SAMPLE PAGES. Primary. Primary Maths Basics Series THE SUBTRACTION BOOK. A progression of subtraction skills. written by Jillian Cockings
|
|
|
- Gwen Floyd
- 5 years ago
- Views:
Transcription
1 PAGES Primry Primry Mths Bsis Sris THE SUBTRACTION BOOK A prorssion o sutrtion skills writtn y Jillin Cokins
2 INTRODUCTION This ook is intn to hlp sur th mthmtil onpt o sutrtion in hilrn o ll s. Th mstry o iint mntl n writtn mthos o sutrtion is intrl to th quisition o si numr skills, upon whih mthmtis is uilt. Without ths soli ountions, hilrn will otn nountr iiultis s mthmtil onpts om mor omplx. Any ps in si numr knowl n unrstnin n l to lk o ility n onin s hilrn r prsnt with mor hllnin mthmtil onpts t shool n in thir vryy livs. Sutrtion skills r prtis hr isrtly in orr to m th prosss, ut on proiiny hs n stlish, th rltionship twn sutrtion, ition, multiplition n ivision n thn onsolit. On this irm rounin o numr is uilt, hilrn n mov orwr onintly in mths. Th xriss in th ook r sin to provi prorssion o vitl sutrtion skills. As nrl rul, th lultions on h p om mor hllnin s hilrn work throuh stions to. Som o th xriss, suh s sutrtin or, r lss hllnin tht thos on prvious ps ut r position in th ook to monstrt th prorssion o onpt. Most hilrn will t som st o this ontinuum in thir unrstnin o sutrtion. By workin throuh th xriss, unr th uin or suprvision o n ult, ny ps in unrstnin or knowl tht hilrn hv will quikly om pprnt. Guin n urthr prti n thn mploy to ill th ps or movin on. On ps whih rly hvily on mntl thniqus, Sor n Tim ror is vill. This will hlp hilrn hon thir mntl sp n ury. By th tim hil hs rh th n o th ook, thir mntl n writtn mthos o sutrtion will mor sur n thy will onint to us n pply thir skills to vrity o mthmtil prolms. This ook hs purposly voi til sriptions o vrious mthos o mntl n writtn sutrtion strtis, prtiulrly xpn mthos o writtn sutrtion. It is importnt tht hilrn r tuht ollowin th poliis n mthos r y thir shool so tht thin n lrnin r onsistnt or th hil. Thr r otn svrl wys to solv mntl or writtn lultion n mor l hilrn will njoy th hlln o isovrin irnt wys to in solution. It is oo i, howvr, to r upon mtho tht works or th hil n is prt o th shool s mntl n writtn lultions poliy. On h p, Mths Monky hs ivn tip to provi som si uin ut this os not mn tht this is th only wy to in solution. (Continu on nxt p) Copyriht HStrt Primry Lt
3 At th k o th ook, thr r lso numr lins n numr squr whih n provi support to hilrn, spilly in th rly sts o thir unrstnin. Mthos o ompt sutrtion r lso monstrt ut it is importnt tht hilrn r shown mor xpn mthos o sutrtion so tht soli ountions r li. Th xpn mthos shown to hilrn shoul lso ollow th lultions poliy o th hil s shool. To omplt mny o th xriss in th ook, hilrn will n squr ppr. SUBTRACTION () Sutrtion is th rmovin or tkin wy o on quntity rom nothr or rsin on quntity y nothr Sutrtion is th invrs (opposit) o ition Sutrtion is not ommuttiv, whrs ition is ommuttiv THE VOCABULARY OF SUBTRACTION sutrt sutrtion tk (wy) minus lv invrs o ition how mny hv on? on lss, two lss, tn lss, on hunr lss how mny wr is...thn...? + quls + ut os not qul wht is th irn twn? rs ru rmov how mny r lt / lt ovr? Copyriht HStrt Primry Lt Th ps o this ook my print or photoopi or us in th purhsin institution only.
4 THE SUBTRACTION BOOK CONTENTS PAGE OBJECTIVE Sutrt numrs rom (numr ons to ) Sutrt ny numrs low Sutrt numrs rom ( or lss) Sutrt numrs rom (yon ) Sutrt numrs rom n low Sutrt ny numrs low Sutrt numrs rom Sutrt numrs rom Sutrt ny numrs low Sutrt numrs rom (multipls o ) Sutrt numrs rom (multipls o ) Sutrt numrs rom Sutrt ny numrs low (not riin th ounry) Sutrt ny numrs low (riin th ounry) Sutrt iit numrs (in missin numrs) Sutrt iit multipls o (not riin th ounry) Sutrt iit multipls o (riin th ounry) Sutrt iit multipls o Sutrt multipls o (in missin numrs) A on to in smll irn (iit numrs) A on to in smll irn (iit numrs) A on to in smll irn (riin th ounry) Sutrt rom ny iit numr Sutrt rom ny iit numr Sutrt rom ny iit numr Sutrt rom ny iit numr Sutrt rom ny iit numr Sutrt rom ny iit numr Sutrt rom ny iit numr (riin th ounry) Sutrt rom ny iit numr Sutrt rom ny iit numr Sutrt rom ny iit numr Roun up n ompnst whn sutrtin,, t Sutrt y prtitionin (iit numrs) Sutrt y prtitionin (iit numrs) Roun own n ompnst whn tkin,, t Us writtn mtho to sutrt rom iit numrs Us writtn mtho to sutrt rom iit or iit numrs Us writtn mtho to sutrt rom iit numrs (Prt ) Copyriht HStrt Primry Lt
5 THE SUBTRACTION BOOK CONTENTS PAGE OBJECTIVE Us writtn mtho to sutrt rom iit numrs (Prt ) Us writtn mtho to sutrt rom iit numrs (Prt ) Us writtn mtho to sutrt rom iit numrs (Prt ) Us writtn mtho to sutrt rom iit numrs (Prt ) Us writtn mtho to sutrt rom iit numrs (Prt ) Us writtn mtho to sutrt rom iit numrs (Prt ) Sutrt imls rom (Prt ) Sutrt imls rom (Prt ) Sutrt imls rom Sutrt imls rom ny iit numr Sutrt imls low (not riin th ons ounry) Sutrt imls low (riin th ons ounry) Sutrt imls rom ny iit numr Us writtn mtho to sutrt imls ( iml pl) Us writtn mtho to sutrt imls ( n iml pls) Us writtn mtho to sutrt imls ( iml pls) Us writtn mtho to sutrt imls ( iml pls) Us writtn mtho to sutrt imls ( iml pls) Us th invrs to in missin iml numrs (Prt ) Us th invrs to in missin iml numrs (Prt ) Sutrt rms n rms Sutrt kilorms n rms (onvrt kilorms to rms) Sutrt ntimtrs n ntimtrs Sutrt mtrs n ntimtrs (onvrt mtrs to ntimtrs) Fin hn rom. Fin hn rom. Fin hn rom. Fin hn rom othr mounts o whol pouns Sutrt p y rounin up n ompnstin Sutrt y rounin up n ompnstin (p n p) Us writtn mtho to sutrt mony Us writtn mtho to sutrt lrr mounts o mony (Prt ) Us writtn mtho to sutrt lrr mounts o mony (Prt ) Us writtn mtho to sutrt numrs with vryin iml pls Sutrt lrr numr rom smllr numr (tmprtur) Sutrt lrr numr rom smllr numr NUMBER LINES NUMBER SQUARE THE WRITTEN COLUMN METHOD OF SUBTRACTION ANSWERS THE SUBTRACTION BOOK Copyriht HStrt Primry Lt
6 OBJECTIVE Sutrt numrs rom (numr ons to ) Nm Yr/Clss Mk sur you know your numr ons to. I it hlps, try usin ountrs. Copyriht HStrt Primry Lt Sor... Tim...
7 OBJECTIVE Sutrt ny numrs low Nm Yr/Clss Try usin numr lin or rulr. You n in numr lin on p. Copyriht HStrt Primry Lt Sor... Tim...
8 Copyriht HStrt Primry Lt Sutrt numrs rom Rmmr to us your knowl o numr ons. Nm Yr/Clss OBJECTIVE Sor... Tim...
9 THE WRITTEN COLUMN METHOD OF SUBTRACTION Th olumn mtho o sutrtion is th most wily us wy to sutrt numrs on ppr. Position th lrr numr ov th smllr numr with th pl vlu olumns (ons, tns, t.) lin up orrtly. Strt in th ons (units) olumn on th riht n work rom riht to lt sutrtin th iits. For xmpl, th lultion woul on lik this: STEP STEP Hr s how to o tk wys! Whn sttin out, writ th lrr numr on top. Th ons (units) n th tns must lin up rully in olumns. Strt with th olumn urthst to th riht, whih is th ons olumn. Tk th ottom iit () rom th top on () to t th nswr (). Copyriht HStrt Primry Lt
10 STEP Now omplt th lultion y sutrtin th iits on th ottom rom thos on th top. Strt on th riht in th ons olumn. So, Ths mthos work or numrs o ny siz! To sutrt numrs with irnt mounts o iml pls, hk out th xmpl low. For xmpl, th lultion.. woul on lik this:... First o ll, lin up th iml points. Put zros to ill th sps to th riht o th in th top numr. This mks th lultion lrr. Copyriht HStrt Primry Lt
11 Lik wht you v sn so r? Rqust your riskr insption opis. W will ispth your opis within hours y nxt y ourir. I you lov your rsours, kp thm n w will pross your orr n sn th ompnyin CDROMs. I you r not stisi, lt us know n w will rrn to ollt thm rom you rohr. W r hr to hlp. I you hv ny qustions rrin our rsours or orrin pross, pls on t hsitt to t in touh with us. Emil: ino@hstrtprimry.om Phon:
1 Introduction to Modulo 7 Arithmetic
1 Introution to Moulo 7 Arithmti Bor w try our hn t solvin som hr Moulr KnKns, lt s tk los look t on moulr rithmti, mo 7 rithmti. You ll s in this sminr tht rithmti moulo prim is quit irnt rom th ons w
# 1 ' 10 ' 100. Decimal point = 4 hundred. = 6 tens (or sixty) = 5 ones (or five) = 2 tenths. = 7 hundredths.
How os it work? Pl vlu o imls rprsnt prts o whol numr or ojt # 0 000 Tns o thousns # 000 # 00 Thousns Hunrs Tns Ons # 0 Diml point st iml pl: ' 0 # 0 on tnth n iml pl: ' 0 # 00 on hunrth r iml pl: ' 0
, each of which is a tree, and whose roots r 1. , respectively, are children of r. Data Structures & File Management
nrl tr T is init st o on or mor nos suh tht thr is on sint no r, ll th root o T, n th rminin nos r prtition into n isjoint susts T, T,, T n, h o whih is tr, n whos roots r, r,, r n, rsptivly, r hilrn o
ECE COMBINATIONAL BUILDING BLOCKS - INVEST 13 DECODERS AND ENCODERS
C 24 - COMBINATIONAL BUILDING BLOCKS - INVST 3 DCODS AND NCODS FALL 23 AP FLZ To o "wll" on this invstition you must not only t th riht nswrs ut must lso o nt, omplt n onis writups tht mk ovious wht h
Decimals DECIMALS.
Dimls DECIMALS www.mthltis.o.uk ow os it work? Solutions Dimls P qustions Pl vlu o imls 0 000 00 000 0 000 00 0 000 00 0 000 00 0 000 tnths or 0 thousnths or 000 hunrths or 00 hunrths or 00 0 tn thousnths
Present state Next state Q + M N
Qustion 1. An M-N lip-lop works s ollows: I MN=00, th nxt stt o th lip lop is 0. I MN=01, th nxt stt o th lip-lop is th sm s th prsnt stt I MN=10, th nxt stt o th lip-lop is th omplmnt o th prsnt stt I
Seven-Segment Display Driver
7-Smnt Disply Drivr, Ron s in 7-Smnt Disply Drivr, Ron s in Prolm 62. 00 0 0 00 0000 000 00 000 0 000 00 0 00 00 0 0 0 000 00 0 00 BCD Diits in inry Dsin Drivr Loi 4 inputs, 7 outputs 7 mps, h with 6 on
(2) If we multiplied a row of B by λ, then the value is also multiplied by λ(here lambda could be 0). namely
. DETERMINANT.. Dtrminnt. Introution:I you think row vtor o mtrix s oorint o vtors in sp, thn th gomtri mning o th rnk o th mtrix is th imnsion o th prlllppi spnn y thm. But w r not only r out th imnsion,
S i m p l i f y i n g A l g e b r a SIMPLIFYING ALGEBRA.
S i m p l i y i n g A l g r SIMPLIFYING ALGEBRA www.mthltis.o.nz Simpliying SIMPLIFYING Algr ALGEBRA Algr is mthmtis with mor thn just numrs. Numrs hv ix vlu, ut lgr introus vrils whos vlus n hng. Ths
Designing A Concrete Arch Bridge
This is th mous Shwnh ri in Switzrln, sin y Rort Millrt in 1933. It spns 37.4 mtrs (122 t) n ws sin usin th sm rphil mths tht will monstrt in this lsson. To pro with this lsson, lik on th Nxt utton hr
CSE 373: AVL trees. Warmup: Warmup. Interlude: Exploring the balance invariant. AVL Trees: Invariants. AVL tree invariants review
rmup CSE 7: AVL trs rmup: ht is n invrint? Mihl L Friy, Jn 9, 0 ht r th AVL tr invrints, xtly? Disuss with your nighor. AVL Trs: Invrints Intrlu: Exploring th ln invrint Cor i: xtr invrint to BSTs tht
EE1000 Project 4 Digital Volt Meter
Ovrviw EE1000 Projt 4 Diitl Volt Mtr In this projt, w mk vi tht n msur volts in th rn o 0 to 4 Volts with on iit o ury. Th input is n nlo volt n th output is sinl 7-smnt iit tht tlls us wht tht input s
OpenMx Matrices and Operators
OpnMx Mtris n Oprtors Sr Mln Mtris: t uilin loks Mny typs? Dnots r lmnt mxmtrix( typ= Zro", nrow=, nol=, nm="" ) mxmtrix( typ= Unit", nrow=, nol=, nm="" ) mxmtrix( typ= Int", nrow=, nol=, nm="" ) mxmtrix(
COMPLEXITY OF COUNTING PLANAR TILINGS BY TWO BARS
OMPLXITY O OUNTING PLNR TILINGS Y TWO RS KYL MYR strt. W show tht th prolm o trmining th numr o wys o tiling plnr igur with horizontl n vrtil r is #P-omplt. W uil o o th rsults o uquir, Nivt, Rmil, n Roson
H SERIES. Decimals. Decimals. Curriculum Ready ACMNA: 103, 128, 129, 130, 152, 154,
Dimls H SERIES Dimls Curriulum Ry ACMNA: 0, 8, 9, 0,,, www.mthltis.om Copyriht 009 P Lrnin. All rihts rsrv. First ition print 009 in Austrli. A tlou ror or this ook is vill rom P Lrnin Lt. ISBN 978--98--9
QUESTIONS BEGIN HERE!
Points miss: Stunt's Nm: Totl sor: /100 points Est Tnnss Stt Univrsity Dprtmnt of Computr n Informtion Sins CSCI 710 (Trnoff) Disrt Struturs TEST for Fll Smstr, 00 R this for strtin! This tst is los ook
QUESTIONS BEGIN HERE!
Points miss: Stunt's Nm: Totl sor: /100 points Est Tnnss Stt Univrsity Dprtmnt o Computr n Inormtion Sins CSCI 2710 (Trno) Disrt Struturs TEST or Sprin Smstr, 2005 R this or strtin! This tst is los ook
CS September 2018
Loil los Distriut Systms 06. Loil los Assin squn numrs to msss All ooprtin prosss n r on orr o vnts vs. physil los: rport tim o y Assum no ntrl tim sour Eh systm mintins its own lol lo No totl orrin o
Cycles and Simple Cycles. Paths and Simple Paths. Trees. Problem: There is No Completely Standard Terminology!
Outlin Computr Sin 331, Spnnin, n Surphs Mik Joson Dprtmnt o Computr Sin Univrsity o Clry Ltur #30 1 Introution 2 3 Dinition 4 Spnnin 5 6 Mik Joson (Univrsity o Clry) Computr Sin 331 Ltur #30 1 / 20 Mik
Indices. Indices. Curriculum Ready ACMNA: 209, 210, 212,
Inis Inis Curriulum Ry ACMNA: 09, 0,, 6 www.mtltis.om Inis INDICES Inis is t plurl or inx. An inx is us to writ prouts o numrs or pronumrls sily. For xmpl is tully sortr wy o writin #. T is t inx. Anotr
Math 61 : Discrete Structures Final Exam Instructor: Ciprian Manolescu. You have 180 minutes.
Nm: UCA ID Numr: Stion lttr: th 61 : Disrt Struturs Finl Exm Instrutor: Ciprin nolsu You hv 180 minuts. No ooks, nots or lultors r llow. Do not us your own srth ppr. 1. (2 points h) Tru/Fls: Cirl th right
Module graph.py. 1 Introduction. 2 Graph basics. 3 Module graph.py. 3.1 Objects. CS 231 Naomi Nishimura
Moul grph.py CS 231 Nomi Nishimur 1 Introution Just lik th Python list n th Python itionry provi wys of storing, ssing, n moifying t, grph n viw s wy of storing, ssing, n moifying t. Bus Python os not
Garnir Polynomial and their Properties
Univrsity of Cliforni, Dvis Dprtmnt of Mthmtis Grnir Polynomil n thir Proprtis Author: Yu Wng Suprvisor: Prof. Gorsky Eugny My 8, 07 Grnir Polynomil n thir Proprtis Yu Wng mil: uywng@uvis.u. In this ppr,
0.1. Exercise 1: the distances between four points in a graph
Mth 707 Spring 2017 (Drij Grinrg): mitrm 3 pg 1 Mth 707 Spring 2017 (Drij Grinrg): mitrm 3 u: W, 3 My 2017, in lss or y mil (grinr@umn.u) or lss S th wsit or rlvnt mtril. Rsults provn in th nots, or in
Planar Upward Drawings
C.S. 252 Pro. Rorto Tmssi Computtionl Gomtry Sm. II, 1992 1993 Dt: My 3, 1993 Sri: Shmsi Moussvi Plnr Upwr Drwings 1 Thorm: G is yli i n only i it hs upwr rwing. Proo: 1. An upwr rwing is yli. Follow th
DUET WITH DIAMONDS COLOR SHIFTING BRACELET By Leslie Rogalski
Dut with Dimons Brlt DUET WITH DIAMONDS COLOR SHIFTING BRACELET By Lsli Roglski Photo y Anrw Wirth Supruo DUETS TM from BSmith rt olor shifting fft tht mks your work tk on lif of its own s you mov! This
a b c cat CAT A B C Aa Bb Cc cat cat Lesson 1 (Part 1) Verbal lesson: Capital Letters Make The Same Sound Lesson 1 (Part 1) continued...
Progrssiv Printing T.M. CPITLS g 4½+ Th sy, fun (n FR!) wy to tch cpitl lttrs. ook : C o - For Kinrgrtn or First Gr (not for pr-school). - Tchs tht cpitl lttrs mk th sm souns s th littl lttrs. - Tchs th
Tangram Fractions Overview: Students will analyze standard and nonstandard
ACTIVITY 1 Mtrils: Stunt opis o tnrm mstrs trnsprnis o tnrm mstrs sissors PROCEDURE Skills: Dsriin n nmin polyons Stuyin onrun Comprin rtions Tnrm Frtions Ovrviw: Stunts will nlyz stnr n nonstnr tnrms
Multipoint Alternate Marking method for passive and hybrid performance monitoring
Multipoint Altrnt Mrkin mtho or pssiv n hyri prormn monitorin rt-iool-ippm-multipoint-lt-mrk-00 Pru, Jul 2017, IETF 99 Giuspp Fiool (Tlom Itli) Muro Coilio (Tlom Itli) Amo Spio (Politnio i Torino) Riro
Using the Printable Sticker Function. Using the Edit Screen. Computer. Tablet. ScanNCutCanvas
SnNCutCnvs Using th Printl Stikr Funtion On-o--kin stikrs n sily rt y using your inkjt printr n th Dirt Cut untion o th SnNCut mhin. For inormtion on si oprtions o th SnNCutCnvs, rr to th Hlp. To viw th
Outline. 1 Introduction. 2 Min-Cost Spanning Trees. 4 Example
Outlin Computr Sin 33 Computtion o Minimum-Cost Spnnin Trs Prim's Alorithm Introution Mik Joson Dprtmnt o Computr Sin Univrsity o Clry Ltur #33 3 Alorithm Gnrl Constrution Mik Joson (Univrsity o Clry)
b. How many ternary words of length 23 with eight 0 s, nine 1 s and six 2 s?
MATH 3012 Finl Exm, My 4, 2006, WTT Stunt Nm n ID Numr 1. All our prts o this prolm r onrn with trnry strings o lngth n, i.., wors o lngth n with lttrs rom th lpht {0, 1, 2}.. How mny trnry wors o lngth
Integration Continued. Integration by Parts Solving Definite Integrals: Area Under a Curve Improper Integrals
Intgrtion Continud Intgrtion y Prts Solving Dinit Intgrls: Ar Undr Curv Impropr Intgrls Intgrtion y Prts Prticulrly usul whn you r trying to tk th intgrl o som unction tht is th product o n lgric prssion
Outline. Binary Tree
Outlin Similrity Srh Th Binry Brnh Distn Nikolus Austn nikolus.ustn@s..t Dpt. o Computr Sins Univrsity o Slzur http://rsrh.uni-slzur.t 1 Binry Brnh Distn Binry Rprsnttion o Tr Binry Brnhs Lowr Boun or
Module 2 Motion Instructions
Moul 2 Motion Instrutions CAUTION: Bor you strt this xprimnt, unrstn tht you r xpt to ollow irtions EXPLICITLY! Tk your tim n r th irtions or h stp n or h prt o th xprimnt. You will rquir to ntr t in prtiulr
UNCORRECTED SAMPLE PAGES 4-1. Naming fractions KEY IDEAS. 1 Each shape represents ONE whole. a i ii. b i ii
- Nming frtions Chptr Frtions Eh shp rprsnts ONE whol. i ii Wht frtion is shdd? Writ s frtion nd in words. Wht frtion is not shdd? Writ s frtion nd in words. i ii i ii Writ s mny diffrnt frtions s you
Outline. Computer Science 331. Computation of Min-Cost Spanning Trees. Costs of Spanning Trees in Weighted Graphs
Outlin Computr Sin 33 Computtion o Minimum-Cost Spnnin Trs Prim s Mik Joson Dprtmnt o Computr Sin Univrsity o Clry Ltur #34 Introution Min-Cost Spnnin Trs 3 Gnrl Constrution 4 5 Trmintion n Eiiny 6 Aitionl
Aquauno Video 6 Plus Page 1
Connt th timr to th tp. Aquuno Vio 6 Plus Pg 1 Usr mnul 3 lik! For Aquuno Vio 6 (p/n): 8456 For Aquuno Vio 6 Plus (p/n): 8413 Opn th timr unit y prssing th two uttons on th sis, n fit 9V lklin ttry. Whn
Paths. Connectivity. Euler and Hamilton Paths. Planar graphs.
Pths.. Eulr n Hmilton Pths.. Pth D. A pth rom s to t is squn o gs {x 0, x 1 }, {x 1, x 2 },... {x n 1, x n }, whr x 0 = s, n x n = t. D. Th lngth o pth is th numr o gs in it. {, } {, } {, } {, } {, } {,
Walk Like a Mathematician Learning Task:
Gori Dprtmnt of Euction Wlk Lik Mthmticin Lrnin Tsk: Mtrics llow us to prform mny usful mthmticl tsks which orinrily rquir lr numbr of computtions. Som typs of problms which cn b on fficintly with mtrics
Constructive Geometric Constraint Solving
Construtiv Gomtri Constrint Solving Antoni Soto i Rir Dprtmnt Llngutgs i Sistms Inormàtis Univrsitt Politèni Ctluny Brlon, Sptmr 2002 CGCS p.1/37 Prliminris CGCS p.2/37 Gomtri onstrint prolm C 2 D L BC
Solutions for HW11. Exercise 34. (a) Use the recurrence relation t(g) = t(g e) + t(g/e) to count the number of spanning trees of v 1
Solutions for HW Exris. () Us th rurrn rltion t(g) = t(g ) + t(g/) to ount th numr of spnning trs of v v v u u u Rmmr to kp multipl gs!! First rrw G so tht non of th gs ross: v u v Rursing on = (v, u ):
Why the Junction Tree Algorithm? The Junction Tree Algorithm. Clique Potential Representation. Overview. Chris Williams 1.
Why th Juntion Tr lgorithm? Th Juntion Tr lgorithm hris Willims 1 Shool of Informtis, Univrsity of Einurgh Otor 2009 Th JT is gnrl-purpos lgorithm for omputing (onitionl) mrginls on grphs. It os this y
8Algebraic UNCORRECTED SAMPLE PAGES. techniques. What you will learn. Australian curriculum. Chapter 8A 8B 8C 8D 8E 8F
8A 8B 8C 8D 8E 8F 8G 8H 8I 8J 8K Chptr Wht you will lrn 8Algri thniqus Epning inomil prouts Prt squrs n irn o prt squrs Ftorising lgri prssions Ftorising th irn o two squrs Ftoristion y grouping Ftorising
Numbering Boundary Nodes
Numring Bounry Nos Lh MBri Empori Stt Univrsity August 10, 2001 1 Introution Th purpos of this ppr is to xplor how numring ltril rsistor ntworks ffts thir rspons mtrix, Λ. Morovr, wht n lrn from Λ out
5/1/2018. Huffman Coding Trees. Huffman Coding Trees. Huffman Coding Trees. Huffman Coding Trees. Huffman Coding Trees. Huffman Coding Trees
/1/018 W usully no strns y ssnn -lnt os to ll rtrs n t lpt (or mpl, 8-t on n ASCII). Howvr, rnt rtrs our wt rnt rquns, w n sv mmory n ru trnsmttl tm y usn vrl-lnt non. T s to ssn sortr os to rtrs tt our
The University of Sydney MATH2969/2069. Graph Theory Tutorial 5 (Week 12) Solutions 2008
Th Univrsity o Syny MATH2969/2069 Grph Thory Tutoril 5 (Wk 12) Solutions 2008 1. (i) Lt G th isonnt plnr grph shown. Drw its ul G, n th ul o th ul (G ). (ii) Show tht i G is isonnt plnr grph, thn G is
On each of them are the numbers +6, 5, +4, 3, +2, 1. The two dice are rolled. The score is obtained by adding the numbers on the upper faces.
Cmrig Essntils Mthmtis Cor 8 N1.1 Homwork N1.1 Homwork 1 A thr shows hr lss 2 six-si i. On h of thm r th numrs +6, 5, +4, 3, +2, 1. Th two i r roll. Th sor is otin y ing th numrs on th uppr fs. Clult th
Graph Isomorphism. Graphs - II. Cayley s Formula. Planar Graphs. Outline. Is K 5 planar? The number of labeled trees on n nodes is n n-2
Grt Thortil Is In Computr Sin Vitor Amhik CS 15-251 Ltur 9 Grphs - II Crngi Mllon Univrsity Grph Isomorphism finition. Two simpl grphs G n H r isomorphi G H if thr is vrtx ijtion V H ->V G tht prsrvs jny
An undirected graph G = (V, E) V a set of vertices E a set of unordered edges (v,w) where v, w in V
Unirt Grphs An unirt grph G = (V, E) V st o vrtis E st o unorr gs (v,w) whr v, w in V USE: to mol symmtri rltionships twn ntitis vrtis v n w r jnt i thr is n g (v,w) [or (w,v)] th g (v,w) is inint upon
Section 3: Antiderivatives of Formulas
Chptr Th Intgrl Appli Clculus 96 Sction : Antirivtivs of Formuls Now w cn put th is of rs n ntirivtivs togthr to gt wy of vluting finit intgrls tht is ct n oftn sy. To vlut finit intgrl f(t) t, w cn fin
Page 1. Question 19.1b Electric Charge II Question 19.2a Conductors I. ConcepTest Clicker Questions Chapter 19. Physics, 4 th Edition James S.
ConTst Clikr ustions Chtr 19 Physis, 4 th Eition Jms S. Wlkr ustion 19.1 Two hrg blls r rlling h othr s thy hng from th iling. Wht n you sy bout thir hrgs? Eltri Chrg I on is ositiv, th othr is ngtiv both
Complete Solutions for MATH 3012 Quiz 2, October 25, 2011, WTT
Complt Solutions or MATH 012 Quiz 2, Otor 25, 2011, WTT Not. T nswrs ivn r r mor omplt tn is xpt on n tul xm. It is intn tt t mor omprnsiv solutions prsnt r will vlul to stunts in stuyin or t inl xm. In
16.unified Introduction to Computers and Programming. SOLUTIONS to Examination 4/30/04 9:05am - 10:00am
16.unii Introution to Computrs n Prormmin SOLUTIONS to Exmintion /30/0 9:05m - 10:00m Pro. I. Kristin Lunqvist Sprin 00 Grin Stion: Qustion 1 (5) Qustion (15) Qustion 3 (10) Qustion (35) Qustion 5 (10)
12. Traffic engineering
lt2.ppt S-38. Introution to Tltrffi Thory Spring 200 2 Topology Pths A tlommunition ntwork onsists of nos n links Lt N not th st of nos in with n Lt J not th st of nos in with j N = {,,,,} J = {,2,3,,2}
Binomials and Pascal s Triangle
Binomils n Psl s Tringl Binomils n Psl s Tringl Curriulum R AC: 0, 0, 08 ACS: 00 www.mthltis.om Binomils n Psl s Tringl Bsis 0. Intif th prts of th polnomil: 8. (i) Th gr. Th gr is. (Sin is th highst
d e c b a d c b a d e c b a a c a d c c e b
FLAT PEYOTE STITCH Bin y mkin stoppr -- sw trou n pull it lon t tr until it is out 6 rom t n. Sw trou t in witout splittin t tr. You soul l to sli it up n own t tr ut it will sty in pl wn lt lon. Evn-Count
CSE 373. Graphs 1: Concepts, Depth/Breadth-First Search reading: Weiss Ch. 9. slides created by Marty Stepp
CSE 373 Grphs 1: Conpts, Dpth/Brth-First Srh ring: Wiss Ch. 9 slis rt y Mrty Stpp http://www.s.wshington.u/373/ Univrsity o Wshington, ll rights rsrv. 1 Wht is grph? 56 Tokyo Sttl Soul 128 16 30 181 140
In which direction do compass needles always align? Why?
AQA Trloy Unt 6.7 Mntsm n Eltromntsm - Hr 1 Complt t p ll: Mnt or s typ o or n t s stronst t t o t mnt. Tr r two typs o mnt pol: n. Wrt wt woul ppn twn t pols n o t mnt ntrtons low: Drw t mnt l lns on
Graphs. Graphs. Graphs: Basic Terminology. Directed Graphs. Dr Papalaskari 1
CSC 00 Disrt Struturs : Introuon to Grph Thory Grphs Grphs CSC 00 Disrt Struturs Villnov Univrsity Grphs r isrt struturs onsisng o vrs n gs tht onnt ths vrs. Grphs n us to mol: omputr systms/ntworks mthml
What do you know? Listen and find. Listen and circle. Listen and chant. Listen and say. Lesson 1. sheep. horse
Animls shp T h i nk Wht o you know? 2 2:29 Listn n fin. hors Wht s this? Wht s this? It s got ig nos. It s ig n gry. It s hors! YES! 2 Wht r ths? Wht r ths? Thy v got two lgs. Thy r smll n rown. Thy r
CSE 373: More on graphs; DFS and BFS. Michael Lee Wednesday, Feb 14, 2018
CSE 373: Mor on grphs; DFS n BFS Mihl L Wnsy, F 14, 2018 1 Wrmup Wrmup: Disuss with your nighor: Rmin your nighor: wht is simpl grph? Suppos w hv simpl, irt grph with x nos. Wht is th mximum numr of gs
CSC Design and Analysis of Algorithms. Example: Change-Making Problem
CSC 801- Dsign n Anlysis of Algorithms Ltur 11 Gry Thniqu Exmpl: Chng-Mking Prolm Givn unlimit mounts of oins of nomintions 1 > > m, giv hng for mount n with th lst numr of oins Exmpl: 1 = 25, 2 =10, =
The University of Sydney MATH 2009
T Unvrsty o Syny MATH 2009 APH THEOY Tutorl 7 Solutons 2004 1. Lt t sonnt plnr rp sown. Drw ts ul, n t ul o t ul ( ). Sow tt s sonnt plnr rp, tn s onnt. Du tt ( ) s not somorp to. ( ) A onnt rp s on n
12/3/12. Outline. Part 10. Graphs. Circuits. Euler paths/circuits. Euler s bridge problem (Bridges of Konigsberg Problem)
12/3/12 Outlin Prt 10. Grphs CS 200 Algorithms n Dt Struturs Introution Trminology Implmnting Grphs Grph Trvrsls Topologil Sorting Shortst Pths Spnning Trs Minimum Spnning Trs Ciruits 1 Ciruits Cyl 2 Eulr
5/9/13. Part 10. Graphs. Outline. Circuits. Introduction Terminology Implementing Graphs
Prt 10. Grphs CS 200 Algorithms n Dt Struturs 1 Introution Trminology Implmnting Grphs Outlin Grph Trvrsls Topologil Sorting Shortst Pths Spnning Trs Minimum Spnning Trs Ciruits 2 Ciruits Cyl A spil yl
Exam 1 Solution. CS 542 Advanced Data Structures and Algorithms 2/14/2013
CS Avn Dt Struturs n Algorithms Exm Solution Jon Turnr //. ( points) Suppos you r givn grph G=(V,E) with g wights w() n minimum spnning tr T o G. Now, suppos nw g {u,v} is to G. Dsri (in wors) mtho or
Construction 11: Book I, Proposition 42
Th Visul Construtions of Euli Constrution #11 73 Constrution 11: Book I, Proposition 42 To onstrut, in givn rtilinl ngl, prlllogrm qul to givn tringl. Not: Equl hr mns qul in r. 74 Constrution # 11 Th
The Plan. Honey, I Shrunk the Data. Why Compress. Data Compression Concepts. Braille Example. Braille. x y xˆ
h ln ony, hrunk th t ihr nr omputr in n nginring nivrsity of shington t omprssion onpts ossy t omprssion osslss t omprssion rfix os uffmn os th y 24 2 t omprssion onpts originl omprss o x y xˆ nor or omprss
DETAIL B DETAIL A 7 8 APPLY PRODUCT ID LABEL SB838XXXX ADJ FOUR POST RACK SQUARE HOLE RAIL B REVISION
RVISION RV SRIPTION Y T HNG NO NOT OR PROUT LL JJH // LR TIL PPLY PROUT I LL TIL INSI UPPR ROSS MMR ON PR RK IS J OUR POST RK SQUR HOL RIL IS MN MS G NUT, PNL RNG 99 PPLY PROUT I LL INSI UPPR ROSS MMR
TOPIC 5: INTEGRATION
TOPIC 5: INTEGRATION. Th indfinit intgrl In mny rspcts, th oprtion of intgrtion tht w r studying hr is th invrs oprtion of drivtion. Dfinition.. Th function F is n ntidrivtiv (or primitiv) of th function
CONVERTING UNITS. Converting Units PASSPORT
CONVERTING UNITS PASSPORT www.mthltis.om.u This ook shows how to writ th sm vlu using smllr or lrgr units o msurmnt. Mny nint ivilistions msur lngths/istns y rlting thm to rtin oy prts. Invstigt ths trms
MAT3707. Tutorial letter 201/1/2017 DISCRETE MATHEMATICS: COMBINATORICS. Semester 1. Department of Mathematical Sciences MAT3707/201/1/2017
MAT3707/201/1/2017 Tutoril lttr 201/1/2017 DISCRETE MATHEMATICS: COMBINATORICS MAT3707 Smstr 1 Dprtmnt o Mtmtil Sins SOLUTIONS TO ASSIGNMENT 01 BARCODE Din tomorrow. univrsity o sout ri SOLUTIONS TO ASSIGNMENT
Nefertiti. Echoes of. Regal components evoke visions of the past MULTIPLE STITCHES. designed by Helena Tang-Lim
MULTIPLE STITCHES Nrtiti Ehos o Rgl omponnts vok visions o th pst sign y Hln Tng-Lim Us vrity o stiths to rt this rgl yt wrl sign. Prt sping llows squr s to mk roun omponnts tht rp utiully. FCT-SC-030617-07
Algorithmic and NP-Completeness Aspects of a Total Lict Domination Number of a Graph
Intrntionl J.Mth. Comin. Vol.1(2014), 80-86 Algorithmi n NP-Compltnss Aspts of Totl Lit Domintion Numr of Grph Girish.V.R. (PES Institut of Thnology(South Cmpus), Bnglor, Krntk Stt, Ini) P.Ush (Dprtmnt
Grade 7/8 Math Circles March 4/5, Graph Theory I- Solutions
ulty o Mtmtis Wtrloo, Ontrio N ntr or ution in Mtmtis n omputin r / Mt irls Mr /, 0 rp Tory - Solutions * inits lln qustion. Tr t ollowin wlks on t rp low. or on, stt wtr it is pt? ow o you know? () n
BASIC CAGE DETAILS SHOWN 3D MODEL: PSM ASY INNER WALL TABS ARE COINED OVER BASE AND COVER FOR RIGIDITY SPRING FINGERS CLOSED TOP
MO: PSM SY SI TIS SOWN SPRIN INRS OS TOP INNR W TS R OIN OVR S N OVR OR RIIITY. R TURS US WIT OPTION T SINS. R (UNOMPRSS) RR S OPTION (S T ON ST ) IMNSIONS O INNR SIN TO UNTION WIT QU SM ORM-TOR (zqsp+)
V={A,B,C,D,E} E={ (A,D),(A,E),(B,D), (B,E),(C,D),(C,E)}
s s of s Computr Sin & Enginring 423/823 Dsign n Anlysis of Ltur 03 (Chptr 22) Stphn Sott (Apt from Vinohnrn N. Vriym) s of s s r strt t typs tht r pplil to numrous prolms Cn ptur ntitis, rltionships twn
SOLVED EXAMPLES. be the foci of an ellipse with eccentricity e. For any point P on the ellipse, prove that. tan
LOCUS 58 SOLVED EXAMPLES Empl Lt F n F th foci of n llips with ccntricit. For n point P on th llips, prov tht tn PF F tn PF F Assum th llips to, n lt P th point (, sin ). P(, sin ) F F F = (-, 0) F = (,
In order to learn which questions have been answered correctly: 1. Print these pages. 2. Answer the questions.
Crystl Rports for Visul Stuio.NET In orr to lrn whih qustions hv n nswr orrtly: 1. Print ths pgs. 2. Answr th qustions. 3. Sn this ssssmnt with th nswrs vi:. FAX to (212) 967-3498. Or. Mil th nswrs to
Formal Concept Analysis
Forml Conpt Anlysis Conpt intnts s losd sts Closur Systms nd Implitions 4 Closur Systms 0.06.005 Nxt-Closur ws dvlopd y B. Gntr (984). Lt M = {,..., n}. A M is ltilly smllr thn B M, if B A if th smllst
Last time: introduced our first computational model the DFA.
Lctur 7 Homwork #7: 2.2.1, 2.2.2, 2.2.3 (hnd in c nd d), Misc: Givn: M, NFA Prov: (q,xy) * (p,y) iff (q,x) * (p,) (follow proof don in clss tody) Lst tim: introducd our first computtionl modl th DFA. Tody
Chem 107: Inorganic Chemistry (40720)
Chm 107: Inorgni Chmistry (40720) Prossor Mtt Lw -mil: lwm@ui.u Oi Hours: W 3:00-4:00p n Thurs 11-noon in NS2 2127 TAs Julit Khosrowi -mil: jkhosrow@ui.u Oi Hours: Tus 2:00-3:00p, 3 r loor tls, Rins Hll
Graphs. CSC 1300 Discrete Structures Villanova University. Villanova CSC Dr Papalaskari
Grphs CSC 1300 Disrt Struturs Villnov Univrsity Grphs Grphs r isrt struturs onsis?ng of vr?s n gs tht onnt ths vr?s. Grphs n us to mol: omputr systms/ntworks mthm?l rl?ons logi iruit lyout jos/prosss f
V={A,B,C,D,E} E={ (A,D),(A,E),(B,D), (B,E),(C,D),(C,E)}
Introution Computr Sin & Enginring 423/823 Dsign n Anlysis of Algorithms Ltur 03 Elmntry Grph Algorithms (Chptr 22) Stphn Sott (Apt from Vinohnrn N. Vriym) I Grphs r strt t typs tht r pplil to numrous
Lecture 20: Minimum Spanning Trees (CLRS 23)
Ltur 0: Mnmum Spnnn Trs (CLRS 3) Jun, 00 Grps Lst tm w n (wt) rps (unrt/rt) n ntrou s rp voulry (vrtx,, r, pt, onnt omponnts,... ) W lso suss jny lst n jny mtrx rprsntton W wll us jny lst rprsntton unlss
INTEGRALS. Chapter 7. d dx. 7.1 Overview Let d dx F (x) = f (x). Then, we write f ( x)
Chptr 7 INTEGRALS 7. Ovrviw 7.. Lt d d F () f (). Thn, w writ f ( ) d F () + C. Ths intgrls r clld indfinit intgrls or gnrl intgrls, C is clld constnt of intgrtion. All ths intgrls diffr y constnt. 7..
Schick CDR consumables catalogue
Shik CDR onsumls tlou usin your Shik CDR positionin systm vrythin you n to t strt 2 2 3 4 Slt th orrt shlth siz or your snsor. Slip th shth ovr th snsor n tth th pproprit imin rins n rms s thy o ll th
EXAMPLE 87.5" APPROVAL SHEET APPROVED BY /150HP DUAL VFD CONTROL ASSEMBLY CUSTOMER NAME: CAL POLY SLO FINISH: F 20
XMPL XMPL RVISIONS ZON RV. SRIPTION T PPROV 0.00 THIS IS N PPROVL RWING OR YOUR ORR. OR MNUTURING N GIN, THIS RWING MUST SIGN N RTURN TO MOTION INUSTRIS. NY HNGS M TO THIS RWING, TR MNUTURING HS GUN WILL
Evans, Lipson, Wallace, Greenwood
Camrig Snior Mathmatial Mthos AC/VCE Units 1& Chaptr Quaratis: Skillsht C 1 Solv ah o th ollowing or x: a (x )(x + 1) = 0 x(5x 1) = 0 x(1 x) = 0 x = 9x Solv ah o th ollowing or x: a x + x 10 = 0 x 8x +
Amphenol Canada Corp.
HT SINK OPTION = PIN STYL HT SINK (NIKL PLT) N LIP (H=.mm; SN HIGHT) = PIN STYL HT SINK (NIKL PLT) N LIP (H=.mm; PI HIGHT) = PIN STYL HT SINK (NIKL PLT) N LIP (H=.mm; TLL) = PIN-FIN HT SINK (NOIZ, LK)N
5/7/13. Part 10. Graphs. Theorem Theorem Graphs Describing Precedence. Outline. Theorem 10-1: The Handshaking Theorem
Thorm 10-1: Th Hnshkin Thorm Lt G=(V,E) n unirt rph. Thn Prt 10. Grphs CS 200 Alorithms n Dt Struturs v V (v) = 2 E How mny s r thr in rph with 10 vrtis h of r six? 10 * 6 /2= 30 1 Thorm 10-2 An unirt
UNCORRECTED SAMPLE PAGES. Length, area, surface 5area and volume. Online resources. What you will learn
Onlin rsours Auto-mrk hptr pr-tst Vio monstrtions o ll work xmpls Intrtiv wigts Intrtiv wlkthroughs Downlol HOTshts Ass to ll HOTmths Austrlin Curriulum ourss Ass to th HOTmths gms lirry Lngth, r, sur
CS61B Lecture #33. Administrivia: Autograder will run this evening. Today s Readings: Graph Structures: DSIJ, Chapter 12
Aministrivi: CS61B Ltur #33 Autogrr will run this vning. Toy s Rings: Grph Struturs: DSIJ, Chptr 12 Lst moifi: W Nov 8 00:39:28 2017 CS61B: Ltur #33 1 Why Grphs? For xprssing non-hirrhilly rlt itms Exmpls:
BASIC CAGE DETAILS D C SHOWN CLOSED TOP SPRING FINGERS INNER WALL TABS ARE COINED OVER BASE AND COVER FOR RIGIDITY
SI TIS SOWN OS TOP SPRIN INRS INNR W TS R OIN OVR S N OVR OR RIIITY. R IMNSIONS O INNR SIN TO UNTION WIT QU SM ORM-TOR (zqsp+) TRNSIVR. R. RR S OPTION (S T ON ST ) TURS US WIT OPTION T SINS. R (INSI TO
Weighted Graphs. Weighted graphs may be either directed or undirected.
1 In mny ppltons, o rp s n ssot numrl vlu, ll wt. Usully, t wts r nonntv ntrs. Wt rps my tr rt or unrt. T wt o n s otn rrr to s t "ost" o t. In ppltons, t wt my msur o t lnt o rout, t pty o ln, t nry rqur
N1.1 Homework Answers
Camrig Essntials Mathmatis Cor 8 N. Homwork Answrs N. Homwork Answrs a i 6 ii i 0 ii 3 2 Any pairs of numrs whih satisfy th alulation. For xampl a 4 = 3 3 6 3 = 3 4 6 2 2 8 2 3 3 2 8 5 5 20 30 4 a 5 a
COMP108 Algorithmic Foundations
Grdy mthods Prudn Wong http://www.s.liv..uk/~pwong/thing/omp108/01617 Coin Chng Prolm Suppos w hv 3 typs of oins 10p 0p 50p Minimum numr of oins to mk 0.8, 1.0, 1.? Grdy mthod Lrning outoms Undrstnd wht
Jonathan Turner Exam 2-10/28/03
CS Algorihm n Progrm Prolm Exm Soluion S Soluion Jonhn Turnr Exm //. ( poin) In h Fioni hp ruur, u wn vrx u n i prn v u ing u v i v h lry lo hil in i l m hil o om ohr vrx. Suppo w hng hi, o h ing u i prorm
Polygons POLYGONS.
Polgons PLYGNS www.mthltis.o.uk ow os it work? Solutions Polgons Pg qustions Polgons Polgon Not polgon Polgon Not polgon Polgon Not polgon Polgon Not polgon f g h Polgon Not polgon Polgon Not polgon Polgon