Glossary. Mathematics Glossary. Elementary School Level. English / Bengali

Transcription

1 Elementary School Level Glossary Mathematics Glossary English / Bengali Translation of Mathematics Terms Based on the Coursework for Mathematics Grades 3 to 5. Word-for-word glossaries are used for testing accommodations for ELL/LEP students Last Updated: 08/10/09 THE STATE EDUCATION DEPARTMENT / THE UNIVERSITY OF THE STATE OF NEW YORK / ALBANY, NY 12234

2 THE STATE EDUCATION DEPARTMENT / THE UNIVERSITY OF THE STATE OF NEW YORK / ALBANY, NY Education - P-16 Office of Elementary, Middle, Secondary, and Continuing Education and Office of Higher Education Office of Bilingual Education and Foreign Language Studies THE UNIVERSITY OF THE STATE OF NEW YORK Regents of the University MERRYL H. TISCH, Chancellor, B.A., M.A., Ed.D.... New York MILTON L. COFIELD, Vice Chancellor, B.S., M.B.A., Ph.D.... Rochester ROBERT M. BENNETT, Chancellor Emeritus, B.A., M.S.... Tonawanda SAUL B. COHEN, B.A., M.A., Ph.D... New Rochelle JAMES C. DAWSON, A.A., B.A., M.S., Ph.D.... Plattsburgh ANTHONY S. BOTTAR, B.A., J.D.... Syracuse GERALDINE D. CHAPEY, B.A., M.A., Ed.D.... Belle Harbor HARRY PHILLIPS, 3rd, B.A., M.S.F.S.... Hartsdale JOSEPH E. BOWMAN, JR., B.A., M.L.S., M.A., M.Ed., Ed.D... Albany JAMES R. TALLON, JR., B.A., M.A.... Binghamton ROGER TILLES, B.A., J.D.... Great Neck KAREN BROOKS HOPKINS, B.A., M.F.A... Brooklyn CHARLES R. BENDIT, B.A.... Manhattan BETTY A. ROSA, B.A., M.S. in Ed., M.S. in Ed., M.Ed., Ed.D... Bronx LESTER W. YOUNG, JR., B.S., M.S., Ed. D.... Oakland Gardens CHRISTINE D. CEA, B.A., M.A., Ph.D.... Staten Island WADE S. NORWOOD, B.A.... Rochester Interim President of the University and Commissioner of Education CAROLE F. HUXLEY Senior Deputy Commissioner of Education, P 16 JOHANNA DUNCAN-POITIER Associate Commissioner for Curriculum and Instructional Support JEAN STEVENS Coordinator, Office of Bilingual Education and Foreign language Studies PEDRO J. RUIZ Acknowledgements: The New York State Education Department Glossaries for English Language Learners were reviewed and updated during the school year. We would like to thank in these efforts the New York State Education Department Language BETACs (Spanish, Asian and Haitian Bilingual Education Technical Assistance Centers), the NYS Office of Curriculum, Instruction and Instructional Technology; the New York City Department of Education Office of English Language Learners, and the NYC Department of Education Translation and Interpretation Unit. The State Education Department does not discriminate on the basis of age, color, religion, creed, disability, marital status, veteran status, national origin, race, gender, genetic predisposition or carrier status, or sexual orientation in its educational programs, services and activities. Portions of this publication can be made available in a variety of formats, including brailed, large print or audio tape, upon request. Inquiries concerning this policy of nondiscrimination should be directed to the Department s Office for Diversity, Ethics, and Access, Room 530, Education Building, Albany, NY

3 Grades 3-5 English about above absolute value accurate accurately label work act it out acute angle acute triangle add addend addition addition fact addition sentence addition sign additive inverses after afternoon algebra algebraic expression algebraic patterns algebraic relationship algebraic relationships algebraically algorithm alike all all together almost amount analog clock analyze angle ( ) angles, adjacent answer ante meridian (a.m.) apex application apply approach appropriate mathematical language appropriate mathematical language organize work arc area argument argument conjecture counterexample arithmetic (numeric) expression arithmetic expression arithmetic fact arrange array Bengali cövq Dc i Pig gvb wbf yj wbf yjfv e wpwýz KvR mgvavb Ki, K i `LvI m~² KvY m~² wî KvY hvm Kiv Awf hvr, h msl v jv K hvm Kiv nq hvm Kiv NUbv ev Z _ i ms hvrb ev K i ms hvrb hvmwpý hšwmk e Í AbycvZ, h msl v jvi hvmdj k~b nq mb msl v c i Acivý exrmwyz exrmvwywzk ivwk exrmvwywzk c vuvb ev web vm exrmvwywzk m úk exrmvwywzk m úk mg~n exrmwy Zi wbq g AvjMwi`&&g&&, wewfbœ av c mgm v mgvavb cöwµqv Abyiƒc, m` k me me gvu cövq cwigvy, msl v A vbvjm Nwo, cyi bv KvUvIqvjv Nwo we køly KvY KvY, mwbœwnz DËi c~e vnè kxl we `y cö qvm cö qvm c wz h_v_ MvwYwZK cwifvlv h_v_ MvwYwZK cwifvlv msmwvz KvR e ËPvc ÿîdj, AvqZb hyw³ hyw³ AbywgZ cvëv ` óvší MvwYwZK (mvswl K) ivwk MwYZ ivwk MvwYwZK web vm web vm

4 as long as associative property attribute autumn (fall) average axis (axes) bar graph base base of a 3-dimensional figure base of a parallelogram base of a polygon base of a polyhedron base of a rectangle base of a triangle base ten number system before below beside between on big/bigger/biggest bisect calculate calendar capacity cardinal numbers (1-10) cent centimeter (cm) chance charts circle circle graph circumference clarify classify triangles closed figure coin collaborate collection common common denominator common factor common multiple commutative property of addition commutative property of multiplication compare compare numbers compatible numbers compensation complementary angles compose a number compose shapes composite number concentric circles conclusion concrete representations h ch ší Abyl½x cökzwz cök wz kir Mo Aÿ Í jlwpî f~wg, Zj il, Zj `k wî-gvwîk AvK wzi f~wg mvgšíwik ÿ Îi f~wg eûf~ Ri f~wg eûzj Ki f~wg AvqZ ÿ Îi f~wg wîf~ Ri f~wg wbavb 10 b ^ic wz Av M wb P ga ezx i wbk U e nr/e nëi/e nëg wølwðz Kiv MYbv Kiv K v jûvi, ZvwjKv, m~wp aviyÿgzv/mvg_ gšwjk msl v m U/kZ mw UwgUvi my hvm, m vebv PvU, mviwy e Ë e Ë jlwpî cwiwa e vl v wîf~ Ri kªwyweb vm Kiv e vk wz gy`ªv mn hvwmzv Kiv msmön mvaviy mvaviy ni mvaviy YYxqK mvaviy wyzk hv Mi wewbgq ag Y bi wewbgq ag Zzjbv Zzj msl v mym½z msl v ÿwzc~iy cwic~ik KvY msl v MVb AvKvi MVb wgkª msl v mg Kw `ªK e Ë Dcmsnvi/wm vší ev Íe cöwzwbwaz

5 cone congruent congruent triangles conjecture connect consecutive consecutive angles constant construct contrast conversion fact convert coordinate coordinate grid coordinate plane corner corresponding angles corresponding sides count back count backwards count on counterexample counting numbers counting numbers cube cubic centimeter (cm3) cubic unit cup (c) currency symbols customary measurement system customary units of measure cylinder data data frequency table day daylight decagon decimal fraction decimal number decimal point decimeter decompose a number decompose shapes decrease decreasing sequences degree degree measure of an angle denominator density design diameter difference differences digit gvpvk wz e, Kvb me mg me mg wîf~r AbywgwZ, Abygvb Kiv ms hvm. ms hvm vcb Ae ewnz mvaviy evûwewkó ci úi mwbœwnz `ywu KvY aªæe MVb Kiv, A¼b Kiv cöwzzzjbv iƒcvší ii e vl v iƒcvšíi vbv¼ vbv¼ QK mwbœ ek mgzj KvY m` k KvY m` k evû Avevi MYbv Kiv D ëv MYbv Kiv b hviqv wecixz D`vniY msl v MYbv msl v MYbv Nb/Nbdj Nb mw UwgUvi MY GKK kxl (wm) g~`ªv wpý cö_vbym cwigvc c wz cö_vbym cwigvc GKK wmwjûvi DcvË DcvË cwimsl v mviwy w`b w`ev jvk `kevû `kwgk fmœvsk `kwgk msl v `kwgk we `y WwmwgUvi msl v wefvrb AvK wz n«vm n«vmµg wwwmö/cwigvc Kv Yi wwwmö cwigvc ni NbZ bkkv, wwrvbb e vm e eavb msl v, ivwk

6 digital clock mvswl K, wwwruvj digits msl vmg~n, ivwkmg~n dime WvBg dimension gvîv discuss Av jvpbv Ki distributive property wefvrb cök wz divide fvm Ki dividend fvr, jf vsk divisibility test wefvrbÿgzv cixÿv divisible wefvr divisible by Kvb wkqzi Øviv wefvr division fvm/wefvrb divisor wefvrk dodecahedron Øv`kf~R dollar ($) Wjvi doubles minus one `y Y _ K GK we qvm doubles plus one `y Yi mv _ GK hvm doubling wø Y Kiv draw a graph ilwpî A¼b draw a graph ilwpî A¼b draw a picture wpî A¼b draw a picture wpî A¼b drawings A¼b edge avi, wkbvi eight AvU elapsed time AwZµvšÍ mgq ellipse ww ^vk wz, Dce Ë endpoint kl we `y eqivalent equations mgv¼ mgxkiy equal (=) mgvb (=) equal to (=) Gi mgvb (=) equation mgxkiy equidistant marks mg`~iezx equilateral polygon mgevny enyf~r equilateral triangle mgevny wîf~r equivalent Z~j equivalent Z~j equivalent decimals Z~j `kwgk equivalent fractions Zzj fmœvsk equivalent numerical expressions Z~j MvwYwZK ivwk equivalent ratios Z~j AbycvZ estimate cövÿjb estimation cövÿwjz wnmve estimation strategies cövÿjb KŠkj evaluate g~j vqb Kiv even number Rvo msl v evening mü v event NUbv/cwiYvg examine cixÿv example ` óvší expanded form m úªmvwiz i~c experimental results cixÿvg~jk dj explain e vl v Kiv explain mathematical relationships MvwYwZK m úk e vl v `qv

7 explore explore mathematical relationships exponential notations extend a pattern extend models extended fact face fact fact family (related facts) factor (noun) factor (verb) factorial fair share fewer fewer than fifths first five flip (reflection) foot (ft) formula formulate conclusions from graphs formulate predictions from graphs four four-digit number fourths fraction frequency table front-end estimation gallon (gal) generate solutions geometric figure geometric pattern geometric solid geometry gram (g) graphical representations graphs greater greater than (>) greatest greatest common divisor (GCD) greatest common factor (GCF) grid group how many guess half hour halves halving heavier height height of a 3-dimensional figure height of a parallelogram height of a rectangle cy Lvbycy Lfv e AbymÜvb Kiv cy Lvbycy Lfv e MvwYwZK m úk AbymÜvb Kiv gvbm~pk A¼cvZb, GKwU Ybxq Ki cšbtcywbk Y bi m wÿß cökvk c vuv b we Ívi Ki g Wj we Ívi Kiv m úªmvwiz NUbv Zj, cvk, evû NUbv m ^Ühy³ NUbv YbxqK/Drcv`K YbxqK ei Ki MŠwYK b vh wnm v ^ízi n Z Kg câgvsk cö_g cuvp Dëv bv (cöwzwe ^) dzu (ft) m~î wpî jl _ K wm vší AvniY wpî jl _ K fwel ØvYx Pvi Pvi ivwki msl v PZy_ vsk fmœvsk cwimsl v mviwy g~ j i cövwšík ch vq M vjb mgvavb ei Ki R vwgwzk AvK wz R vwgwzk c vuvb R vwgwzk AvK wzwewkó R vwgwz MÖvg mwpî Dc vcbv, ˆiwLK Dc vcbv ilwpî e nëi n Z e nëi e nëg Mwiô mvaviy wefvrk Mwiô mvaviy YbxqK wmöw, QK KZ msl v K i MÖæc Abygvb Ki Aa N Uv A a K wøav wef³ Kiv A cÿvk Z fvix D PZv wîgvwîk e i D PZv mvgšíwik ÿ Îi D PZv AvqZ ÿ Îi D PZv

8 height of a triangle wîf~ Ri D PZv heptagon mßf~r hexagon lu KvY higher D PZi horizontal Avbyf~wgK hour N Uv hour hand N Uvi KuvUv hundred chart kz mviwy hundred thousands jÿ hundred thousands millions nvrvi KvwU hundreds kz kz hundreds place kz Ki Ni hundredths kzzg, kzvsk hundreths kzzg, kzvsk hypotenuse AwZf~R icosahedron 20 cvk -wewkó eûzjk ÿî ev cwj nwªb hv mgevû wîf R Øviv MwVZ nq identify kbv³ Kiv identify the problem mgm v kbv³ Ki identity element for addition ms hvrb Kivi Rb A f` gšwjk c`v_ identity element for multiplication Y Kivi Rb A f` gšwjk c`v_ impossible outcomes Am e cwiywz improper fraction AcÖK Z fmœvsk inch (in) Bw increase e w Ki increasing sequences ewa Z µg inequality AmgZv input values gvb emv bv inscribed polygon AšÍe ûf ~R inside Af šíi integer c~y msl v interior angles AšÍt KvY interpret e vl v Ki interpret models g Wj e vl v Ki intersect ci úi Q` Kiv intersecting lines ci úi Q`bKvix ilv invalid approach Awm cöwµqv inverse operations weez wµqv inverse property weez cök wz investigate AbymÜvb Ki irrational numbers Ag~j` msl v irregular polygon welg eûf~r irregular shape welg AvKvi irrelevant information AcÖvmw½K Z_ isosceles triangle mgwøevû wîf~r justify mg_ b Ki key sequence cöavb µg key to a graph Í ilwp Îi m~î kilogram (kg) wk jvmövg ( KwR) kilometer (Km) wk jvwguvi (wkwg) kite Nywo label work wpwýz KvR language of logic(and, or, not) hyw³i fvlv large/larger/largest e nr, e nëi, e nëg

9 last least common denominator (LCD) least common multiple (LCM) leg of a right triangle length less less than (<) lighter like (common) denominators likely line line graph line of symmetry line plot line segment line symmetry listen liter (L) logical reasoning long/longer/longest longer longer than look for a pattern lower lowest terms (simplest form) make a chart make a diagram make an organized chart make an organized list make conjectures make observations map legend map scale mass match mathematical statements mathematics mean measure measurement median mental math meter (m) metric system of measurement metric units of measure mile milliliter (ml) millimeter (mm) millions minuend minus minus sign minute minute kl jwnô mvaviy ni jwnô mvaviy MywYZK (jmv ) mg KvYx wîf~ Ri evû, Z e AwZfzR bq ˆ`N Kg jnyzi Zzjbvg~jKfv e nvév m` k nimg~n m e ilv ˆiwLK Í jlwpî cöwzmvgm ilv ilv wpî e Ëvsk ilv ilv mgwgwz kvbv wjuvi (wj) hšw³k Kvh KviY `xn /`xn Zi/`xN Zg `xn Zi Zzjbvg~jK `xn c vuvb LuvRv Zzjbvg~jK wb P jwnô ivwk (mij iƒc) mviwy ˆZwi Kiv WvqvMÖvg ˆZwi Kiv myk Lj mviwy ˆZwi Kiv myk Lj ZvwjKv ˆZwi Kiv AbywgwZ wbg vy Kiv ch eÿy Kiv gvbwp Îi ms KZ gvbwp Îi j fi wgj MvwYwZK wee wz MwYZ ga K, Mo cwigvc Ki cwigvc/gvb ga gv/ga ilv gvbmv¼ wguvi (wg) gwuªk c wzi cwigvc gwuªk c wz Z cwigv ci GKK gvbj wgwj wjuvi (wgwj) wgwj wguvi (wgwg) `k jvk (wgwjqb) h msl v K we qvm `qv nq we qvm we qvm wpý wgwbu, weeiy wgwbu, weeiy

10 minute hand mixed number mode money months of the year more more than (>) more/most morning multiple multiple representations multiplicand multiplication multiplicative inverses multiplier multiply negative number negative rational numbers next nickel night nine nonagon nonstandard measure nonstandard representations nonstandard units noon not equal to (¹) not equal to = number number in words number line number model number sentence number system numeral numeration numerator numeric expression numeric patterns numerical problems numerically objects objects created using technology obtuse angle obtuse triangle octagon octagon parallel lines odd number one one-digit number ones ones place open figure wgwb Ui KvUv hšwmk msl v msl vmwiô gvb A_ ev iv gvm AwaK Zzjbvg~jK ewk ewk/me P q ewk mkvj eny eny Z i cªwzwbwaz Kvix MyYbxqK MyY Kiv weez /e Í MyYb YbxqK, MyYK MyY Ki FYvZ K msl v FYvZ K hšw³k msl v ciezx wb Kj, 5 m U gv bi g~`ªv ivz bq bqf~r AcÖwgZ cwigvc AcÖwgZ cöwzwbwaz AcÖwgZ GKK ga vnè mgvb bq mgvb bq msl v msl vi K_vq cökvk msl v ilv b ^i cöwzgvb ev K i b ^i msl v c wz msl vm~pk/msl vmz msl vqb, msl v K K_vq cökvk je msl vm~pk ivwk msl vm~pk c vuvb msl vm~pk mg mv msl vmzfv e welq, e cöhyw³ e envi K i cö Z e KvY j KvY wîf~r Aóf~R mgvšíivj evû Aóf~R e Rvo msl v GK GKivwk msl v GKK gy³ AvK wz

11 open sentence gy³ evk operation wµqv operational method/operation Kvh cöyvwj oral representations kvwãk cöwzwbwaz order k Ljv, µg order of operations wµqvµg ordered number pair hymj msl vµg ordinal numbers web Í msl v organize web vm Kiv organize work Kg web vm organized chart web Í mviwy organized list web Í ZvwjKv origin Drm ounce (oz) AvDÝ over Dc i, Avevi, ewk pan balance c vb e vjvý parabola Awae Ë parallel lines mgvšíivj ilv parallelogram mvgšíwik ÿî part Ask part-to-part ratio wewfbœ As ki AbycvZ part-to-whole ratio mg MÖi mv _ As ki AbycvZ pattern c vuvb penny cwb (GKkZ fv Mi GK fvm) pentagon câf~r percent kzvsk perimeter cwimxgv perpendicular lines j ^ ilvmg~n personal references e w³mz Z_ per-unit rate GKK g~j physical models fšz Av`k pi cvb pictograph wpî jl pictorial representations mwpî cöwzwbwaz pint (pt) cvb U place value vbxq gvb plane mgzj plane figure mgzj AvK wz plot A¼b Kiv, cwikíbv Kiv plus hvm point we `y poll fvu Kiv polygon eûf~r polyhedron enzjk positive number abvz K msl v positive power of Gi abvz K NvZ positive rational numbers abvz K hšw³k msl v possible outcomes m ve dj post meridian (p.m.) Acivnè pound (lb) cvdû (cv) power NvZ power of Gi NvZ predict c~e vfvm Kiv prediction c~e vfvm

12 prime factorization prime number prism probability problem solving strategies process of elimination product proper fraction property protractor pyramid Pythagorean Theorem quadrangle quadrant quadrilateral quart (qt) quarter questions quotient radious random number randomly range rate ratio rational number rationale ray real number real world math real world situation reasonable estimates reasonableness reasonableness of a solution recognize rectangle reference frame regroup (regrouping) regular polygon regular polyhedron related facts relation symbol relevant information remainder repeated addition repeated subtraction repeating decimal rhombus right angle rotation round a number rounding rule ruler gšwjk YK wby q gšwjk msl v Zwkiv KuvP/wcÖRg m vebv mgm v mgvavb KŠkj Ac bv`b cöwµqv Ydj/Drcbœ e cök Z fmœvsk ag /cökzwz KvY cöwigvck wcivwgw wc_v Mvixq Dccv` PZzf~ R/PZz vy cwiwai GK PZy_ vsk PZzf~ R/PZz vy KvqvU wmwk (GK PZz_ vsk) cökœ fvmdj e vmva G jv g jv msl v G jv g jvfv e we Í wz nvi AbycvZ hšw³k msl v gšj hyw³/ hšw³k wfwë iwk ev Íe msl v ˆ`bw `b MwYZ ˆ`bw `b NUbv hšw³k cövÿjb hšw³kzv mgvav bi hšw³kzv ^xk wz AvqZ ÿî cwipvqk KvVv gv bzzb `jwefvrb Kiv mylg eûf~r mylg enzjk mswkøó Z_ m ^Ü wpý cövmw½k Z_ Aewkó c~bive Ë hvm c~bive Ë we qvm c~bive Ë `kwgk welg KvY mvgšíwik ÿî/i ^vm mg KvY NyY b c~y msl vq cwiyz Kiv m úbœ Kiv m~î/ixwz/wbqg cwigvck

13 same sample space scale drawing scale on a graph scale to measure mass scalene triangle scientific notation seasons in relation to the months second sector semicircle set of data set of objects seven shape share shorter shorter than show side similar figures similar triangles similar triangles square similarities simplest form simplify an expression simplify fractions single event single-event experiment six sixths size skip count slide (translation) small/smaller/smallest solid figure solution solution(s) solve solve a simpler problem some sort special case speed sphere spring square square array square number square of a number square root of a number square unit standard measure standard notation mgiƒc bgybv cwimi j A¼b jlwp Îi j fi cwigvck welg wîf~r ˆeÁvwbK cözxk FZzi mv _ m úwk Z gvm wøzxq/gyn«z kvlv/wefvm Aa e Ë DcvË web vm e ivwk mvz AvK wz eèb AwaKZi Lv Uv P q Lv Uv ` k cvk Abyiƒc AvK wz m` k wîf~r m` k KvY wewkó em ÿî mv` k mijzg AvK wz Kvb ivwk K mijxkiy Kiv fmœvs ki mijxkiy GKK ` óvší GKK ` óvšíwewkó cixÿv Qq lôzg AvKvi MYbv _ K weiz _vkv Mov bv (Abyev`) ÿz`ª/ÿz`ªzi/ÿz`ªzg c~y Nbv¼ mgvavb mgvavbmg~n mgvavb Kiv mij mgm vi mgvavb Kiv wkqz web vm we kl D`vniY MwZ ejq emší em em web vm em msl v msl vi em msl vi em g~j em GKK cöwgz cwigvc cöwgz A¼cvZb

14 standard representation standard units stem-and-leaf plot step graph straight angle strategies substitute substitution subtract subtraction subtraction fact subtraction sentence subtraction sign subtrahend sum summer supplementary angles survey symbols symbols in verbal form symbols in written form table take away tall/taller/tallest tallies tally mark ten ten thousands tens tens place tenth term terminating decimal tessellation theorem third thirds thought process thousands thousandths three three-digit number three-dimensional figure tiling time to challenge thinking to clarify thinking to elicit thinking to extend thinking together ton translate trapezoid trial and error cöwgz cöwzwbwaz cöwgz GKK KvÐ _ K cvzv ch ší (ïiæ _ K kl ch ší) MÖvd K Aej ^b K i mij KvY KŠkj cöwzkí cöwz vcb we qvm Kiv we qvm we qv Mi aviyv ev K i c _KxKiY we qvm wpý we qvr mgwó MÖx m ú~ik KvY Rwic cözxk cözx Ki gšwlk iƒc cözx Ki wjwlz iƒc mviwy mwi q bqv j ^v/awakzi j v^/awakzg j ^v Uvwj wgj wpý `k `k nvrvi ` ki Pj `k Ki Ni GK `kgvsk c`, ivwk, kz mmxg `kwgk web Í Kiv Dccv` Z Zxq GK-Z Zxqvsk wpšíbwµqv nvrvi nvrvi GK-mnmªvsg wzb wzb ivwki msl v wîgvwîk AvK wz UvBwjs mgq wpšív K P v jä Kiv wpšív K e vl v Kiv wpšív K cökvk Kiv wpšív K cömvwiz Kiv GKmv _ Ub Abyev` AmgvšÍivj evû PZzf ~R mwvk DËi bv cviqv ch ší cö Pó Ae vnz ivlv

15 triangle true/false turn (rotation) two two-digit number two-dimensional figure types of representations under understand unit unit fraction unit fractions unlike denominators unlikely use manipulatives valid approach value variable Venn diagram verbal expression verbal form of reasoning verbal language verbal process verbal symbols verify claims of others verify results vertex vertical vertical angles vertices volume week whole whole number whole numbers whole unit width winter work backwards write an equation written form of reasoning written language written representations written symbols yard (yd) year zero zero as the identy element in addition zero property of addition zero property of multiplication wîf~r mz /wg_ v gvo bqv/µgvbyhvqx `yb `yb ivwki msl v wøgvwîk AvK wz cöwzwbwa Z i cökvi f` wb P, Kg Abyaveb Kiv GKK GKK fmœvsk GKK fmœvskmg~n Amv` k nimg~n nqbv cwipvjbvi KŠkj e envi wm c wz g~j /gvb cwiez bkxj ivwk e Ë jlwpî gšwlk Awf e w³ hyw³i K_ iƒc K_ fvlv gšwlk cöwµqv gšwlk cözxk A b i `vwe cögvwyz Kiv d ji wbf yjzv cögvy kxl j ^ kxl KvY kxl Nbdj, e i cwigvy, AvqZb mßvn c~y c~y msl v c~y msl vmg~n c~y GKK cö kxz m~pbvi w` K AMÖmi niqv mgxkiy MVb Kiv hyw³i wjwlz iƒc wjwlz fvlv wjwlz cöwzwbwaz wjwlz cözxk MR eqi k~b hv Mi k~b cwiwpwz hv Mi k~b ag MY bi k~b ag