Mukati
- Tsanangudzo yenhamba dzechisikigo
- Simple Properties of natural numbers
- Tafura yezvakasikwa manhamba kubva pa1 kusvika ku100
- Ndeapi maoparesheni anogoneka pane natural manhamba
- Decimal notation yenatural number
- Quantitative meaning of natural numbers
- Nhamba imwe chete, nhamba mbiri uye nhamba nhatu dzechisikigo
- Multivalued natural numbers
- Properties of natural numbers
- Zvimiro zvenhamba dzechisikigo
- Properties of natural numbers
- Natural manhamba manhamba uye kukosha kwedijiti
- Decimal nhamba system
- Mubvunzo wekuzviongorora
Kudzidzwa kwemasvomhu kunotanga nenhamba dzechisikigo uye mashandiro nadzo. Asi intuitively isu tatoziva zvakawanda kubva paudiki. Muchinyorwa chino, tichajairana nedzidziso uye kudzidza kunyora uye kududzira nhamba dzakaoma nemazvo.
Muchinyorwa chino, tichaona tsananguro yenhamba dzechisikigo, nyora zvivakwa zvadzo zvikuru uye masvomhu akaitwa navo. Isu tinopawo tafura ine manhamba chaiwo kubva pa1 kusvika ku100.
Tsanangudzo yenhamba dzechisikigo
Integers - idzi ndidzo nhamba dzese dzatinoshandisa pakuverenga, kuratidza nhamba yeserial yechinhu, nezvimwe.
Natural series ndiko kutevedzana kwenhamba dzese dzemusikirwo dzakarongwa muhurongwa hwekukwira. Ndiko kuti, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, zvichingodaro.
Seti yenhamba dzese dzakasikwa inoratidzwa sezvinotevera:
N={1,2,3,…n,…}
N is a set; hazvina magumo, nokuti kune ani zvake n kune nhamba huru.
Nhamba dzakasikwa ndidzo nhamba dzatinoshandisa kuverenga chimwe chinhu chaicho, chinobatika.
Hedzino nhamba dzinonzi zvisikwa: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, nezvimwewo.
A natural series kutevedzana kwenhamba dzese dzakasikwa dzakarongwa muhurongwa hwekukwira. Mazana ekutanga anogona kuonekwa patafura.
Simple Properties of natural numbers
- Zero, non-integer (fractional) nenegative manhamba hadzisi manhamba chaiwo. Somuenzaniso:-5, -20.3, 3/7, 0, 4.7, 182/3 uye zvakawanda
- Iyo diki nhamba yakasikwa imwe (maererano nepfuma iri pamusoro).
- Sezvo zvakasikwa zvakatevedzana zvisingagumi, hapana nhamba huru.
Tafura yezvakasikwa manhamba kubva pa1 kusvika ku100
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
| 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 |
| 31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 | 40 |
| 41 | 42 | 43 | 44 | 45 | 46 | 47 | 48 | 49 | 50 |
| 51 | 52 | 53 | 54 | 55 | 56 | 57 | 58 | 59 | 60 |
| 61 | 62 | 63 | 64 | 65 | 66 | 67 | 68 | 69 | 70 |
| 71 | 72 | 73 | 74 | 75 | 76 | 77 | 78 | 79 | 80 |
| 81 | 82 | 83 | 84 | 85 | 86 | 87 | 88 | 89 | 90 |
| 91 | 92 | 93 | 94 | 95 | 96 | 97 | 98 | 99 | 100 |
Ndeapi maoparesheni anogoneka pane natural manhamba
- kuwedzera:
nguva + nguva = nhamba; - kuwanda:
multiplier × multiplier = chigadzirwa; - kubvisa:
minuend - subtrahend = musiyano.
Muchiitiko ichi, minuend inofanira kuva yakakura kudarika subtrahend, kana zvisina kudaro chigumisiro chichava nhamba isina kunaka kana zero;
- division:
dividend: divisor = quotient; - kupatsanura nekusara:
dividend / divisor = quotient (zvasara); - exponentiation:
ab , apo a ndihwo hwaro hwedhigirii, b ndiye exponent.
Ndeapi Natural manhamba?
Decimal notation yenatural number
Kuchikoro, tinoenda kuburikidza nemusoro wenhamba dzechisikigo mugiredhi rechishanu, asi kutaura zvazviri, zvinhu zvakawanda zvinogona kujeka kwatiri kunyange kare. Ngatitaure nezvemitemo yakakosha.
Tinogara tichishandisa manhamba: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. Pakunyora chero nhamba chaiyo, unogona kushandisa nhamba idzi chete pasina mamwe mavara. Tinonyora nhamba imwe neimwe mumutsara kubva kuruboshwe kuenda kurudyi, tichishandisa hurefu hwakafanana.
Mienzaniso yekunyora kwakarurama kwenhamba dzemusikirwo: 208, 567, 24, 1467, 899112. Iyi mienzaniso inotiratidza kuti kutevedzana kwenhamba kunogona kusiyana uye dzimwe dzinogona kudzokororwa.
077, 0, 004, 0931 mienzaniso yezvinyorwa zvisizvo zvenhamba dzechisikigo, nekuti zero iri kuruboshwe. Nhamba haigoni kutanga kubva paziro. Iyi ndiyo decimal inomiririra nhamba chaiyo.
Quantitative meaning of natural numbers
Nhamba dzechisikigo dzinotakura chirevo chehuwandu, ndiko kuti, dzinoshanda sechombo chekuverengera.
Fungai kuti pamberi pedu tine banana 🍌. Tinogona kunyora kuti tinoona 1 bhanana. Muchiitiko ichi, nhamba yechisikigo 1 inoverengwa se "imwe" kana "imwe".
Asi shoko rokuti “chikamu” rine imwe revo: icho chinogona kurangarirwa sechose. Chinhu cheseti chinogona kuratidzwa neyuniti. Semuenzaniso, chero muti unobva pamiti yemiti inhengo, chero shizha kubva kune seti yemashizha iyuniti.
Fungai kuti pamberi pedu tine mabanana maviri 🍌🍌. Nhamba yechisikigo 2 inoverengwa se "mbiri". Uyezve, nekuenzanisa:
🍌🍌🍌 Zvinhu zvitatu ("zvitatu")
🍌🍌🍌🍌 4 zvinhu ("mana")
🍌🍌🍌🍌🍌 5 zvinhu ("zvishanu")
🍌🍌🍌🍌🍌🍌 Zvinhu zvitanhatu ("zvitanhatu")
🍌🍌🍌🍌🍌🍌🍌 7 zvinhu ("zvinomwe")
🍌🍌🍌🍌🍌🍌🍌🍌 8 zvinhu ("zvisere")
🍌🍌🍌🍌🍌🍌🍌🍌🍌 9 zvinhu (“zvipfumbamwe”)
Basa guru renhamba yakasikwa kuratidza huwandu hwezvinhu.
Kana rekodhi yenhamba inoenderana nenhamba 0, inobva yanzi "zero". Yeuka kuti zero haisi nhamba chaiyo, asi inogona kureva kusavapo. Zero zvinhu zvinoreva hapana.
Nhamba imwe chete, nhamba mbiri uye nhamba nhatu dzechisikigo
Nhamba yedijiti imwe chete yakasikwa inhamba ine chiratidzo chimwe uye digit imwe. Nhamba pfumbamwe dzechisikigo manhamba: 1, 2, 3, 4, 5, 6, 7, 8, 9.
Nhamba dzemadijiti mbiri ndedziya dzine zviratidzo zviviri uye manhamba maviri. Nhamba dzinogona kudzokororwa kana dzakasiyana. Somuenzaniso: 88, 53, 70.
Kana seti yezvinhu ine zvipfumbamwe uye imwe zvakare, saka tiri kutaura nezve 1 gumi ("dozeni rimwe") rezvinhu. Kana rimwe gumi nerimwe zvakare, saka tine makumi maviri ("makumi maviri") zvichingodaro.
Muchidimbu, nhamba ine manhamba maviri iboka renhamba dzenhamba imwe chete, apo imwe inonyorwa kurudyi imwe kuruboshwe. Nhamba iri kuruboshwe inoratidza nhamba yemakumi munhamba yakasikwa, uye nhamba iri kurudyi inoratidza nhamba yezvikamu. Kune 90-manhamba-mbiri-yakasikwa manhamba muhuwandu.
Nhamba dzemadijiti matatu manhamba ane manhamba matatu nemadijiti matatu. Somuenzaniso: 666, 389, 702.
Zana iboka remakumi gumi. zana rimwe nerimwe - 2 mazana. Ngatiwedzerei mamwe mazana - mazana matatu.
Aya ndiwo manyorerwo enhamba ine manhamba matatu: manhamba chaiwo anonyorwa imwe mushure meimwe kubva kuruboshwe kuenda kurudyi.
Dijiti rimwe rekurudyi rinoratidza nhamba yezvikamu, rinotevera rinoratidza nhamba yemakumi, uye rekuruboshwe rinoratidza nhamba yemazana. Nhamba 0 inoratidza kusavapo kwezvikamu kana gumi. Saka 506 imazana mashanu, 5 makumi uye 0 mamwe.
Mana-manhamba, mashanu-manhamba, matanhatu-manhamba uye dzimwe manhamba echisikigo anotsanangurwa nenzira imwechete.
Multivalued natural numbers
Multi-digit natural manhamba ane maviri kana anopfuura manhamba.
1,000 ndeye seti ine mazana gumi, 1,000,000 churu, uye bhiriyoni imwe miriyoni. Mamirioni ane chiuru, chimbofungidzira! Ndiko kuti, isu tinogona kufunga chero yakawanda-yakakosha nhamba yakasikwa seti yeimwe-yakakosha manhamba chaiwo.
Semuenzaniso, 2 873 206 ine: 6 zvikamu, 0 makumi, 2 mazana, 3 zviuru, 7 makumi ezviuru, 8 mazana ezviuru uye 2 mamiriyoni.
Ingani nhamba dzakasikwa dziripo?
Imwe-manhamba 9, maviri-manhamba makumi mapfumbamwe, matatu-manhamba 90, nezvimwe.
Properties of natural numbers
Isu tatoziva nezvezvinhu zvemanhamba echisikigo. Uye zvino ngatitaure pamusoro pezvinhu zvavo zvakadzama:
Tsanangudzo yenhamba chaiyo
Nhamba dzakasikwa ndidzo nhamba dzatinoshandisa kuverenga chimwe chinhu chaicho, chinobatika.
Hedzino nhamba dzinonzi zvisikwa: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, nezvimwewo.
A natural series kutevedzana kwenhamba dzese dzakasikwa dzakarongwa muhurongwa hwekukwira. Mazana ekutanga anogona kuonekwa patafura.
Zvimiro zvenhamba dzechisikigo
Idiki nhamba yechisikigo: imwe (1).
Nhamba yakakura kwazvo yechisikigo: haipo. The natural series hariperi.
Mukutevedzana kwechisikigo, nhamba imwe neimwe inotevera yakakura kupfuura yekutanga neimwe: 1, 2, 3, 4, 5, 6, 7, nezvimwe.
Iyo seti yeese manhamba echisikigo inowanzo rehwa netsamba yechiLatin N.
Ndeapi maoparesheni anogoneka pane natural manhamba
kuwedzera:
nguva + nguva = nhamba;
kuwanda:
multiplier × multiplier = chigadzirwa;
kubvisa:
minuend - subtrahend = musiyano.
Muchiitiko ichi, minuend inofanira kuva yakakura kudarika subtrahend, kana zvisina kudaro chigumisiro chichava nhamba isina kunaka kana zero;
division:
dividend: divisor = quotient;
kupatsanura nekusara:
dividend / divisor = quotient (zvasara);
exponentiation:
ab , apo a ndihwo hwaro hwedhigirii, b ndiye exponent.
Saina makosi emasvomhu evadzidzi kubva kumagiredhi 1 kusvika 11!
Gadzirisa basa rako rechikoro remasvomhu ye5.
Mhinduro dzakadzama dzichabatsira kunzwisisa nyaya yakaoma kwazvo.
tora
Properties of natural numbers
Isu tatoziva nezvezvinhu zvemanhamba echisikigo. Uye zvino ngatitaure pamusoro pezvinhu zvavo zvakadzama:
- seti yenhamba dzakasikwa dzisingaperi uye dzinotangira pane imwe (1)
- nhamba yega yega inoteverwa neimwe inodarika imwe yapfuura na1
- mhedzisiro yekupatsanura nhamba chaiyo neimwechete (1) nhamba chaiyo pachayo: 5 : 1 = 5
- mhedzisiro yekupatsanura nhamba chaiyo yega unit (1): 6 : 6 = 1
- commutative mutemo wekuwedzera kubva pakurongekazve kwenzvimbo dzematemu, mari yacho haichinji: 4 + 3 = 3 + 4
- mutemo wekubatanidzwa wekuwedzera mhedzisiro yekuwedzera mazwi akati wandei haienderane nehurongwa hwekushanda: (2 + 3) + 4 = 2 + (3 + 4)
- mutemo unochinja wekuwedzera kubva mukutenderwa kwenzvimbo dzezvinhu, chigadzirwa hachichinji: 4 × 5 = 5 × 4
- associative mutemo wekuwandisa mhedzisiro yechigadzirwa chezvikonzero hazvinei nehurongwa hwekushanda; unogona kuda kuita seizvi, zvakada kudaro: (6 × 7) × 8 = 6 × (7 × 8)
- mutemo wekugovera wekuwanza maererano nekuwedzera kuwedzera huwandu nenhamba, unofanirwa kuwedzera temu yega yega nenhamba iyi uye wowedzera mhinduro: 4 × (5 + 6) = 4 × 5 + 4 × 6
- mutemo wekugovera wekuwanza neruremekedzo rwekubvisa kuwedzera mutsauko nenhamba, unogona kuwanza nenhamba iyi wakapatsanurwa nekubviswa, wozobvisa wechipiri kubva pachigadzirwa chekutanga: 3 × (4 − 5) = 3 × 4 - 3 × 5
- mutemo wekugovanisa neruremekedzo rwekuwedzera kugovanisa nhamba nenhamba, unogona kupatsanura temu yega yega nenhamba iyi wowedzera mhinduro: (9 + 8) : 3 = 9 : 3 + 8: 3
- mutemo wekugovera wekuparadzanisa maererano nekubvisa kugovera mutsauko nenhamba, unogona kupatsanura nenhamba iyi kutanga kuderedzwa, wozobvisa, uye kubvisa yechipiri kubva pachigadzirwa chekutanga: (5 - 3): 2 = 5: 2 - 3 : 2
Natural manhamba manhamba uye kukosha kwedijiti
Yeuka kuti nzvimbo iyo iyo dhijiti inomira murekodhi yenhamba inoenderana nekukosha kwayo. Saka, semuenzaniso, 1123 ine: 3 mauniti, 2 makumi, 1 zana, 1 zviuru. Panguva imwecheteyo, tinogona kuigadzira zvakasiyana totaura kuti munhamba yakapihwa 1123, nhamba 3 inowanikwa muzvikamu zvemayuniti, 2 mumakumi gumi, 1 mumazana mana, uye 1 inoshanda sekukosha kwezviuru. digit.
The digit ndiyo nzvimbo, nzvimbo yedijiti mukunyorwa kwenhamba yakasikwa.
Chikamu chimwe nechimwe chine zita rayo. Iwo manhamba akakosha anogara ari kuruboshwe, uye mashoma akakosha manhamba anogara ari kurudyi. Kuti uyeuke nekukurumidza, unogona kushandisa tafura.
Nhamba yemanhamba inogara ichienderana nehuwandu hwemavara munhamba. Tafura iyi ine mazita emanhamba ese enhamba ine mavara gumi nemashanu. Mavara anotevera anewo mazita, asi haawanzo shandiswa.
Dijiti rakaderera (risinganyanyi kukosha) renhamba yakakosheswa yakawanda ndiyo mayunitsi.
Nhamba yepamusoro-soro (yepamusoro-soro) yenhamba yakakosheswa yakawanda ndiyo idijiti inoenderana neruboshwe pane nhamba yakapihwa.
Iwe wakamboona kuti mabhuku ezvinyorwa anowanzoisa nzvimbo diki kana achinyora manhamba akawanda. Izvi zvinoitwa kuitira kuti nhamba dzechisikigo dzive nyore kuverenga. Uye zvakare - kuparadzanisa makirasi akasiyana enhamba.
Kirasi iboka remanhamba rine manhamba matatu: mayunitsi, gumi nemazana.
Decimal nhamba system
Vanhu panguva dzakasiyana vaishandisa nzira dzakasiyana dzekunyora nhamba. Uye imwe neimwe nhamba system ine mitemo yayo uye maitiro.
Decimal number system ndiyo inonyanyo shandiswa nhamba dzenhamba dzinoshandiswa kunyora manhamba gumi: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
Muchirongwa chedesimali, kukosha kwedijiti imwe chete kunoenderana nenzvimbo yayo mukunyorwa kwenhamba. Semuenzaniso, nhamba 555 ine manhamba matatu akafanana. Munhamba iyi, nhamba yekutanga kubva kuruboshwe inoreva mazana mashanu, yechipiri - makumi mashanu, uye yechitatu - mayuniti mashanu. Sezvo kukosha kwedijiti kuchienderana nenzvimbo yayo, hurongwa hwenhamba yedesimali hunonzi positional.
Mubvunzo wekuzviongorora
Ingani manhamba echisikigo anogona kumakwa pane coordination ray pakati pemapoinzi ane coordes:
0 ne15;
20 ne50;
100 uye 130?
Источник - Онлайн школа Skysmart: https://skysmart.ru/articles/mathematic/naturalnye-chisla