e n chat?

tan qu�ng sat ch ua 72o/o sat v6'i 1 5 tan q u � ng sat c h ua
40% sat. Hoi sau kh i tr(>n xong thl h o n hqp qu�ng sat chua bao n hieu p h a n tra m sat?
Bid 1 20. Ngt10'i ta tr¢ n 35

Rise above oneself
g ras p the world

thl auqc h a i s o co tong I a 84,6. Ti m h a i so d6 .
Ia

3

5

so Ia 7,9. Neu t a tan g m()t s o le n 4 ! a n va g iu n guyen
duqc h a i so co h i¢u Ia 46. Ti m h a i so do.
Bai 45 .. H i�u cua h a i

Bid 46. H i�u hai so Ia 60,7. Neu

2818. nm hai so da cho.

so tru gap len 2 la n t hi dvqc so moi lon han so b ! tru

H a i so t h � p p h a n c6 ton g Ia 60,9. Neu d O'i dau
m(>t h a n g , roi trlt di so ldli thl Ou'9'C 2 1 018. TJ m h ai SO 00.
Bai

kia thi

.p hay

cua so be

1s a n g phai

·


ARCH I M ED ES SCHOOL

·

Bai 48. 11m. hai sci th?p ph a n co tong Ia 76,8. N�u d oi dau phay cua so be sa n g trai
m9t hang, r6i l ay h i�u gl ua so lan va n o ta dtic;:fc 3 7,64.

E.

BAlTOAN VE PHA TRQN DUNG DICH, QU�NG

Vi d l:f 1 :

Pha i ao them vao 1 20g d u n g djch n VO'c cam chua 1 5°/o ca m

m..toc Ia de ':'fliQ'c dung d ic h n uac cam chua 1 Oo/o cam ?

56 gam nu6c ca m nguyen c h at Ia: 1 20

Bai 49. 11m sO' th� p p h a n A. D!ch dau phay sang trai mqt hang ta dttqc so B. Con neu

djch da·u p hay cua A sang p h a i l h a n g

ta duqc so C . Tong cua 3 so A, B, C U1 . 1 3 51975.

ket qua thu auqc g i�m ai so v6'i ket qua dung Ia 4 1 2r2. Tim so tl;l' n hien

d6.

·vi dy 2: M9t n g uoi tr(>n 3 tan. hon hqp

m¢t b 9 n q u en dau phay a h a ng th�p phan va d�t tfhh n h v c<)ng hai so tv nhien nen

=

=

1 8 (g)

1 80 (g)

qu�ng chlia 45o/o Ia s a t v6'i 7 tan h6n h<;tp

Hoi se dvqc h o ri hQ'p q u� ng v6'i bao nhieu phan tra m sat?
Bai giai

7

X.

X

Tong l uqng sat Ia: 1 ,35 + 3,85 = 5/2 (tan)

45 : 1 00

=

1 ,35 (tan)

55 : 1 00 ;::: 3,85 (tan )

% sat trong hort hqp l uc s a u Ia: 5,2 : (3 + 7) = 0,52 = 52 %
E>a p so: 5 2%

BiH 1 1 5. P h a i ph a 4kg mu6i voi. bao n hieu ki- l o-g a m nt�6c Ia oe du'Q'c: m¢t bl nh ntf6'c
. m u 6i chua 20o/o muoi?

Bai 1 1 6.
Bai S 1 . Tong cua m{>t so th�p p h a n vai m(>t so tV n h i e n Ia 47,5. Kh i c<)ng hai s6 nay

1 5 : 1 oo

Bap so: 6og

Lu'Qng sat trong han hqp thu h a i Ia:

_

x

Kh 6i l uc?n9 nuac Ia pha them Ia: 1 80 - 1 20 � 60 (g)

Lu'Qng sat trong h o n hqp thu nhat Ia: 3

pha nr m{>t h9c Sin h da O�t tfnh n ham n h u' doi VOi phep tru h a i SO tV n hien V �r van
d a n h dau phay (j ket q u a thu Ou'Q'C. tha n g h a n g voi dau ph ay cua so th� p p ha n . V1 the

bao n hieu g a m

Bai g i a i ·

Kh oi IV<�ng dung d( c h Ide sa u Ia: 1 8 : 1 o · x 1 00

q u � n g ch Lra 55% Ia sat .

Bai so. Khi tru m9t so tV n h ien di m<)t so th�p p h a n co m c)t chu so d p h an th�p

Toa n s :- Quyen 2 . 1

fYl{>t ngVoi do th e m SOg muoi vao m ¢t bln h chua 450g n u'Bc m y o l lo�i 1 QO;&.

Hoi n g uoi d6 n h � n du'Q'C m(>t bl n h chua bao ·n hieu p h a n

tram. muoi?

ket qua Ia 1 60. 11m ha i so ban aau.

Rise above oneself
and gra s p the

wo rld

Archi m edes School

Aschoo l .edu.v n

5
4
1


5-

m ua

da g i a m 1 5 % g ia t ien m ¢t

b a� n g -1
3

m ua.

h()p so v6'i g i a n it� m yet. N g uoi a6 eta m a n g ve ba n l q i va

Hoi g ra n i em yet m oi c u a mqt hqp sO'a Ia b a o n h ie u ?

lL
20�o
so

l a 80,5.
so
m ()t
H i�u
q ue n d a u p h a y 6 h a ng t h � p p h a n va a�t tfn h n h u
h a i so tV n h i e n n e n ket q ua I a

40.

Kh i c h i a m qt so t h � p p ha n c6 c h u so a h a n g th�p p h a n Ia 5 cho 1 251 m9t
aa bo q uen chU SO 1 d ha n g aO'n Vi cua SO t h � p p him 00, Vi v�y ket qua
th u ciuqc giam di s o vai ket qua du ng Ia 5,984. Hay ti m so th�p p h a n a6, biet ra n g ca
h a i tnJong hQ'p deu Ia phep c h i a· het. .
Bai 53e

hQC s i n h

B id 1 1 3 .. M ¢ t eva h a n g

ban � so hang v a dliQ'c l i H

20% s o vai gia m ua .

So con l 9 i b a n

l o 1 Oo/o s o voi g i a mua. Hoi kh i b a n h et s6 h ang, eva h E m g Ia h a y lai v a l o l a i b a o n h i e u

phan tra m ?

Bid

Thay cac c h u ca i

a. 3a,b x O, b

20o/o so h a n g vai l a i suat 3 0%. Do khon g ban duqc h et
hahgr chu c ua h a n g giam gia 30o/o so h a n g .con l � i va da b a n het. Hoi cua h a n g l _a i hay
Ia va lai lo bao n h ieu p h a n tram so vOi g i a m u a?

c. a b, a b : a,b

=

1 6, a b;

=

a b, a;

ba n g c a c c h Ct s6 t h fch hqp:
b.

a, be x

4, 1 = 1 5, a bc;

d. aa/ a a : a b , a = a, a.

Bid 1 1 4. Mqt cU'a h a n g ban

Rise a bove o n es e l f

and grasp the

Arch i m edes School
Asch ool .edu.vn


ARCH IMEDES SCHOOL
J.

;

A

K'

BA I 2: Tl SO
,

LY THUYET

.

Ba i 1 1 0. Co

PHAN TRAM
v

Toan s - Quyen 2.1

Ha

gU'i tiet ki�m 60 000 000 dong v&i lai suat i a O,S?A> mgt th a ng . Hoi:

a) Sa u 1 thang thl co" lia c6 bao n h ieu tien rai?

b) Sau 2 t h a n g co Ha c6 bao n hieu th� n lai?
von cu a tha n g sa�.

Tror:tg toa n hqc, phan tram Ia ti so the hi�n duoi d�ng phan so c6 mau so Ia 1 00.
·
Tuy n hien, nguoi ta th van g d u ng ki hi�u 0/o de thay ch? ca c phan so c6 m a u so Ia 1 00.

.

1 25
5
12
1 89
.
V I, d u:
= 5% , - = 1 2 5o/o,
= 1 2°,-b;- = 1 89% .

. 1 00
1 00
1 00
1 00

Biet

liH cua thang tnJac dl1qc nh�p vao
.

.

.

-

-

Chu y: Cac so tlj n hien cuhg co the doi sang phan tram.

2
0 0 ;:=
1 00%; 1 2·= 1 00
VI d u. : 1 = 1

1 00

1 00

+

+

1 2009t>

.

f>O.i SD th�p phan sa n g phan tram: ta chi can d !ch dau phay sang p h a i

them kLhi�u %.

Vi

=

·

d l:l: 1 134 = 1 34%; 0,345

=

34,5%; 2,5

Boi ph an so sang pha n tram:

=

2 hang va

250o/o

Cach 1 : Chuyen ph a n so sang so th�p pha n rei doi s a n g ph a n tra m .
I �•:,

•

1
13
I
V I d u: - = 0, 25 = 25o/o; - = 2, 6 = 260°/o
5
. 4
.

Cac h 2: N ha n phan

s6 d6 voi

V'1 d u: 7 =7 x l. 00% = 35%
+

.

20

20

f)oi p han t ra m sa n g phan so ho�c so th� p p h a n

Vi du:

. 24% = 01 24; 26% =

II. cAc D�NG BAI T�P

26 =

1 00

Bai 1 1 1 . Co ThQ glii tiet ki�m m(>t so tien voi lai suat 0,75% m¢t tha ng; Sau m¢t
thang co n h� n du<;1c 450 ooo don g th�n lai. Hoi:

1 00 roi them kf h i�u %.

�

nhv phep chia voi so 1 00.

,

a) Tfnh s6 tien goc ma co ThQ eta g ui luc da u .

b) Sa u h a i tha n g _co Th9 c6 bao n h ieu ti e n ca g6_c va lai? Biet lai cua tha n g tn.toc au'gc
n h�p vao von cua tha ng sa u.

50

A. TfNH TO.AN
Kh i

g�p cac phep tinh co chua phan tra m � ta· phai doi p h a n tra m sa n g so th�p

phan ho�c p h a n s6.roi thtfc h i�n nhti bl n h thuong.

' h t"1. s o
"" p h an
� tra m : o,3·7 ; 1 ,26; 0,405;
B.a1
" · ss v·1eA't cac
., so sa u th an
...

•

"'

Rise above oneself
and gras p the world

.

50
12

-

7 -

8

4

· 27

; - ; 1-; - .

1 25

12

Archimedes Scho o l
·Aschool.edu.vn


cU'a h a n g
d!n h g ia ba n ba n g bao n h ieu

B a i 1 07. C o s o

mua

t ra m g i a m u a ?

85o/o

b u 6 n tra i cay n ha b<;t n H a d�t h a ng 2,5 ta n ca m voi g i a 1 5 0 0 0 do n g
m<)t ki-lo-ga m . T i e n v� n ch uyen Ia 2 5 00 ooo dong. Tran g qua tri n h v� n ch uyen
1 2°/6 so ca m bi hong. Hoi can ban

s6 cam con l�i voi gia bao n h ieu tien 1 kg de thu l a i 1 0%?

ti

Viet

sau

23 %; 5°/o; 1 3 6°/o;

1 44o/o; 9 0 % ; 1 2,24°/o; 3 6,7 8°/o; 1 0 24,2o/o.

B il i 5 7 .

Viet cck ti so p h a n t ra m s a u tha n h p h a n so toi g ia n : 50o/o; 75%; 48o/o; 1 25o/o;

220o/o; 3 7,5o/o; 62,5%.

B a i 58 .. ThtJc hi�n p hep tin h (vi et ket q u a duoi dc;t n g %) :
B li i 1 os. Gia h o a ngay b�t tang 20% so voi thang 1 1 .

Gia h o a tha ng gieng l�i g i a m

20% so voi n g a y tet. H o i g ia h oa thim g g ieng s o voi g,ia h oa tha n g 1 1 th!ing n a o
dat h an va dat hem bao n h ieu phan tra m ?

22o/o + 45% =

------�-

1 2% + 36% + 45%

3 0% + 40°/o

+

80%

=·
=

215°A1 + 7,25% + 1 8,5°;iJ
1 25% - 1 5°/o

45% - 35% + 25% =

khai tnJang, m(>t . cU'a. h a n g . b a n x e d�p giam g i a l So/o cho
san p ham aau tien va 30% cho sa n pham thu hai c u ng l o� i . M� c u a La n da mua h a i
x e cung lo� i c h o h a i chi e m . La n d i h9c. H o i mE; e ll a La n da tiE�t ki�m dlfqc b a o n h i eu
tien, biet g ia g6c cua 1 xe Ia 1 600 000 dong?

=

=

250% - 1 OOo/o =

B a i 1 09. N h a n d!p

-----

-------'-

Bai 59 .. Th tJc h i�n p h e p t fn h (vi et k et q u a duoi - d 9 n g s6 t h � p pha n ) :

1 2%

X

1 5o/o

X

36

X

40

= --------:---,--

25°/o =
60°/o =

5 0 % X 1 20o/o

20%. : 4 =
30 : 5 0o/o

=

-----'--

_______

---

= ----------

80 % : 4 0 % = ---------1 02% ; 60% = ------

R i s e above o n es e l f
a n d g rasp th e wo r l d

Arc h i medes S c h o o l

A sc h o o l .ed u .v n


ARCHI MED ES SCHOOL

Bai 1 02.

-Bai 60 .. Bien vao cho cham (viet ket qua dlfoi d c,t n g so th�p phan):

a) 35,7% + 1 2�3% =
d) 1 5,3o/o
g) 1 70%

x

x

4

SOo/o

=

___

---

Bai 61 . Tfnh:
.

5
3

a) 75% x 4 + 221 5 : 3 - 1-

b) 98% - 24°/0 =

---

e) 396% : 1 5 =

_
__

h) 71o/o ; 1 Oo/o

c) 1 00% - 5 1 % =

f)
i)

8 1 °!& : .9%

52% : 1 04%

b) 5 - - 20% + 11 2 x 25%

=

=

___

- Quyen 2. 1

hoa· trong 3 ngay. So h oa ban dt1Q'c ngay thu hai tang 1 2% so voi
nhat. S o hoa ba n duqc ngay thu ba giam 1 2% so voi ng ay thu haL Hoi trong
ngay thu hhat va ngay thu ba thl ngay nao co Tra ng ban duqc nhieu hoa. hdn?
ngay thu

Co Tra n g ban

Toan s

---

---

1

2

Bai 1 0.3. Mva n con lai 1 2%. Hoi ngay thuang khong h9 g ia thl ella hang dl!Q'C l a i baa n h ie u
phan tram?

3
1
c) 1 2 : - + 75°/o x - - 1 6 >< 5 0%)
2
4

1

d) 4, 25 3- + 6591> : 260o/o
�

Bai 62. Ti m x, biet:
b)

X :

2

2 0 % + 1 ,2

=

1 2 : 0,4

Bai 1 044

M¢t cera h a n g ban ban h k�o con m¢t so ba nh kh6ng ba n het trong Tet,
cua h a ng hi;l g ia -20°/o. Van khong bah duqc, cua hang l�i h? g i a 1 5°/o g i a da h? va ban
het so b a n h d6. Tu y v�y, c lt'a hang va n co n H � i i 5,6o/o. Hoi neu ban het s6 b a n h do
trong Tet thl cua hang lai baa n h ieu ph a n tra m ?

Bai 1 os. Neu

ba n m
phan tram so v6'i gia m u a ?
c) 1 25o/o

xx=

1 ,9 - 1 ,5

Rise above o n eself
g rasp the world

and

d)

X:

so voi gia ban thl avqc laJ bao nh ie u

3 0o/o + 1 , 1 5 = 1 ,1 5 X 1 0 1

Archimedes School

AschooLed u.vn


M¢t
5
dong. Bi et s6 tien l a i bang 25%

000

Ia 2
s6
von. Tfn h g ia von moi ch iec do n g h6�

1.

M u o n ti m tl �6 p h a n tra m

so a va

Bu6'c 1 : Ti m ti s6 cua a va -b.

BLJ'd'c 2: N ha n thu'dng d6 voi 1 00 va viet t h e m kf h i � u % vao ben p h a i tlch ti m duqc

h o � c doi th u'c m g d6 th� m h so t h � p ph2m roi ch u ye n s a n g p h a n tra m

Vf

Bai 99. Mqt cua

hang ba n t h t;fc pham sau k h i ba n h et h a n g da t hu ve so tien I a
3 4 5 00 O Q O don g Tlnh ra auqc l a i 25% s o voi von eta b6 ra. Hoi cua hang da bo ra
bao nhieu von de m u a h�mg?
.

.

1 : Mqt 16'p h Q c c6 24 hQc sin h n cr va 1 6 hQc s i n h n a m . Tfn h :

a) TI so p h a n tra m cua so hQC s i n h n cr s o voi to n g so h QC s i n h c u a ca 1 6'p.
b) TI s o phan tra m cua s6 h QC s i n h n a m s o v ai tong so h QC sinh ca l op.

a) Ton g so h9c sin h c a l op Ja: 2 4 + 1 6

TI so p ha n tram cua so

hQC s i n h

Bai g i a i

40 (hqc s i n h )

=

nu so vai to n g so h QC s i n h cua ca l dp Ia:

24 : 40

b) TI so p h a n tra m cua so h QC s i n h n a m

=

so

0,6

=

60o/o

v6'i tong so h QC s i n h ca I C1p Ia:

1 00% - 60% = 40%

Bai 1 00. Mqt n g u'O'i vay 20 0 0 0 000 don g vd'i l a i suat 1 % than g.

nguai a6 ph a i tra bao n hieu tien? (Bh�t lai avqc nh?p vo n
.

Hoi

sau 3 t h fm g
de tfn h lai tiep th a n g sa u).

Bap so: a) 60°/o

VI dt} 2 :

b) 40%

Ngay thuong m u a 5 bong h o a h et 1 0000 don g . V6'i so t i e n n ay n g ay Tet chi
mua dun g ay Tet ?
Bid giaf .

M9t b on g h oa n gay th uan g m ua het so tien Ia: 1 oooo : s

=

2000(aong)

M9t bon g h oa n g ay tet m ua het so th�n I a : 1 oooo : 4 == 25 00(dong)

Tl so ph a n

ban m(>t chi�c Tivi voi g ia 2 s ooo ooo do n g Tuy
nhien de thu h u t kha ch hang, eva hang quyet d!n h giam gia hai ta n lieh tiep, moi lan g iam

Bid 1 01 . M{>t c lia

hang di�n

tli d!nh

'

1 0% so voi gia ban trvoc d6. Hoi sau hai I an g ia m gia thl gia ch iec Tivi Ia bao nhieu?

Rise a bove o neself
t h e wo rld
and

.

2 . Bai t�p

tram g i ua g i a h oa ngay t h uong va g ia hoa ngay Tet Ia:

B i d 63 . Tim

a) 24 va s o

2000 : 2500 = 0,8

= 809.-b

8a p so: so%

ti s6 ph a n tram cua h a i s6 s a u :
b ) 1 9 va 2 0

c) 0, 1 7 v a 4

-d) J ,3 va 260

Arc h i medes School

Aschoo l .ed u.vn


ARCHIM EDES SCHOOL
Bid

64. NgVO'i ta d�t m<)t dogn day t ha n h hai dog n. f)o� n thli n h at dai 27cml do9 n
thu har d a i hdn doq n th u n h at 6cm . Hoi do� m day thlr h a i bang b a o n hieu phan tra m
OOqh day ba n aau?

Ngay th u 2 g i a m¢t cai but fa: 2 3 000 - 23 ooo

So tie n ban hang ngay th li hai Ia: s' 225

so

4.

Vf d� 7:

1 0°/o. H6i

a) 56

bi do ch i em bao n h i e u phan tra m_? -----,----,.-

b) So b i trang ch iE�m bao n h ieu phan tra m ?

_
_

_
_
_
_
_
_
_
_
_
_
_
_
_

X

( 1 5 - 5)

=

323 0 00 (dong)

X

40 + 20 000

X

0 1 0 9 6 = 9,6o/o

=

1 5 = 5 00 000 (dong)

Bili giai

ban sau khi g i a m g i a ta: 1 OO% - 1 .2% = 8 8%

1 1 0% : 88

N eu kho n g g i a m g ia thl l a i:
Vi

1 Oo/o = 1 1 Oo/o {gi a mua)

1 00% +

chi ban 88°!0 gia trvoc day nen cu n g l ugn g h a n g ay ban gia ng ay thubng se Ia:

16 20%

vai g ia

l� i v6'i

g ia

C o i gia

von m u a ha n g ia 1 00%

� so

h a n g thl

so

x

1 00 =

1 25 o/o ;- 1 OOo/o

d� 8: M<)t eva h a n g ban dugc

Ban

M9t tu i chua 1 o vie n bi a6, 2 0 b i trang va so bi xanh. Hoi:

850

Mqt cua ha n g quyet di n h giam .gia 1 2o/o cac m�t hang trong ngay rna van l a i
neu khong g ia m g ia thl etta h a n g lai bao. n h i e u phan tram?

pha n tram?

B il i 67.

850 (dong)

Coi gia ban l uc .c hva giam Ia 1 00%.

VI

b) C ua hang aa vliqt m uc ke ho�ch b a o n hieu phan t ra m ?

21

21

Bai toan ve tinh lai, lo khi tang h.o �c giam gia

Do lai 1 Oo/o nen so ti!�n ba n dugc I a :

a) Clia h a n g cia t h lfc hi�n bao nhieu phan tram ke ho<;�ch?

+

=·

·B ap so: lai 9,6o/o

Gia

Bai 66. M9t caa· h a n g d�t ra ke hoqch t h a n g nay b a n auqc 1 200kg 990, n h un g thlfc
te cua h a ng ban dvgc 1 500kg g (}o. Hoi:

5%

- Tong tien thu duc;;c sa u khi b an het h � mg Ia: 225 ooo + 323 ooo = 548 ooo (dong}

o/o tien lai I a: {548 ooo - s ao ooo) : soo ooo

so

.X

(40 : 2)

X

N gu'oi nay mua hang voi so tien Ia: � 000

Bili 65. Mot
ban nu. Biet so ba n n u n h ieu h on
. lop co so ban n a m bang .!
.
3
.
.
.
.
b9n narn l a 1 6 hQc sinh. Tfn h ti s6 phan tram s6 b 9 n nam voi tong so h 9c sin h l op d6.

Toan s - Quyen 2. 1

=

1 25 % ( g i a

25o/o

mua)

Dap so: 25%
a g thl

� s6 h n

thay l a i 20°/o, sau a6 ban so h a n g co n

m ua. Hoi cU'a hang ban het so hang thl lai bao n hieu .
Bai giai

so tien thu avq

c

Ia:

�

Bi;\n s6 hi mg cOn l<;�i thu duqc s6 tii!n Iii:

Tong so ti"en t h u dliQ'C Ia:. 96o/o + 1 6°;6 =

V�y cua hang lai: 1 1 2°/o - 1 OOo/o

=

x.

(1 OO% + 20°;&) = 96% (gia mua)

(1-�)

x

(1 00% - 20%) = 1 6% (gia m u a )

1 1 2% ( g ia m u a)

1 2°/o

£lap so: l a i 1 2o/o

c) S o bi xa n h chi�m bao n h ieu phan tram?

d) B a o nhiE?u phan tra m so bi kh o n g phai b i do?

26 1

Rise above oneself
a n d grasp the world

__
_
_
_
_
_

_
__
_
_
_

Archi m edes S chool

Aschool.ed u .vn


3:

MQt n g uO'r
b a n h a n g val g i a
sa n
Ia 5 0
ta ng g i a 1 0% . H o i n g uoi a 6 ba n h a n g vai g ia m 6'i I a b a a n h ie u ?

G i a b a n ta n g I a : 5 0 o o o
G ia moi I a : 50 000

V i d t;� 4 : Mqt

do n g

di n h

Hoi q u yen s a c h g i a m gia bao n h i e u p h a n tra m ?

+ 5 000 = 5 5 000 (do n g )

Da p so: ss ooo ao n g

n g uoi da n g

G ia ban giam Ia: 1 20 ooo

B ili giai

x

5 % = 6 ooo (dong)

ve tin h

� to

Tro n g vuO'n tro n g ba l o 9 i cay: ca m, q uy-t, b uo i .

Biet � to

n g so cay I a ca m ,

n g s 6 ca y I a q �yt, con . l 9 i Ia 1 5 cay bu'ai. H o i ca y b uoi ch iem bao n h ie u p h an tram

ton g so cay t ro n g vU'on?

mol Ia: 1 20 000 - 6 000 = 1. 1 4 000 (do n g)

3 .. Bai toan

000

1 Oo/o = s ooo (do n g )

x

b a n h a n g v&i gia 1 20 000 do n g mqt sa n pham va q uyet
di n h g i a m g i a 5o/o. Hoi n g lfo i a6 ba n h a n g vai g ia m6'i I a b a o n hieu?

Gia

g i � s o ooo a6ng da n g

MQt q uyen

Dap so: 1 1 4 ooo do n g

lai va lo khi ba n n hh�u m�t ha ng

fo avqc xac ain h khi cac m�t h a n g auqc ba n h et . To n g lai h ay lo a vqc tfnh
khi ban het h a n g da m u a .
- Ul i h ay

Vf d l:J 5 : M9t n g ubi m u a 4 0 chai n lioc v6'i gia 5 ooo don g m9t c h a i va 1 5 c a i b u t v6i
g i a 20 000 do n g mqt ca i ve b a n . N g uoi n a y q uyet d!n h chi lay lai 1 Oo/o m9t chai n uoc
va 1 5% m qt ca i but. Neu ban h et ha n g thl nglioi n ay l a i bao n hieu pha n tra m ?
Bid giai

N g vai n a y m ua h a ng v6i so th�n L3: 5 ooo

. So tien l a i kh i b a n n vac I a : 5 000
56 t i e n lai kh i ban b ut I a : 20 ooo

X

x

40

15

X

x

x

x

40 + 20 oo_o

15

=

1 0% = 20 000 ( dong)

1 5o/o = 45 ooo (do n g )

soo ooo (don g)

Ton g tiE� n l a i khi b a n het h a n g I a: 20 ooo + 45 ooo = 65 ooo (do n g )
_
P h an tra m s 6 tien lai Ia: 6 5 000 : 500 000 = 0, 1 3 = 1 3 %

Ba i

70.. M()t th u' Vi�n c6 so sa c h g i a o khoa
.

g a p ruoi s o sach g i a o khoa va con l� i

a ) Tfnh tong

s6 sach trong thu vi�n .

chh�m ±

t o n g so sach, so sac h khoa h QC

I a 750 q u ye n sach va n h9c.

b ) H o i so sach khoa hQC c h i em bao n hh�u phan tra m t o n g s o sach?

Dap so: 1 3 °k

Vi d t;� 6: M 9t n g tJO'i m u a 40 cha i n l16'c va

1 5 G�·i b ut ve ba n: Bh�t g ia ·1 c h a i n lfoc I a
5 000 don g, 1 c3 i b ut Ia 2 0 0 0 0 do n g . N g uoi nay q u yet d! nh c h i lay l a i 1 0% m()t c h a i
n uac va 1 5 % mb ut Sang ngay thu h a i q uyet d! n h g iam g ia moi lo� i h a n g 5% va ba n het h a n g . Hoi
n g uO'i d6 l a i h ay lo b a o n h ieu p h a n tram?
Bid

N g ay th u 1 g i a

Ngay thu 1

gia

m()t chai n u6'c Ia: 5 0 0 0 + 5 000

m9t ca i but

Ia:

20 000 + 20 000

56 t i e n ban h a ng n g ay thu 1 I a : 5 500
Ngay th u 2 g ia

I

giai

X

a n d g ra s p the wo rl d

X

1 0°/0 = 5 500 (do n g )

1 5%

=

23 000 (dong)

(40 : 2) + 23 000

m 9 t c h a i n ude I a : 5 500 - 5 5 0 0

R_i se a bo ve o n e self

X

x

So/o

=

X

5

=

2 2 5 00 0 (do n g )

5 2 2 5 (do n g )

Biti 7 1 .. An d9c mgt q uyen sach t ro n g ba n g ay. N gay thu n h at An OQC auqc 20o/o -so
t r a n g sach. Ngay thu h a i, A n dqc duqc 3 715% s6 t r a n g sach con I 9 L N g a y thu bar A n
OQC not 50 � ra ng sach.

a) Tfnh tong so t rang c u a q uyen s a c h d6.

b) Tfn h tl so pha n t ra m so tra n g s a c h A n d<;>c tro n g n g ay t h u h a i v6'i n g ay th u b a .

c ) Tln h t1 s6 p h a n t ra m so tra ng sach An a<;>c tro n g n g ay th u h a i v6'i n g a y th U' n hat.
Arc h i m edes S c h o o l

Aschool.ed u .v n