2017 Summer Assignment MATH 601: Math 6 MATH 601A: Basic Pre-Algebra 6

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1 2017 Summer Assignment MATH 601: Math 6 MATH 601A: Basic Pre-Algebra 6

2 Summer Math Review Packet MATH 601: Math 6 MATH 601A: Basic Pre-Algebra Newfield Avenue Stamford, CT (203) Please complete the worksheets that follow and return them to your Grade 6 teacher in the fall. Optional websites and apps that can offer additional math practice: o Thinking Blocks section specifically related to Singapore Math o Thinking games for math Knowledge for the Journey

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6 - âl j3ðrd ri+ðw -"tod çt ÛBÐ 'Ð? O t 8 C 1c i8!lt!t yz ú!-ç "81 Al f4 çc ÌÐ VL t{, c1 7 UI { 'fri u/ 8t t rjl rl fìl

7 sefrse Ëfue ËelEæwËmg prøhícms. sfuew vr;er wøyk. Gtnpt*+e Al'l "-* Å A z-. U 6,rJ88 4,8? ,459 Ë 23_ 2 ç,9t4?6. 3 j, i 3 i FËãÍ En ææeh bïænf.wñrtu Ífte eæ*ecr e zs *sen Cop+i-n"_t ) x2Ð:--X--ieirs = -- fens 2A" 69x4t: _ x _Èens -- Ei ò.5-ë) Singopore ivtqål P -ccíice,

8 Cornç\e--{e bo-l4n u :ord?rôbl c,lnrìs ;;;"*;;;;;;;;"'nïtå-i.";;;;"ã;äl=:;;;;;;";;;;;"ï,"åçrr;-lãffi ;;; be ughi 7 suf*sa -ds í*r he " ehìeeire rt. w?nivs.a-s her iüiae biii? i + ë ë * e = ë + r, = e = è ç È I e? = ê è I + + É ê ç z è2 e = e + e + e z ë 9ãê s, É åè É = á ç í tt*- Saåtir *=k+d 25* cu-**=f=*s Ë+r ihe bak"+ sa!*, Sh+ sofd,õ*7c +f ihe cupca-k+s En åh= n':*me*g i ðz{ o/* *Êirz= -e - c=inde- ' sr ihe aë-ont+gn. H=,. 1 å?iêe-iþ *zsp=akes dêd she s+åë? H*,.d îr.afty cup-*etles #åd *cë s+!ë.? æz 'ê +?-Ð F=- -Í.-t=t-E+--s +rqct,= -,.- rr+{; ='=æ. ==.??"Èc7r+= =-5.*.v.+ 3

9 58.,{ fcciery niakes 2,275. ciches in a v- eek. -#o'+ ri",ãn-v wctcheé'd*esii nrake in 3 davs? EZ.,Ashirt costs &.283 *nci * Ìie casis Ê e. Dc' id -baught 4 shiräs cnd 3 ties. llo'ro ri^ruch did he spenc clicgether? SG. A pui-se cot' s 4izmes cs n-uch cs c.jress.!ithe purse cosis 927&, hcw much doesa -rnu c -r+n.i nn fhe nirrse and.3 cresses? JrJUr u G-ft 'rrøjprõbtøøts 34 Singcpore Vlcih Prsctice

10 @E-- 'i- L I"t t ÈL 4.3 Àt I JC ådë Ê}tese Eyigez": æns. =ÞgrEËe efr h #ns'éìrer n Ë?s sircpéest forcfi" 'jd r -F- -i- -= - 7"-ç 'rz- 6-12: 5&" ru,/ -) ' 't{1 ' 1ft - L I-L,l Il.i U +l< -:'--1- ÊÜ! ' I r- - tr2 F,4 J! Lj _ ç/1 - rl-a,t,fi 1'8'4 i3s!^!-- {IJLJ u// Subfreet fhesc fraefeans" Wrfte ee h ee? /L {,-Û./ I 4 1,/4 Drj,t/L ' õ 'tj 4 -_-: 7i l- Å I 62. -it- ñ t-lj aì 7 =-ã rlt Ð _-: 4

11 S*Eve zê=e *r*fuec-mes e*i*l t,j /l. ^- +i " ^ tt t-í : =îi vã';- f '- t àê. t ^.+ zl vt t L -r - rju: { J- -, /4 ir.j = ^- - : í-,ç -i G1 _ -À.1 \-/!4 - L't _ Å'= e 4 i _f I F _ ri! -J - r.j 4 I V '; I - 7i. Au+?*: ti -7' - -ì,i x&4: S*E s= Êfue E*EEa=*eEæg frkø"éf yæéåí -w-ævè< E-* ÊLze ÊFæ*æ -fuei*=as" t 77 " J+di bck+ ð = ca'<ç, She gûve * "î iå?+ her ;,e!ghb+i '#hai ir+cic* *f the c+ke c;c sne ö hcve!ei+.?! 1J- Ar, er.r-çt ccn hcs c riìcss "f t ãb. Hhen it is filiec r'çiåh scn,*, ií hc's ü rncss "t + ihe mass +i the sanc i*?he cc 'l ib. Fi ':d Si n r:+ ns;r= i.l,.r ;h P r - rii

12 -.Wî -=w-{4,srgþtøgs t2#.j,;lia* m*wæ44 Êa-'*r n= i*r $1 4 eat* æ-*ú 2Y ijt* lavo ns fcr fi/haå E= the ã,.jerage pe!îti*rij'uii.=.n re+e1vo*' íæi the 6Eæ' ' **7 &4is *a+h. *E*vn'n ha-s +z+ë +e *e+-+12eee?e+zz+e=+è=-? èe9a? É2=-+92>+ c!+-r rns?21,i* a =Ez* 15 sh*+, 3 ee+w -s ha';= a- s!e+ t* sh+e, Êg a =Ez* 12 sh+=,\nha+,es ih+ =*:,iei=-g+ =hee s!z+ af åh+ 3 *[*' *ns? I 7'*=t<=P..E?=*=t=-iús=c=-8'1=*='->=''-é.:'Ét?: +?*Pt;7t+=

13 sorve-,.*",,ff.ff.r,::]-,,ïî:ï-.:-:',ff.:re,ow 1&. There were 32 children c t c party. There werê I mcre boys thcn girls. tf I girls v.,/or-e g[o.sses, v hot frceiion of the girls wore glosses of ihe psrty? There were iû4 peopie ct c nuseu*. å af the peop[e were \4 omen. tf ihere werezb ö children at fhe museury, haw man)/ men \rr'ere ihere? 18. Ana hod some money. She used * "t it ia buy c pair of shaes which cosf $?6. ff she spenf,.} snother f oi the moûey to buy c dress, how n ue h did she spend cltogether? êv Singcpore Moth Proctice Level4A

14 ìj -7 3,çû4 x I : (1 ) 3t,232 (2) 31,232 (3) (41 3i,52t 32,520 _),r.i í\ ö lloin many qucriers oi'e there r,* 51? 4' ij ) /al1 \, ) IJ iç trj (41 2A.3 LJ A nrcvie thesteï- sald i,659 iickets on Thursdoy cnd three tinres cs mcny fickets on Fridoy. Hcw men,v* iickeis d;d t sell on both doys? {1} 3.31I (3i 6,&36 (2\ 4,977 (4) 8,295 ( ) 1 û. Anyç spent $40 cnd hcd $ I û f efi. Whct frociion of he ' mtney diej she spend? (1),i tr (3),3 7 í2j 1 ^ (4j /4 E J ( The follewing tcble shsws Lily"s grades in four subieets. Study Ít esrefully ond crnswer questions 1 1 cnd I2" 5ubfeef EngIish Math Science SoclaI siudies Grsde 74?û Whot was fhe tctql score for Li[y's best three subiects? (1) 2]e (3) 2s4 (2) 228 (4J 246 ) oì o1 12. Whaf was fhe difference beiween the highesf ond?he [owesf scores? (l) e (3) l8 (2j r5 (4) 27 gopore Math Procïice Level 4A çx

15 gz g -='i1é7 =}âl=v* Ð? "F=4H7de -=ü*fr ål31 3!è=1ec&3 e: Ð#a i L1ÐEJ SgL flêð-re #i *åqd+. sã,å1ê-4e; iå g,i+ fruaa g.cr. 'einuii:.1 33+;i. s-4i=,+ï âs Ð:lcî?uËls e -Çt i 'gæ* é Ê*åêe9 Ê+Ê G=+èÈ4êÐ?*+e+È = e+eà++9èãs 4èaâê å +êõeêéëêð ÃetëÒ É+âê+ êê=èèe4?344+ se+nu i ls ç L 4 1# t\"j-tr 1Z 111rlr' ÅÐ*! l.i frt "êifiuttij ;+,e sêi Gj ag sìå e= i uo :ees s+ eis paatisulð+lil ue il'ge* ++èê4@éè+ã4+eè&' z+è9ã+++ê4a+êq?âeâë?gaèevë+eè+teèc Sr qqad Wam vfpq aø\ô\lt^pj) z1âeë1!ðè++çeð+èþ 1e e " À I

16 I s*å*se?tuc ræråo***?räfukç=*5?*'*!,##krk Ën itue- sp*ee tueëev 41 ' t'l"-' Fcy ssve# ss3* + m+nëh fcr eighi n-ronåhs. He ihen bc,-rght a feievisian sef +ni c sie:-eo 'AF ec- +'rvi*g $?ç5 -' +;- åhe sie -eû, h+ hcci.s'ê,85g l.#" #;; *;;ä':;;ïr - ^a') Jt i r** ieievisior Ån Â soccer bsii ccsis s i 5 n^,e -e ihan a back. é" rern+ie-ccniroíiei car cosis $ ]?g rncre ihan ihe s+ccer 'bci\" if ih+ r+rr:cïe-c+;'iåraiied ccr cosis szst,whoi ís ihe ccsi of Íhe book? S.íngccos-e i.tla'rh?r atìi ce

17 &rvnp\ø+e bâph word Pró61øvwS FÄlrt:F4a-Ëh i ExLÈi Meirra has IlZ siamps. E of ihem are locai stamps ani the resi are foi+ign -ctamðs. {aj Hov.,fiãny fcieigr-.' sia ps cìoes she have? ll') i{aw íi'ìan} rn+re iocai stamps ihan fareigr,-. sta -;-:ps sces she haue? 2 Th+re are 288 nrarkers in a box. Lj s cr them are rec. The resi a,e biue. ia) ffov'r many bíue n:ark+rs are there? (bi Hor s many niore blue markers than.ed markers aíe there? f ã,ãt+ I=EEEGæ

18 ExercÍse flq tah / Areu und Perimeter [l ] A, Find fhe srccl snd pêrimetcr sf e h rectengee or SEUCIre. I t) L Lttl -o éem PenimeiÊF = 4 crr 5 cn: Arec Penime 'er : J óm ém.4,g-ea Perimeåer = 62

19 frr Covnp\e, â-\\ trja'td PÐbØm3 Do fhese pro-blcm-fr Shg ry a!! ysur wøk clegflv a K:yl,e uses j & çi* sîcmps ta m'ãke e; pieëure. tf cceh siærrtç rf;*asares *3 e m bv 2 em, {trtå Èh= arec ef the på=èi;:-e. eaieeran v snås t* e*rpei h;s!în"ëng rggeæ F"**r"+rhieh rftecsures 8,"4 'by eyå Ef the e*-rper e+sës gl5 F+r sq E&re yard, h** muei= musè eenrers.* püy t* bwy Ëhe earp*ë he neeefs? A reeècr=g';ear Erle#su cs 28 m *y 1& eosf af pu*;;-*g neé eiround iè ;Ë I "ræ cf; eesfs $Ë? Ë is Èhe &3

20 vç L'e,Ðie;+f;6:q Ð srl,l e;cñ;; 1,3:.#,A ig} 'a ôuepa; +i.!1 +G Ll4p:/À ÐLl+ Fu:J iu] it f 11 i re+a*"r red ço,ns Êqå GÅÐ'q e ñuo4>e-r Gi{ì pu* æ;=nbs eq {. :e+ë{"urr+d slg '.tst. ryw+ F sl Gtl4 =gõunpsr ið t{4pya ãt+ jl ' 'tj VZ 3l e Õuc+=Ðiz Ø fð rejð ÐL{í ñ 'cêic s+å pu J "að ZÐ sz ÐrÐfibs Ð +Ð,,s+Ðwl;ãd =q S u,r'a opuå Wam \1æ a1'a1dwø;

21 tu æe Ðxæreise 23 / Cornp\ '-i Ñci,Z Tan*þ3 Find the perïrueëcr ef æa,ch æf rhe fcllo*øi*g fígures. {A.ru fhe angles üræ right angles.} I 1',Å. : C * 14 i!.t / tiz Á t-. r t'j tit! L i3-r* '!CIt,' lr i m 7öm J^.Ì Lj Í Ltir =;* err, I crc ti r*. Ê. -*. \J \*iit i3cm 67

22 Co-mp\ø'{e LdMs Gt (r er 3 7. Find ti+e vafue cf eseh *í the feëla'rdng: 9Á*L"vÞ sêr\='^qi {bi 14Ð-4tx3 L g idi tûr-é.t.4 8x6+14 if) Êû+i&+6 (s) i7 x f û - 5 {h} 77+&x& Í* x9

23 Counp\Ø\ tt C, e_ f 7. Find r*e vcir:e aí eteh a{-ti-re faissveine: {ni {1? + 1r,} + 5 ibi 17 x {.ç - 4} TLË {=1.i,8-6'i idi i14+åixs {*i 1t x. iis -: 5) if) iltt-44s " 7 7v. ie -3j {h} {7e- 1Ê) x it ( 22

24 {, Zxg*{a-AZi+t i.r } {þ-g,ixe+9.þz p*{s-irixa {s) g.{ +Bi) +û9 1.É, É2,-iç-aûx {pi ax{z +Þ}x 1JJ çxi -#)+FL {q) e * {y + fii + ( a *1 d,w A,p1qltlvt ) :frwa*o\1ai ãæ io LlrÐa "åç Ðírlt""r ãlla pu:j -î

25 ( EXERCISE 6 T " Muteip[g. &.t6 x 2.üt = t.12 x. ltt Cxmryïek Q, C, t ibj *.34 x 3e t = 6.8 x 4tt = {d} 3"f 2 x 5tt = 64"5 x 6ttt = {fi 3?.t8 x 7û** =.54 x 8tût = {h) 3.V4 x 9Sût =.:! rï

26 7. Ë-'lultípig. CcvnptØ-\ - rõuj q+ \ ûr\d {#- 3 ît [Å- VFE E& J--.. ÍjL l; &7 ñ ÕFl q? fl"5e Rau 2 1.æ6 \J L -L,J 7.3? /+ô 4?'"û& va Jç 3 Sh*de ehe spcces whieh eantcin the cnswers tr che cbove. Ysr- Éái[E find the pi-ëze &ndrevt wcn _ i6 48ç.72 -.iit lê"'nl 5ct Li.t i aå 7È, 45, i e 154t.e 17A.54 31,2" E e8 T-shi:'t wctch Éandrew's pnlze Es c 4A ti

27 le-ie Rr[ (é) Þ tind zstv" z ï Y - 17tr B A 14Q. Find zdbc" n.l00" {B} tr L Find zgrh" 20" E/'- t\, t-l {e} M Fi rd ztu1np. (10) N 140" c o F nd zstx. X 105

28 fun^þte-fe- futt (6 ) A F ABCD is q rhornbus. Find Zx B D E c lv\ A ABCD is q rhornbr. s. Find zx" B D t I ) B AECD^is o por-ollelognorn " Finð zx" C D t? ) B A ABCD is o trcpezold. tind zx" '15" c D t'l Ir t\ r \., I A A.EEF ond CDFG ore trapezoids" tind lx. G l \ \\ D E F 107

29 UNIT Notes Concept: Angles on o stroight line The sum of angles on a straight line is 180" Concept: We con drow o triongle from given dimensions using ruler, protroctoç ond set squores. B 60" 120. Za + Zb = 60o + 120" = 180o Concept: Angles ot o poinl The sum of angles at a point is 360". 83" Draw a triangle ABC where i) AB is 4 cm long, and ii) Angle A is 68" and Angle B is 57". A Concept: Porollelogrom, rhombus, ond lropezium ore four-sided figures. C Za + Z-b + Zc + Zd = 57" + 83o + 95o + 125" 360" Concept: Verticolly opposite ongles Vertically opposite angles are equal Za=Zb=57o 57" Concept: Types of triongles lsosceles triangle equilateral triangle 57. right-angled triangle Parallelogram Rhombus Trapezium Opposite sides are parallel. Opposite sides and opposite angles are equal. Each pair of angles between two parallel lines adds up to 180o. Opposite sides are parallel. Four sides are equal. Opposite angles are equal. Each pair of angles between two parallel lines adds up to 180". One pair of opposite sides is parallel. Each pair of angles between parallel sides adds up to 1B0o Concept: Sum of ongles in o triongle is 180" Za + Zb + Zc = 48o + 75o + 57o = 18oo Find the missing angle. Za = 180" - 24o - 45o = 111o Concept: We con drow o squore / rectongle / porollelogrom / rhombus / tropezium from given dimensions using ruler, protroclor, ond sel squores. For example, draw a rhombus where i) AB is 4 cm long, it) AB // DC, and iii) Angle ABC is 120' A B D C 7 6 Math Practice the SingaPore 2O12 Marshall Cavendish

30 UNIT Notes Concept: Moking sense of overoges. The average of something is the sum or total amount divided by the number of items. Average = Sum or Total AmounVNumber of ltems Concepft Find the lotol omount given the overoge ond the number of ilems. 1. The average height of 3 bamboo sticks is 65 centimeters. Find the total length of the 3 bamboo sticks. Find the average of each of the following sets of 65 x 3 = 195 items. i)5,6,8,3,6,8 Sum= =36 Average=36+6=6 ä) 2.17 yards, 3.12 yards, 4 yards, 1.39 yards Sum = = Average = = 2.67 yd.,y l i O. O kilograms, 23.2 kilograms, kilograms sum = = 42 Average = = 14 kg The total length of the 3 bamboo sticks is 195 centimeters. 2. The average weight of a cookie is 16 ouncès. Find the total weight of 50 such cookies. 50x16=800 The total weight of 50 such cookies is 800 ounces iv) 493 gallons, 539 gallons sum= =1032 Average = = 516 gal 64 Mdth Practice the SingaPore 2O12 Marshall Cavendish Corporat on

31 UNIT Averoge POINTS 7 through 4 are worth 3 points each. For each question' options are given. One of them is the correct answer. Make choice (7, 2, 3, or 4). Write the number of the correct answer in the brackets Províded. The average of 5 and 9 is (1) e+5 (3) 14x2 (2) e-s (4) The average of 25, 24, and 23 is (1) 24 (3) 4e (2) 25 (4) 72 () 3. 4 is the average of (1) 12 and2 (3) 3 and 5 (2) 3,6, andt (4) 3 and 1 4. The average cost of 3 books is $2.10. Their total cost is (1) $0.70 Q) $2.13 (3) $5.10 Ø) $6 30 () Section B Questíon s 5 through 1O are worth 3 points each. Write your answers in the spaces provided. For questions that require uníts, give your answers in the units stated. 5. Pail A can hold 2.7 gallons of water. Pail B and Pail C togethei can hold 0.3 gallons more than Pail A. Find the average capacity of the three pails 2O12 Marshall Cavendish Corporation Math Practice the SingaPore WaY

32 UNIT Notes Concept: A rotio is o stotement thot shows how two or more similor quontities relote to eoch olher in size. Jenny has some colored beads. 6 are green and 5 are orange. So, the ratio of the number of green color beads to the number of orange beads is 6 : 5. Concept: Comporing three quontities. Susan has some stamps. 24 are local stamps, 8 are foreign stamps, and 10 are collectibles Express the number of local stamps to the number of foreign stamps to the number of collectibles as a ratio. 24: B: 1O ln its simplest form, the ratio is :5 Concept: We con either multiply or divide qll the quontities in o rotio to find their equivolent rolios For example,find an equivalent ratio of 4 : is an equivalent ratio of 4 :7 4.7 is the simplest form of B : 14. Concept: We con find one quontity given the other quontity ond we cqn find their rotio A length of thread was cut into two pieces in the ratio 3 : 5. The shorter piece was 21 in. Find the length of the longer piece. 21 in. 3 units 7 --> 21 in. 1 unit =7 in. 5 units -* 1äJ,. The length of the longer piece is 35 2O12 Marshall Cavendish Corporation Math Practice the Singapore Way 35

33 UNIT Rotio POINTS 50 Section A Qr estron s 7 through 8 are worth 2 points each. For each question' four options "r" gir.r, one of them is the correct answer' Make your ino r. (1, 2, 3, or 4). Write the number of the correct answer in the brackets Provided' 1. Which one of the following is equivalent to ib : 15? (1) 3:2 Q) 5:6 (3) 6:5 (4) 15:18 2 e small and () 3 The total weight of a box and its contents is 1,875 ounces. The weight of the box is 375 ounces. The ratio of the weight of the box to that of its contents is (1) 1 : (3) 1: 4 5 (2 ) 4) ( 4 The lengths of the three sides of a triangle are 30 inches, 40 inches, and 48 inches. The ratio of the length of the shortest side to the length of the longest side is (1) 3:4 (3) 1:16 (2) 5:B (4) 3:48 () 5 There are 20 pears, 10 oranges, and 24 apples in a basket' What is the ratio of the number of apples to the total number of pieces of fruit in the basket? (1) 4'5 (3) 5 :21 (2) 4:9 (4) 10 :27 () 36 Math Practice the SingaPore 2O12 Marshall Cavendish Corporation

34 UNIT Notes Concept:ldentifyingtheboseofotriongleonditscorrespondingheight. Any one side of a triangle may be the.base' no matter how it is rotated' The height of a triangl.-i,.h..p.,pendicular height from the base to the highest or farthest Point of the triangle heiqht height base base we can use mathematical formulas to help us find the area of a triangle 1 Area of triangle = i. " base x height i. Find the area of the triangle ABC' A 2. Find the area of the triangle DEF Area of trianqle = t" base x height 6 cm = 1* 14 x 5 2 C 8cm Area of triangle = I" base x height z x8x6 = 24 cmz B = 35 sq. in. D F 14 in E 26 Math Practice the SingaPore 2O12 Marshall Cavendish Corporation

35 UNIT Areq of o Triongle POINTS 50 Section A Questions 7 through I are worth 3 points each. Far each question, four options are given, One of them is the correct answer. Make your choice (7, 2, 3, or 4). Write the number of the correct answer in the brackets Provided' Study the figures below and answer questions 1 through 4' cm.e î 1cm A B c D Which of the above triangles has the largest area? (1) A Q) B (3)c Ø) D () 2. Which two of the above triangles have the same area? (1) AandB Q) BandC (3) A and C (4) C and D 3. Which of the above triangles has an area of 6 cm2? (1) A Q) B (3) c (4) D 4. What is the total area of triangles B and C? (1) 10 cm2 (2) rc! cm' (3) 20! cm' (4) 21 cmz 2O12 Marshall Cavendish Corporation Math Practice the SingaPore WaY 27

36 F Ê;, UNIT Notes Concepl: Using the percentoge symbol (o/ol. We use the symbol "o/o" Io represent percentage A percent means 1 out of 100. Express each of the following as a percentage ii) 0.72x100=72o/o x o/o 2, Express 15o/o as a fraction in its simplest form 15Vo = Express 65Vo as a decimal. 65cl/o = I 100 = 0.65 Concept: Expressing o port of o whole os o percenloge. ln a bag of marbles, f, of the marbles are ceramic marbles. What percentage of the marbles are ceramic marbles? f, x f OO =37.5o/o 375% are ceramic marbles. Concepft Finding o percenloge of o whole. There are 25 books in the class library. 40o/o of the books are fiction books and the remaining books are nonfiction books. How many nonfiction books are there? 100% -40%=6o0/o Z Concept: Solving up to 2-step word problems involving soles tox. Kelly bought $85 worth of purchases. lf she has to pay 7% in sales tax, how much must she pay in all? 7 x$85=$ $85+$5.95=$90.95 Kelly has to pay $90.95 in all. Concepft Solving up to 2-step word problems involving discounts. Stevie bought a $556 guitar at a 35o/o discount. How much did he pay for the guitar? 100o/o-35o/o=65%io 65 " $ Stevie paid $ for the guitar Concepl: Solving up to Z-step word problems involving qnnuol interest. Jennifer took out a 1-year loan of $25,400 from a bank. The bank charges 8% interest per year. How much interest does Jennifer have to pay on the loan?,å t $25,400 =$2,032. Jennifer will have to pay $2,032 in interest on the loan. Number of nonfiction books =!9 " 25 q t t There are 15 nonfiction books. = 15 o 201 Cavendish Corporation Math Practice the Singapore Way 59

37 Percentoge (al: Percentoge of o Quontity A. Find fhe volue of eqch of the following. (l ) B% of 250 cm l2l 20% ol $ I 0ó0 (3) 34% of 300 s l4l 45% of ao ks (5) 50"/" of 7 50 m (ó) 78% of 500 ml B. Do fhese problems. Show oll your work cleorly. (l ) There ore 385 people in o swimming pool. 60% of them ore children. How mony children ore there? (21 of 88 students, 75% possed the exqminotion. How mqny students possed the exominotion? 88

38 UNIT Notes Concept: We con represent o decimol os o froction by converting it to o froclion wilh o denominolor of 10, 100, or 1,000. Write the following decimals as fractions or mixed numbers a) = '- 10 ^6.3 = l- = l b) 2.s = ^51 = + 1æ -51 = 1æ c) = ' = g * 125 Concefi: When o decimol is multiplied by tens, hundreds, or thousonds, eoch digit of the number shifts by one, two, or three ploces to the ploce volue on lhe left. I 1 B 1000 Thousand Hundreds Tens Ones Tenths Hundreds Thousandth x x ,U x 1,000 i. Mulliply 7.ì3.l by l0,.ô3 I xto=71.31 ii. Multiply 7.'13ì by 100, ßtll xtoo=713.1 iii. Multiply by 1,000 7 I 3 I x 1,000 = 7,13. Concepft When o decimol is divided by tens, hundreds, or lhousonds, eoch digil of the number shifts by one, two, or three ploces lo the ploce volue on the righl. Thousand Hundreds Tens Ones Tenths Hundreds Thousandth i. Divide 24ó1.0 by 10 r-\ 2 4 6'l+10= ii. Divide by r\-\.l t+100= iii. Divide by., ó l+1, 00O = Math Practice the SingaPore 2O12 Marshall Cavendish

39 UNIT Decimols POINTS 50 A 1 through 9 are worth 2 points each. For each question, options are given. one of them is the correct answer. Make choice (7, 2, 3, or 4), write the number of the correct answer in brackets provided tens B hundredths 2 thousandths = (1) 0.s82 (3) so 82 (2) s.82 (4) so.og2 2 ln 7.608, the digit 8 is in the (1) hundredths ( l tenths place (2) ones (4) thousandths () 3. Which one of the following is incorrect? (1) 3,600 g = 3.6 kg (2) 2,860 m = 28.6 km (3) 5 m, 30 cm = 5.3 m (4) 4.3 L- 4L,300 ml 4. Which one of the following is the smallest? (1) 0.04 (2) 0.2 (3) (4) Which one of the following is incorrect? (1) 0.086=fi* 1 (3) 0.02s = ,000 (2) = B thousandths (4) = # () 6. Which one of the following is the best estimate for x 30.12? (1) 59 x 30 (2) 60 x 31 ( {3) 60x30 (4) 59 x 31 2O12 Marshall Cavendish Corporation Math Practice the Singapore Way 45

40 7. J written as a decimal is (1) 0.3 (2) 3.8 (2) (4) B3 B. 21, ,000 = (1) 2,180 (3) 21.8 (2) 218 (4) 2.18 () x 1,000 = (1) o.o7 (3) 7 (2) 0.7 (4) 7,ooo Section B QuestionslothroughlTareworth2pointseach.Writeyour answers in therp"ã., provided. For questions that require units' gíve your answers in the units stated' 10. 2tens 5 hundredths B thousandths written as a decimal is 11 lo#poo written as a decimal is 12. Arrange these decimals in decreasing order: 2.9,2]5,3.1, rounded off to 2 decimal places is written as a fraction in the simplest form is 15. Find the difference between 0.02 kilometers and 85 meters kilometers 16. What fraction of the figure is shaded? Write your answer as a decimal 17. Write 2.3 as an improper fraction 46 Math Practice the SingaPore 2012 Marshall Cavendish Corporation

41 UNIT Notes Concepf: Associotion of o froction with division Fractions and division are closely related' Cut a Pie into three equal Parts' Each part will then be one-third of the whole divided into 3 equal Pafts = 1 3 Concept: Conversion between froctions ond decimols' We can convert a fraction to a decimal by: i) finding its equivalent fraction with a denominator of 10, 100, or 1,OOO, or ii) doing long division' trxpress # "ra decimal. Express r J as a decimal' 20 20x x8 _ 160 1,000 = 0.16 Concept: Addition ond subtroction of ProPer froctions ond mixed numbers. We can add and subtract unlike fractions by converting the fractions into like fractions and adding them together. Add I and 1. 1 """ B """ 2' 4 3 1= B 8 = x x _ We can add or subtract mixed numbers by first converting the fractional parts of the mixed numbers to like fractions, then adding or subtracting the whole numbers before adding or subtracting the fractional parts' Add 4 )anaz Z oi*2+=+$+z -11 =c)- 12 Subtract6fandl r)-- -5 ^ l-=o _tr3 Concept: Mull pl coî on of o proper froction ond o proper/ improper froction. We can multiply a fraction by another fraction by first multiplying the numerators and then multiplying the denomi nators separately. Mu : trpy by ã 2 5x2 x x M Z 4 U X 8 - J- nivry f,ny ] 5 I x5 2 4 x Concept: Multiplicolion of o mixed number ond o whole number. We can multiply a mixed number Multiply f ] Uy t. with a whole number by first converting the mixed númber to, 1" 3 = L x 3 an improper fraction, and then = 21 _ 5! multiplying the numerator of the 4 ' 4 improper fraction by the whole number. Concept: Division of o proper froction by o whole number When we divide a fraction by a whole number, we are dividing the fraction into smaller parts. Divide å ou t -=- 3 'l 3 1x4 8 2 =--- It is the same as findins 8 2x4 * 34 " å 5o, we can also say: B 126 f +:- 1_ " a 1 5 2o'12 Marshall Cavendish Corporation Math Practice the SingaPore WaY 21 I ßffi --T--l

42 UNIT Froctions POINTS 50 Section A Questions 7 through I are worth 2 points each, For each question, four options are given, One of them ls the correct answer' Make your iho r" (7, 2, 3, or 4). Write the number of the correct answer in the brackets Provided- 1. Which one of the following is incorrect? (1) += z) (3) i=t (2)!=z*z (4) rå=ä () 2, Which one of the following is incorrect? (1) 1.i= 1+ Q) (3),+-,!=rt (4) 3* 4 Ê zl=zl ) 3. Which one of the following is incorrect? (1) z- += h (3) =,å '1- 'å 4. Which one of the following is incorrect? (1) å"å=å (3) lo*u=à,r5 (2) z] - _r1 '6-'12 (4) (2) å' (4) 1* t -'r1 t -'Ã ( ( 5. By how many minutes is:] hours longer than 1fr froursz (1) 60l minutes Q) 62 minutes (3) 75 minutes (a) 100 minutes 22 Math Practice the SingaPore 2O12 Marshall Cavendish Corporation

43 6. John had $120 He spent $15 in one store and $25 in another What fraction of his money did he have left? (1) å e)i (3) ; Ø)+ ( ) 7. Paul earns $900 a month. He spends $0:O and saves the remainder What fraction of his expenses are his savings? (1) ;"4 Q) 1 (3) * (4) + B Jeff wants to buy a camera that costs $3S0. He has onty I needed. How much more does he need? (1) va Q) $142.s0 (3) $zss (4) $231.s0 of the money Section B Questr-ons 9 through 15 are worth 2 points each. Write your answers in the spaces provided. For questions that require units, give your answers in the uníts stated. 9 Find the value of Z When a number is divided by 32, the answer is f. What is the number? 11 How many times is a bag weighing Zf kitograms as heavy as a bag weighing 400 grams? 12 olko-t1kq+12ko= 4-5 ks g 13 Find the value of 1? write f, lel i, i, and j n order, beg nn ng w th the sma est: Find the product ot fi ano f O 2012 Marshall Cavendish Corporation Math Practice the Singapore Way 23 (un,t \I þ"'.