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5 - 1 1 ae u c h o h QC T6 m¢t c6 1 h a i 1 2 e m . 56 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 vien kE;o? I . A . N-HAN SO TH�P PHAN 1 . vO'i so n h ien - Lam tlnh nhlf I a n h a n cac so t V n h i en . 1 : 1 ,2 4 = ? X - f) � t dau p h ay d tkh cu ng v! tri v6'i dau 1 ,2 phay a so th�p phan. X 4 4,8 _ Bai 1 60 M <) t khoi h9c si n h tham gia dong dien. N eu xep 1 2 e m m ¢ t ha n g thl t h ua 2. Nhan so th�p phan vai 10; 100; 1000; .. • . • 6 em. Neu xep 1 4 em m¢t ha n g thl ding th U'a 6 em n h un g ft· cfi 2 hang . Hoi c6 N ha n so t h � p p ha n voi 1 0; 00; 000; tuc Ia d i dau p hay sang phai 3; . . . i u si 1 1 . . . a 1 ; 2; bao nh e hqc nh tham g ia don g dien? chG' so ttio'ng ung . Vi d ':J 2: 3,1 871 X 1 00 = 3 1 8, 7 1 3 . N han soth� p phan v6i so th�p phan - N han n h ll nh an cac so tl! nhit�n. Vi d �;� 3: 1 ,24 3,6 = ? X ---··· --------------------------- - sa hang th� p phan Ci tkh bang ton g so 1 ,24 hang th� p p h a n d cac thua so. X 3,6 + 744 3 72 4,464 4. N ha n so th�p phan v6'i 0,1 ; 0,01 ; o,oo 1 ; .. .. N ha n so thc}p p h a n voi 0 1 ; 0,0 1 ; 0,00 1 ; tuc Ia doi d au phay sa n g trai 1 ; 2; 3; . . . , . . . chu so t uong ling. Vi d l.} 4: 5 62,2 X 0,1 = 5 6,22 s . Tinh chat - Tfnh chat g i a o hoan: a x b = b x a Vi d� 5: 2,3 X 5 = 5 X 2,3 = 1 1 ,5 - Tfnh chat ket hqp: (a x b) x c = a x (b x c) Vi d �;� 6: (0,8 75) 1 25 7 5 X (0,8 X 125) = 715 1 00 = 750 X X .= , X - Tfn h chat phan p h oi cua phep n han a6i voi phep cc)n g : (a + b) X c = a c + b X c X 7: 2,5 X 613 + 2,5 X 3,7 = 215 (6,3 + 3,7) 2,5 X 1 0 25 X = = R i s e a bove o n es elf Arch i m ed e s School a n d g ras p the w o r l d Asc h oo l .ed u .vn
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ARCHIMEDES SCHOOL Toah s Q uyen 2.1 - B. (HIA SO TH�P PHAN Bai 1 56. M9t ddn Vi b¢ d9i can sang $6ng. N�u moi thuyen ch d 1 5 n g V6'i thl thlta C hia so so 40 nguoi chua duqc sang song. Neu moi thuyen ch6 20 n g uoi thl con t h ua 1 th uyen . 1 . th� p phan cho ty' n hh�n d9i Hoi c6 bao nh!eu thuyef} va dan vi b9 d6 co bao nh ieu n g uai? .- Tn..toc.het chia ph�n ng uyen ch so do. vr d'J 1: s,28 :4 = ! o -: Viet dau p hay vao ben p h a i t h u'on g 5J28� tr�oc khi lay chu so aau tiE�n (J pha n th�p 1 2 f 1',32 . p h a n ct}a s6 b j chia� 08 - Tiep tttc chia . phan th�p phan cho so d6. 0 2. Chia sotl! nhh�n cho so tl!nhien (thu'dng Ia soth�p phan) - Viet dau phay vao ben phai so thuong . Vf d y 2: 1 9: 4 ? n h6m di hai hong. Neu moi thl thua q ual = Bai i 57. M¢t b � n ru n h a u qua b�h 5 q ua 11 - Viet t h e m mqt ch u s o 0 vao b e n p h a i so 19 � neu moi b�n 6 qua thl m¢tb9 n khong ha i duc;;c qua nao. Hoi n h6m c6 bao nhieu b �Hi du va ti �l? tvc chia. 30 1 4175 Va hai OU(JC bao nhieu q u a hong? - Neu p hep c h ia van con dv thl viet them 20 m¢t ch a so 0 vao ben phai so du' va tiep tyc chia. 0 3 . Chia sot l! n h ien cho soth�p phan - f)em chu so hang th�p phan cua so chia VI d fJ 3: 38: 9,5 = ? roi viet vao ben phai so b! chia cung m ¢t � 380 1 chu so o. 00 4 - 86 dau phay 0 so chia roi chia n h li chia hai so ttj n h it�n. 4. Chia soth�p pha n cho soth�p phan bao Bfd 1 58. M¢t to xe c6 m¢t so xe tai, neu moi xe cho 1 5 9 9 0 thl con th ieu 1 xe, Bern xem co baa n h ieu cha so (1 ph�n Vf d y 4: 19,72 :5�8 :::: ? 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 � th� p p ha n c u a s6 chia thl c huyen dau 1 972 � nh ieu bao g?o? phay (j so bi chia sang ben phai bay 232013,4 nhiE�u ch u so. dau roi thlfc hi n 0 - Bo p h ay (J sO ch ia � p h e p chia n h u chia cho so tV n hien. 5. Chia soth�p phan cho 1 0; 1 00; 1 000; . . .. Ch i so th � p p han cho 1 O; 1 00; 1ooo; . ta chi vi�c ch uyen dau phay san g tn§i 1 ; 2; 3; a . . chu so. . . . "Vi dl:I S� 41 ,84 : 1 0=4, 1 84 Rise a bove oneself A rch i m edes School and g rasp the world Aschoo l . ed u .v n · .
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,.... ,...,. .,. __. .... phai m <?t so n h a u d a djn 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 f)�t roi . t[n h tfn h : m o i 1 40 I I t h ieu 1 00 v1 • n g ay chi d?t dVQ'C 1 45 c3i. Hoi' ngay va so ao aa d!n h theo ke h O<;!Ch c u a a ) 1 , 2 0,6 b) 5 1 4, 5 c) 7,92 : 6 ·d) 5 76 : 45 X X moi n h 6 m . Bai 2 . Tfn h: a ) 45,1 78 x 1 00 - 90, 32 b) 0, 1 862 1 x 1 000 + 3 1 8, 02 B a i 1 54 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 moi ba n ngoi 4 n g uai thl 2 nguoi chua c6 cho ngoi . Hoi c6 bao n h ieu nguai dlf hQp va bao nhh�u ban? 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 B a i 3 . llm y, b h:?t: Bfd 1 55 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 a) 0,4 X Y = 0,6 X 1 0 b) 1 05 : y= 7,46 - 3,26 .. 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 ? c) y + 1 ,59 = 1 2 x 2,5 d) 3,75 : y= 3 : 4 I R i se a bove o n e se lf Archi medesAschool .ed u .vnSch o o l a n d g ra s p th e wo r l d
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ARCHIMEDES SCHOOL Toa n s - Quyen 2. 1 _ Bai 4. Tfn h ban g each hqp ly: Bai 1 SO. Bac Tan thu hoc;lch xoai va cho vao hqp dem di ban. Neu moi 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? c) 1, 07x 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 th u ho�ch th6c, neu chia moi bao 35kg thl con thua 7 7 kg, e) 1, 98 : 1 2 + 41 02 : 1 2 con neu chia moi bao 40kg thl con thua 22kg. Hoi dQt <16 thu hoc;lch alJQ'C baa nhh?u ki-lo-ga m th6c? g) 2, 37 x 57, 8 +23,7 x 4, 22 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 vien 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 bao n h i eu tui? i) 0, 6 x 2�, 1 7 x 6 + 3 x 26, 83 x 1,2. j) 0, 8 x 23,6 x 3 -4, 8 x 1, 8 6 1 Ri se a bove oneself Arch i me des School a nd g rasp the world Aschool.edu.vn
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Lop m u a Neu m ua 4 q 90 q uyen1 neuquyen ? 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 .:!2:(3-�]=2,5 1 b) 1, 5 x y : 2 = 2 - 1 2 5 y . 7 . ( a101 2 2 c) 1 - 1 , 1 + y ) : 0 d) (y + 4 ) : 0, 5 + 1-:- = 1 3 - = 3 3 B a i 1 48.. An h c h ia tao cho cac ems n eu chia 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 chia tao? Bid 6. Ti m Y� bh�t: a) y x 3, 6 + y x 6, 4 = 1 81 9 b) 9,4 : Y. + 5, 3 : y = 1 4 Bid 1 49 . M¢t oia hang ban 9 9 0. Neu chia mo� tui 1 7kg thl t hieu 20kg, n eu chia moi tui thl th ieu Hoi c6 b ki-l o-gam g�o chia vao d) y : 0, 4 - y : 0, 5 = 1, 2 20kg 80kg . cua hang ao n h ieu va dU'Q'C bao n h i t� u t u i ? (moi tui co so 9 9 0 b a n g nhau) Bai 7 . Tfnh nhanh: a) 3 x (36, 2 -6, 5�) + 7 x 36, 2 + 3 x 0, 52 Rise a bove o n eself A rchi medes School g rasp the wo rld AschooLed u .v n
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ARCH IM EDES SCHOOL Toa n s - Quyen 2. 1 b) 258,93 x (76;1 -1 4, 3)�1 58, 93 x (72+ 4, 1)+ 258,93 x 1 4, 3 BAI 3: HAl' . H I EU SO. -. � I. LY THUYET 1 . Cac bliO.c giai d�ng bai t�p hai hi�u so Buac T: Tofll tat bai toan. Bciac 2: llm hi�u thanh phan. Buac 3: 1lm hi�u tong. · c) 1 5,2 x 34, 5 + 1 5, 2 x 471 5 + 84, 8 x 82 Buac 4: Tam thanh p han. Butte 5: Ti m tong. 2. ca c: d�ng bai t�p Vi dl}: Co g iao chia VCJ cho 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. 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 Bai giai Tom tat: 3 q uy�n /em : thua 4 quyen 4 q uyen/em : thieu 4 quyen Chenh l�ch so v& m¢t em giua 2 each chia Ia: 4 - 3 = 1 (quyen) Chenh l�ch tong so vo du chia g iua 2 each chia Ia: 4 + 4 = 8 (quyen) Bid 8 . Trung b1n h moi p h ut 6 to di duqc t2km. Hoi 6 to d6 di 45 km het "bao lau? (c6 thesadvngsado dexac djnh hi�u tong) 56 hoc s i n h I a: 8 ; 1 = 8 (em) Tong so vo co giao chia Ia: 8 X 3 + 4 = 28 (quyen) fla p so: 8 em, 28 quyen vC:J Bai 9. Hai t h u n g c6 tat ca 2 1 4,5 1 ft dau. Sau kh i do 1 0, 5 l it dau tv t h u n g thu nhatsa ng · - II. LUY�N T�P thu n g. thu hai thl .so dau (J th u ng thu n hat b�ng � so dau b thu ng thu hai. Hoi ltk -oai 1-46� -ch! cho cac neu moi em thl thua neu moi ch ia k�o em, 6 chiec 4 chiec, e m 3 va uq2 ��o? c6 a dau? 8 chiec thi thiE�u 6 chiec. H6i c 6 bao n h ieu chiec k�o baa n h ieu em d 'chia dau moi thung b o n h ie u 1ft 8 1· Rise a bove oneself Archi medes School and g rasp the world Aschool.edu.vn
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40% Ia n a m . kl I I, ti m so t h � p so sao 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 n6 cho n h a u thl g ia cua so d6 ta n g l e n 1 0 i a n . l op n hiE�u 1 1 . Tln h : a ) 1 1 6 7 4 1 - - o 6 + - b) - + 1 - - 0, 8 6 30 30 1 5 � I Bid 1 44 i M9t g ia sach c6 3 n gan. So sach & ngan thu n hat bang 66 <vo so sach b .. _ nga 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 gia c6 - tat ca bao n h teu q uye n sac h ? Biet ran g ngan thu ba nhieu han ngah th d' hai I a 45 quyen sach. c) 2 9 d) 1 . 3 5 2 - : 2 + 1 8 - -5 3 1 2 x - + 1 6 x - .:... 3 6 x -2 4 9 . ' 1 I 1 4 Bai 1 45.. Trang s6 hQc sinh t h a m g ia lao a¢ n g b uoi sang, 40% Ia hqc sinh 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 hQC s i n h lop 6 giam 75°/o, so hQc sinh lop 1 tang 25%, so hQc s i n h lop 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¢ng b u oi sang? 1 . 1 1 f) l : 1 7, 5 x 24 + 1 3, 4 x 24 - 7, 9 x 24 e) 1. 5 : ...:.. + 0, 4 x - + 1 - _ 2 6 3 1 + 4 +7 + .. + 55 + 58 - 39 x 1 1 Rise a bove oneself Arch i m ed es School a n d g rasp the w o r l d As choo l . e d u .vn
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· ARCHIMEDES SCHOOL Toan s - Quyen 2. 1 qs,9; . Bai 1 2 Cho day so; _1 , t ; 2, 2; 3r3; . � · ; 1 1 1 0,0. 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 .. s6 c6 s6 ta ng them 20%? a) Day nay bao n hieu h9ng? b) So h�ng thu 30 cua day Ia so nao? Bai 1 3 . Cho day s6: o, 1 ; o,o-1 ; o,oo 1 ; � . . a) So h�ng thu 1 ooo c6 bao nhiel.J chCrso o pha n th�p phan? 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 1 5% · chieu r¢ng thl di$n tkh ta n g them 20o/o dm2 • b) 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 nhieu chu so 0? Bai 1 4. Cho day c6 quy lu�t sau: 1,21 ; 1,23; 1 ,25; 1 ,27; . . . ; 2,3 1 . a) Day tre n c6 baa n hieu so th�p phan? b) Tfnh tong cac so th� p p ha n cua day tren. Bili 1 42 . Khoi l ugng cong vi$c tang l en 50% n h ung nang suat lao a¢ng chi tang 25%. H o i phai ta n g s6 c6ng n h a n len bao nh�eu phan tram ae h o a n th� m h cong vi�c du n g thai h � n ? · Bai 1 s. nmx 1 biE�t: a) (x +O�S)+(x +0,25)+(x+ 0,1 25) + (x + 0, 0625) = 1 Rise above oneself Arch i m edes School a nd g rasp the world AschooLedu .vn
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Do i : 3 2o/o = 0,32; 1 Oo/o = 0, 1 . N eu coi kho i l uqng c o n g vi?c.cu Ia i adn vi t hl khoi 'h iqng c6n g vi�c m6'i so vdi vi�c cG Ia: 1 + 0,3 2 = 1 ,3 2 Neu cof nang s u at l a o dqng c G I a, 1 ddn vj n a n g suat d() n g mcri so v6'i. nang S U ai(t l.ao uqng cu .a:..=f " _ , , 1 + (\ 1 = 1 1 V y I f)e th{jc h i�n dvqc khoi l vqng c6ng vi$c moi voi 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 tram so c6n g n ha n p h a i ta ng them so voi so cu Ia: 1 ,2 - 1 = 012 = 20o/o 2o% c) x x 01 1 + x x 0, 3 + x x 0, 5 + �. + x x 21,7 = 2376, 2 Bap so B a i t�p .. Bai 1 3 7 M(lt so sa u khi g ia m di 20o/o thl pha i tang them bao n h i e u phan tra m so m oi de l�i au'Q'c so cu? · · ( J d) 23 3 0 , 44 x x + x x 5 - - + - x 2, 24 = 1 55 1 4 B a i 1 38. M<?t so tan g them 259·6 th1 phai g iam di bao nhieu p h an tram so moi de l9i . du'qc s o cu? .. B a i 1 39 Di�n tfch cua m<)t hl n h chu n h�t se thay doi the nao n eu tang chit�u dai cua n6 l e n va giam chieu r<)ng cua n 6 di 20%? B a i 1 6. T111h hqp I f: 20% a) 2, 3 + 2� 7 + 3, 1 + 3, 5 + ... + 24� 3 + 24, 7 Rise above oneself Arch i m edes Schoo l a n d g rasp the worl d AschooLe d u .vn
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ARCH I MEDES SCHOOL Toan 5 - Quyen 2. 1 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 mQt so h3i toa n ve ti so phan tram.. co the h LJong dan hQc s i n h alia ve cac dc�mg toa n q uen thu9c nt;lti tong - ti, hi$u - ti,. . . de· t1m ra_ da p so n ha n h han, de hi�u hdn. · Vf dl;l l : Tong cua hai s6 bang 25% thucrng cua hai so d6 cung bang 25o/o. Tim hai so d6. Bili giai: c) 1 0, 1 +1 1, 2 + 1 2, 3 + 1 3, 4 +...+ 93,7 +94,8 Ta c6 sa do: so thu n hat: }0,25 so thu hai: S6 thu nhat Ia: 0,25 : (1 + 4) 0,05 = so thu hai Ia: o,25 - o,os = 0,2 £>ap so: o,o5; o,2. Vi d� i: Gia g iay viet nam nay bang 1 20% gia· giay n a m ngoaL Hoi val so tien mua du<;1c 1 50 t� p g iay & th ai ctiem n a m ngoai thl n a m nay m u a du'<;1c bao n hieu t�p g iay? Bai 1 7. .. Tong cua hai so la 1 2,4. Biet so th u nhat bang � so th u haL llm hai s6 d6. 3 Bili giai: n s6 ay a nay so vai nam ngoai 1�: 1 2091:1 6 gia gi n m = 5 Vi cung m¢t so tien t h1 s6 g iay mua duqc ti I� ngh!ch voi ti so gia nen sO tien d6 nam nay m u a avqc I a : 1 50 x 5 : 6 = 1 25 (t� p) f)ap s6: 1 25 t� p giay. Vi d�;� 3: Kh6i h.tqng cong vl�c tang 32°/o. Hoi phai tang so nguoi lao d¢n g them bao _M9t n hieu phan tra m de nang SU!lt lao d(>ng ta n g 1 0%? B�ti 1 8. hlnh ch G' rih�t co chit�u dai gap rllfli chie u r¢n g . Biet c;hieu dai lon hdn chieu r(>n g Ia 2,4cm. Tfrih di�n tfch hl nh cha nh�t do. Bai giai ca�:::h 1 : Neu coi khoi I VQ'ng cong vi$c cO Ia 1 00% thl khoi luqng tof)g vi¢c mC1i so vC1i cong vi�c c:u Ia: 1 OOo/o + 32o/o = 1 32%. Neu coi na ng suat lao d(>ng cu Ia 1 00% th1 n a ng suat lao d(>ng m6t so voi nan g suat tao d<) ng cu Ia: 1 OOo/o + 10% = 1 1 Oo/o f)e thtjc hi�n avqc khoi h.tqn g cong vi�c moi voi nang suat lao a(>ng 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 ng them so vai so cu I a : 1 20o/o - 1 00% = 20% Dap so: 20% Rise a bove oneself Arch i medes Schooi a nd g ra s p the world Asch o o l .ed u.vn ·
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9 1 .3 3 S o/o s o c6 Ia 1 1 2 hai. 9 hln h thoi a6. 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 nh ieu ngu'di ? B a i 20. Tong cu a h a i so th�p p ha n Ia 22,5 va hi�u cua chung Ia 1,22. Tim hai so t h� p phan d6. Bai 1 35. M9t tinh c6 2 tri�u dan, trung bln h moi nam da n so cua tin h d6 l�i tang 5°!0 so voi nam tni6c. Hoi hai nam sau, tinh d6 c6 bao n hieu n g ucri? B ili 2 1 . ll m hai so c6 th llcmg Ia 2020 -va- hi¢u cua chung 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 them 1 0% so cong n han so voi nam tru6'c. Hoi sau ba namr n ha may c6 tat ca bao nhieu cong nhan? Bai 22 Ti m h a i so c6 tong va thudng cua chung aeu ban g 0,25. .. Rise above oneself Archimed es Sch ool grasp world Aschool.ed u.vn
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ARCH I M EDES SCHOOL Toa n s - Quyen 2. 1 Bid 23. Tt m· hai so co thvang va hi�u cua ch ung deu bang o,s . G. BAi TOAN LIEN QUAN £>EN DAN SO · 1 . Ly thuyet 56 dan nam· nay = so dan nam tnJoc a6 + % s6 dan n a m tnJac d6. Vi d�: Cuoi nam 2000 nvacta c6 78· tri�u nguoi Hoi cuoi na m 2002 da n so nuoc ta Ia . ba o n hieu neu moi nam dan so tang 2%? Bai 9iai Bai 24. So sanh: A = 2, 1 93 x21 9,9 va B = 21,96 x 21,96 . So dan nam nay = s6 dan ·na m tnta a6 2% so dan nam trvac d6. c + Cuoi nam 2001 sod a n tang them Ia: 78 000 000 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 ,-1_., � f)au nam 201 8 cua tri�u Dau 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 Bai 1 3 1 . da n so Vi�t N a m khoang 95 nglf<:ti. na m 20 1 9 be thl duqc thudng Ia 3,4va du 0,024. dan so cua Vi�t Nam khoan g 96,9 tri�u ngubi. a) Hoi tu dau nam 201 8 den dau nam 201 9 d a n so cua Vi�t Nam ta n g them bao nh ieu phan tram? b) Neu tu ctau nam 201 9 den dau nam 2020 dan so cua Vi-�t Nam cGn g ta n g vai ti l� tre n thl dau nam 2020 dan so cua Vi�t N a m Ia bao n h ieu ngVai? Bili 26. Bao thu n hat n hieu hdn bao th u hai 25,4kg g9o. N eu cho them vao moi bao 1 ,7kg 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. Bid 1 32. Dan so cua m{>t xa cuoi nam 201 8 Ia 1 0 000 nguai. Biet rang ti I� tang da n 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? Bai 2 7 . Tfch cua hai so Ia 3 3,375. Neu tang thua s o tha nhat 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 Archi medes School and g rasp the world Asthool .�du.vn
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65%. n h �t bay h ai I a bao n h ie u ki- l o-g a m vi h1 n h c h u n h�t m 6'i gap 5 l a n di�n trl n h phai say kh o n g c 6 s lj h a o h l:Jt nao khac n g oa i n lfoc) . B a i 29 M9t hlnh chu n h�t c 6 ch u vi 26dm . Biet rang, n eu tang chiE�u dai l e n gap 2,5 .. lan thi c h u vi se hang 38dm. Tfn h chieu dai va chieu n?ng hln h chu n h�t d6. Bid 1 30. Nguoi ta p h oi 780kg th6c tuail sa u kh i p hoi thl kh6i higng th6c g i a m 1 30kg. Tfnh ty so phan tram g i ua hiqng nu'oc va h Jqng thuan h � t c6 tro n g th6c da phai Biet . rang trong th6c tu'd'i n u'oc chiem 25o/o va trong q u a trl n h p hd'i khong c6 slf hao hl:lt nao kha c ngoai n u'6'c. Bai 30 M(>t a(>i cong n ha n da l a m. xong q uang duong AB trong 3 tuan le. Ju� n .1� .. aa u n g u'oi ta lam au'Q'C 0,5 quang au'O'ng . Tuan le th u h a i l a m duqc 018 quan g dvang con l � i. Tuan le thu ba lam duqc 3,5km n ua thl xong to�m b9 qua n g aU'C1ng AB. Hoi quang duong AB dai bao n h i e u ki-16-met? Rise above o n eself Archimedes Schoo l and g ra s p the wo rl d As c h o o L e d u .v n
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ARCHI M EDES SCHOOL . Toan s - Quyen 2. 1 Bai 3 1 . Cho 56 20l 9. So nay se thaydoi the nao neu Bai 1 25� Lvc;tng ntt6'c trong h C;\t htoi chiem ty I � 48%, trong kho chiem I� 1 0%._ : h�t ti a) VH�t them dau phay vao gi U'a chii' so 1 va 9� Hoi phai 1 ,08 tan h9t tudi se duqc bao n hieu ki-lo-gam h9t kho? Bai 32. Cho m()t s6 .th�p p han c6 hai ch u. s6 a phan th�p phan. So nay se tang g iam f)� bao nhieu lan neu: 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. c6 340kg h<;�t kho thi can dem pho'i bao n hieu ki-lo-g a m h�t tuui? a) Bo dau phay di: b) Chuy�n dau phay sang ben trai m¢t hang: c) Ch uyen dau phay sang ben phai m¢t 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. dau phay Tinh ti so phan tra m giua l u'Q'ng n uoc vii l lfqng th uan h�t co trong h9t aa phdi kh6. d) Chuyen sa n g ben phai hai hang: Biet di ng trong h9t tllO'i luqng nuoc ch iem ti l� Ia 20o/o? Bid 33. Cho so 2 1,89. Hoi so nay se thay doi the nao r:eu: a) Xoa bo 2 chO so cr phan th� p p h a n : b) Thay cac chu so 1 bang chu so 9 : 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 Bid kho. Hoi lliqng nVdc can bay h ai di Ia baa nhleu ae lu'qng ca phe kh6 th u .alfqc chi c6 34. ti l� nvoc Ia 4%? a) 1 3,52 ba ng bao n hieu lan t352? Bap s6: _______________ b) 2,0 1 9 bang bao n hieu lan 0,020 1 9? f)ap so: c) 0,362 bang bao nhieu la n o,00362? Bap so: ______________ d) 216 bang bao n h ie u lan 260? 8a p so: ________________ e) 0,1 045 ba ng bao nh h?u la n. l 04,5? Dap so: ______________ 16 1 Rise a bove ones e lf Arch imedes School 49 and g rasp the World Aschool.ed u.vn
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dau p h ay c u a so 1 8, 1 7 1 don vi. Ti m sa th� p p ha n d6. Ta c6 sO' ao: ( 1 OOo/o) (1 OOo/o) Phoi H9t tvai Bai 36. Kh i d �ch ch uyen dau phay cua so th�p phtm S Q n g phai m <)t h a n g t hl so a6 tang them 469,683 ao'n vj. Ti m so th�p p h a n d6. Nvac A Th u a n h9t Th u a n h 9t N uoc B (= N uoc A - n voc bay hoi) Chu y: Lu't;tng thuan hqttrong hgt tUai va hQt kho la bang nhau. 0dgng bai nay luon can tim au'qcsolu'qng thuan hqt tn.tac. (Thuan h9t Ia phon hgt khong chua nuac). . . . . . Vi d �: Phai 3,6 t� th6c tu'oi t hl avqc bao n h ieu t� th6c kho? Biet l uqng n uoc tro ng th6c tuoi Ia 3 0o/o va trong th6c kho Ia 1 0%. Bid 3 7 . Khi dich ch uyen dau phay cua so th� p phan sa n g trai hai h a n g thl. so d6 sai giai g i a m di 2 1 0, 1 77 adn vi . llm so th�p p h a n do. Bai 3,6 t� = 36ok9 LVqng h�t thuan I a : 360 x ( 1 oo - 30) : 1 oo = 252 (kg) Trang th6c tho th1 h.tqng h9t thw3n chiem so phan tra m Ia: 1 00°/o - 1 0°/o = 90% LVQ'n g th6c kho thu duqc Ia: 252 : 90 x 1 oo = 280 (kg) = 2,8 t9 £>a p sO: 2,8 t? Bili 1 23 Luqng chua· trong h 9 t tuai Ia C6 s a u khi phai kh6 Bai 3 8. Ti m h a i so th�p p h a n c6 h i� u Ia 1 1 5,7. Neu dai dau phay cua so be sang phai n ttoc 55°/o. 3 00kg h 9t tttai .. n h � di SOkg Tfn h ti so p h a n tram nttoc trong h�t da phoi kh6. · m9t hang, roi c9ng -voi so lon ta dugc 1 66,3 . . Bid 1 24. LVQ'ng n uac trong co tuai I a 5 5%, trong co kh6 I a 1 0°/o. Hoi p hdi 1 50kg co Bai 39.. Tong cua h a i s o th�p p h a n bang 1 1 6,55 4. Neu djch dau p h ay cua s o thu n hat tutti ta auqc bao nhieu ki-lo-g a m co kho? sang ben trai hai c h O' so ta se avqc so thu haL Tt m hai so d6. Rise a bove oneself Archimedes Sch ool and g ra s p the world Aschoo l .ed u .vn
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ARCH IMEDES SCHOOL Toan 5 Quyen 2. 1 - . Bai 40. Hi�u cua hai s6 th�p phan bang 1 23,75� Neu d!.ch d au p h ay cua so th U' nhat. Bili 1 2 1 . c6 50 tan q u�ng sat chua 55°/o sat. Sau khi trqn them vao 30 tan qu�ng sat sang ben .ph a i hai ch O' so ta se avqc so th u h a i. Tim hai so a6. 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 so 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 1o�i I I, tong kh6i lvqng Ia 1 2 tan khoi sat n g uyen chat trong qu� n g lo�i I Ia 1 ,8 tan/ trong qu�ng lo�i I I Ia 1 ,6 tan. Biet ti I� sat ng uyen chat trong qu� ng lo<;1i I hdn ti I� sat nguyen chat trong qu�ng lo�i II Ia 1 Oo/o. Tinh khoi luqng moi lo�i qu� ng� 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. -----------------------------------------------------�------� 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 sang trai m<?t chu so ta auqc so t h u hai, dich dau phay c u a so th.d hai san g trai m¢t c h u s 6 ta au'qc s ot h u ba. 18 1 Ris. e. a bove oneself Archimedes School and grasp the world AschooLedu.vn
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1 n uoc I a 3 5 ba o n h ieu ki-1 6-g a m n voc I a de avqc m ¢t lo«? i d u n g d j c h c h ua 2% m u 6 i ? thl auqc h a i s o co tong I a 84,6. Ti m h a i so d6. 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 Bai 45.. H i�u cua h a i so Ia 7,9. Neu ta tan g m()t s o len 4 !an va g iu n guyen kia thi · 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 duqc h a i so co h i¢u Ia 46. Ti m h a i so do. 1 0% muc>l? · Bi d 1 1 9.. Pha 650g d u ng d ich m 16'c cha nh chua 1 2°/o c ha n h ng uyen chat va 3 50g Bid 46. H i�u hai so Ia 60,7. Neu so tru gap len 2 la n t hi dvqc so moi lon han so b ! tru d u ng djch n u6'c_ c ha n h chU'a 1 5% cha n h nguyen chat thl dvqc dung djch chva bao da 2818. nm hai so cho. n h ieu phan tram chanh ng uyen chat? Bai Hai so t h � p p h a n c6 ton g Ia 60,9. Neu d O'i dau .phay cua so be 1sa n g phai Bid 1 20. Ngt10'i ta tr¢ n 35 tan qu�ng sat ch ua 72o/o sat v6'i 1 5 tan q u � ng sat c h ua m(>t hang, roi trlt di so ldli thl Ou'9'C 2 1 018. TJ m h ai SO 00. 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? Rise above oneself g ras p the world
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ARCH I M ED ES SCHOOL Toa n s :- Quyen 2 . 1 · Bai 48. 11m. hai sci th?p phan co tong Ia 76,8. N�u d oi dau phay cua so be sa n g trai E . BAlTOANVE PHA TRQNDUNG DICH, QU�NG m9t hang, r6i l ay h i�u gl ua so lan va no ta dtic;:fc 3 7,64. Pha i ao n VO'c /o bao n hieu Vi d l:f 1 : them vao 1 20g dung djch cam chua 1 5° ca m g a m m..toc Ia de ':'fliQ'c dung dich n uac cam chua 1 Oo/o cam ? Bai g i a i · 56 gam nu6c cam nguyen chat Ia: 1 20 x 1 5 : 1 oo 1 8 (g) = Kh oi IV<�ng dung d(ch Ide sa u Ia: 1 8 : 1 o · x 1 00 1 80 (g) = Kh 6i luc?n9 nuac Ia pha them Ia: 1 80 - 1 20 � 60 (g) 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 hang ta duqc so C . Tong cua 3 so A, B, C U1 . 1 3 51975. Bap so: 6og ·vi dy 2: M9t nguoi tr(>n 3 tan. hon hqp qu�ng chlia 45o/o Ia sat v6'i 7 tan h6n h<;tp qu �ng ch Lra 55% Ia sat. Hoi se dvqc h o ri hQ'p q u� ng v6'i bao nhieu phan tra m sat? Bai giai Lu'Qng sat trong hon hqp thu nhat Ia: 3 X 45 : 1 00 = 1 ,35 (tan) Lu'Qng sat trong han hqp thu hai Ia: 7 X. 55 : 1 00 ;::: 3,85 (tan) Tong l uqng sat Ia: 1 ,35 + 3,85 = 5/2 (tan) Bai so. Khi tru m9t so tV n h ien di m<)t so th�p phan co m c)t chu so d phan th�p % sat trong hort hqp l uc sau Ia: 5,2 : (3 + 7) 0,52 52% = = 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 nhien V �r van E>a p so: 5 2% danh dau phay (j ket q u a thu Ou'Q'C. tha n g hang voi dau phay cua so th�p phan. V1 the 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. BiH 1 1 5. Phai pha 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. fYl{>t ngVoi do the 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 nh�n du'Q'C m(>t blnh chua bao ·n hieu p h a n tram. muoi? Bai S 1 . Tong cua m{>t so th�p p h a n vai m(>t so tV nhien Ia 47,5. Khi c<)ng hai s6 nay 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 ket qua Ia 1 60. 11m hai so ban aau. Rise above oneself Archi m edes School 1 45 and gra s p the wo rld Aschoo l .edu.v n
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5 - m ua H i�u l a 80,5. so m ()t da g i a m 1 5 % g ia t ien m ¢t h()p so v6'i g i a n it� m yet. N g uoi a6 eta ma ng ve ba n l q i va q ue n d a u ph ay 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 b �a n g - m u a . 40. 1 20�lLo so 3 Hoi g ra n i em yet m oi cua mqt hqp sO'a Ia b a o n h ie u ? Bai 53e Khi c h i a m qt so th�p p ha n c6 c h u so a h a n g th�p phan Ia 5 cho 1 251 m9t hQC sin h 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 so vai ket qua du ng Ia 5,984. Hay ti m so th�p phan a6, biet rang ca h a i tnJong hQ'p deu Ia phep c h i a· het. . M ¢ t eva a ng ban �so hang v a dliQ'c l i H vai gia m ua . So con l 9 i b a n Bid 1 1 3.. h 20% s o l o 1 Oo/o s o voi g i a mua. Hoi kh i ban h et s6 hang, eva h E m g Ia hay lai v a l o la i b a o n h i e u phan tra m ? Bid Thay cac c h u ca i bang c a c c h Ct s6 t h fch hqp: a. 3a,b x O, b = 1 6, a b; b. a, be x 4, 1 = 1 5, a bc; c. a b, a b : a,b a b, a; d. aa/ a a : a b , a = a, a. = Bid 1 1 4. Mqt cU'a ha ng ban 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 hang giam gia 30o/o so hang .con l � i va da b a n het. Hoi cua hang l_a i hay Ia va lai lo bao n h ieu phan tram so vOi g i a m u a? Rise a bove o n es e l f Arch i m edes School and grasp the Asch ool .edu.vn
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ARCHIMEDES SCHOOL Toan s - Quyen 2.1 BA I 2:, . Tl; SOK' PHAN TRAMA v Ba i 1 1 0. Co 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? J. LY THUYET b) Sau 2 than g co Ha c6 bao n hieu th�n lai? Biet liH cua thang tnJac dl1qc nh�p vao Tror:tg toa n hqc, phan tram Ia ti so the hi�n duoi d�ng phan so c6 mau so Ia 1 00. von tha n g sa�. · cu a Tuy n hien, nguoi hi�u de thay ch? so a so Ia . . . ta th vang d u ng ki 0/o cac phan c6 m u 1 00. I, u: 5 1 25 12 1 89 . V d . = 5% , - = 1 2 5o/o, = 1 2°,-b;- = 1 89% . - - . 1 00 1 00 1 00 1 00 Chu y: Cac so tlj n hien cuhg co the doi sang phan tram. u 1 1 00 %;1 2·= 2 2 9t> VI d . : = ;:= 1 00 1 00 = 1 00 1 00 1 00 . + f>O.i SD th�p phan sa n g phan tram: ta chi can d!ch dau phay sang phai 2 hang va · them kLhi�u %. Vi dl:l: 1 134 = 1 34%; 0,345 = 34,5%; 2,5 = 250o/o + Boi ph an so sang pha n tram: I �•:, • Cach 1 : Chuyen pha n so sang so th�p phan rei doi sang pha n tra m . II u: 1 1 3 = V d - = 0, 25 = 25o/o; - = 2, 6 260°/o. . 4 5 N ha n phan s6 d6 voi roi h i�u 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 Cac h 2: 1 00 them kf %. thang co n h�n du<;1c 450 ooo dong th�n lai. Hoi: V' d1 u: - = - x l 00% = 35%7 7 . a) Tfnh goc ThQ eta luc da u . s6 tien ma co g ui . 20 20 f)oi p han t ra m sa n g phan so ho�c so th� p p han nhv phep chia voi so 1 00. 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. 26 = Vi du: 24% = 01 24; 26% =. 1 00 5 0 II. cAc D�NG BAI T�P A. TfNH TO.AN Kh i g�p cac phep tinh co chua phan tra m � ta· phai doi phan tra m sa n g so th�p phan ho�c phan s6.roi thtfc h i�n nhti bl n h thuong. 1 2 7 - 4 ·27 B " · ss.a1 v· A't1e cac., so sa u th 'anh t"1. so"" ph �an tra m :... o,3·7 ; 1 ,26; 0,405; ; - ; 1 - ; - . • "' . - 50 8 1 25 1 2 Rise above oneself Archimedes Scho o l and gras p the world ·Aschool.edu.vn
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