Nhamba dzese nezvivakwa zvavo
Nhamba dzesere ndeimwe yepfungwa dzinokosha mumasvomhu, asi dzinoita basa guru muhupenyu hwezuva nezuva. Patinoverenga zvinhu, patinoona tembiricha dziri pasi pe zero, patinoverenga huwandu hwepasi mubhesi, kana kunyora purofiti nekurasikirwa mubhizinesi, tiri kutobata nenhamba dzesere ...
Tsanangudzo yeIntegers
Manhamba ese ari maviri ane nhamba dzine nhamba dziri negative, zero, uye nhamba dziri positive. Chiratidzo chinowanzo shandiswa kumiririra nhamba dzese ndiZ (chinobva pashoko rechiGerman rekuti Zahlen, rinoreva "nhamba"). Kazhinji, nhamba dzese dziri 1 dzinogona kunyorwa seizvi:
…, -3, -2, -1, 0, 1, 2, 3, …
Kusiyana nenhamba dzese dzine nhamba 0 chete uye nhamba dzakanaka, nhamba dzese dzine nhamba dzisina kunaka saka dzakakwana pakutsanangura mamiriro akasiyana-siyana.
Mienzaniso yeVanhu Vane Integers Muhupenyu Hwezuva Nezuva
Nhamba dzese dzakabatana zvakanyanya nemabasa evanhu. Mimwe mienzaniso yekushandiswa kwadzo inosanganisira:
1. Kupisa kwemhepo: Kupisa kwe -5°C kunoratidza kuti tembiricha iri pasi pe zero nemadhigirii mashanu.
2. Kureba: Kureba kwemamita -20 kunogona kureva nzvimbo iri pasi pegungwa nemamita makumi maviri.
3. Mari: Mari yasara ye -50.000 inoratidza chikwereti kana kushomeka kwe50.000.
4. Uriri hwechivako: Uriri -1 kana -2 hunowanzo shandiswa pabasement.
5. Mapoinzi emutambo: Mune mimwe mitambo, mapoinzi anogona kuwedzera kana kuderera, nokudaro zvichisanganisira mapoinzi akanaka neasina kunaka.
Kubva mumienzaniso iyi zvinoonekwa kuti nhamba dzese dzinotibatsira kuratidza mamiriro ekuti “zvinopfuura”, “zvishoma pane”, kana “zvakaenzana” ne zero senzvimbo yekutarisa.
Mutsetse Wenhamba Yese
Kuti tinzwisise nhamba dzakazara, tinowanzo shandisa mutsetse wenhamba. Mutsetse wenhamba mutsetse wakatwasuka unoisa nhamba munzvimbo dzakatarwa:
– Nhamba dzakanaka dziri kurudyi rwe zero.
– Nhamba dzisina kunaka dziri kuruboshwe rwezero.
– Kana kukosha kuri kure kurudyi, ndiko kukura kwacho.
– Kana kure kuruboshwe, kukosha kwacho kudiki.
Nemutsetse wenhamba, tinogona kuenzanisa nhamba dzese zviri nyore. Semuenzaniso, -2 yakakura kupfuura -5 nekuti -2 iri kure kurudyi kupfuura -5.
Hunhu hweIntegers
Manhamba azere ane hunhu hwakawanda hwakakosha mukushanda kwemasvomhu. Hunhu uhwu hunobatsira zvikuru patinoita maverengero, patinoita nyore kutaura kwealgebra, kana pakuratidza pfungwa.
1. Hunhu Hwakavharwa (Kuvharwa)
Seti yenhamba dzese dzinovharwa pasi pemamwe mabasa, zvichireva kuti kana tikaita mabasa iwayo panhamba dzese, mhedzisiro yacho icharamba iri nhamba dzese.
– Kuwedzera: Kana a na b vari nhamba dzese, saka a + b inhamba dzese.
Muenzaniso: -3 + 7 = 4
– Kubvisa: Kana a na b vari nhamba dzese, saka a − b inhamba dzese dzenhamba dzese.
Muenzaniso: 5 − 12 = -7
– Kuwanza: Kana a na b vari nhamba dzese, saka a × b inhamba dzese.
Muenzaniso: (-4) × 6 = -24
Zvisinei, nhamba dzese hadzigari dzakavharwa pakupatsanurwa, nekuti mhedzisiro yekupatsanurwa inogona kuva chidimbu.
Muenzaniso: 1 ÷ 2 = 1/2 (kwete nhamba yakazara).
2. Zvinhu Zvinoshandiswa Pakutengeserana (Kuchinjana)
Hunhu hwekuchinja hunoreva kuti kurongeka kwenhamba kunogona kuchinjaniswa pasina kuchinja mhedzisiro.
– Kuwedzera: a + b = b + a
Muenzaniso: 2 + (-5) = (-5) + 2 = -3
– Kuwanda: a × b = b × a
Muenzaniso: (-3) × 4 = 4 × (-3) = -12
Zvakakosha kurangarira kuti kubvisa nekupatsanura hazvisi zvinhu zvinochinja-chinja.
Muenzaniso: 7 − 2 ≠ 2 − 7.
3. Hunhu Hwekubatana (Kuisa Mumapoka)
Hunhu hwekubatana hunoreva kuti marongerwo anoitwa nhamba muchikamu chekushanda hachichinji mhedzisiro yacho.
– Kuwedzera: (a + b) + c = a + (b + c)
Muenzaniso: (1 + 2) + 3 = 1 + (2 + 3) = 6
– Kuwanda: (a × b) × c = a × (b × c)
Muenzaniso: (2 × 3) × 4 = 2 × (3 × 4) = 24
Kungofanana nekuchinja-chinja, pfuma yekubatana haishandewo pakubvisa nekuparadzanisa.
4. Zvimiro Zvekuparadzira (Kupararira)
Hunhu hwekuparadzira hunobatanidza mashandiro ekuwanda nekuwedzera kana kubvisa:
– a × (b + c) = (a × b) + (a × c)
Muenzaniso: 3 × (2 + 5) = (3 × 2) + (3 × 5) = 6 + 15 = 21
– a × (b − c) = (a × b) − (a × c)
Muenzaniso: 4 × (10 − 3) = 40 − 12 = 28
Hunhu uhwu hwakakosha zvikuru mukurerutsa mafomu e algebraic uye kugadzirisa ma equation.
5. Zvinhu Zvinoumba Kuzivikanwa (Kuwedzera uye Kuwanda Kwekuzivikanwa)
Chitupa inhamba isingachinje kukosha kweimwe nhamba kana ichishandiswa.
– Chiratidzo chekuwedzera ndeche 0: a + 0 = a
Muenzaniso: -9 + 0 = -9
– Kuzivikanwa kwekuwanda kwezviverengero i1: a × 1 = a
Muenzaniso: 8 × 1 = 8
Kuzivikanwa kunotibatsira kunzwisisa pfungwa isina kwayakarerekera mukushanda kwemasvomhu.
6. Zvinhu Zvakasiyana (Manhamba Akapesana)
Nhamba yese ine inverse yekuwedzera, iyo inopesana nenhamba iyo kana yabatanidzwa pamwe chete inoguma ne0.
– Chinosiyana na a ndi -a, saka: a + (-a) = 0
Muenzaniso: 6 + (-6) = 0, uye -4 + 4 = 0
Zvisinei, haasi manhamba ese ane inverse mukuwanza. Semuenzaniso, multiplicative inverse ye2 i1/2, iyo isiri integer.
7. Zviratidzo Zvakanaka Nezvakaipa Zviri Kushanda
Munhamba dzese, zviratidzo zvakanaka nezvakaipa zvinopa mitemo yakakosha mukuwanda nekupatsanura:
– (+) × (+) = (+)
– (+) × (-) = (-)
– (-) × (+) = (-)
– (-) × (-) = (+)
Muenzaniso:
– 3 × (-2) = -6
– (-5) × (-4) = 20
Pakuwedzera nekubvisa, tinowanzo shandisa pfungwa yemutsetse wenhamba kana mutemo:
– Kuwedzera nhamba dzisina kunaka kwakafanana nekubvisa.
– Kubvisa nhamba isina kunaka kwakafanana ne "kuwedzera".
Muenzaniso:
– 7 + (-3) = 4
– 5 − (-2) = 7
Mhedziso
Nhamba dzesere inhamba dzine nhamba dzisina kunaka, zero, uye nhamba dzakanaka. Nhamba idzi dzakakosha zvikuru nekuti dzinogona kutsanangura mamiriro akasiyana-siyana muhupenyu, akadai sekupisa kwepasi pezero, kurasikirwa nemari, kana nzvimbo dziri pasi pegungwa. Nhamba dzesere dzine hunhu hwakakosha hwakadai sekuvharwa (kwekuwedzera, kubvisa, uye kuwanda), commutative, associative, distributive, identity, uye additive inverse. Nekunzwisisa hunhu hwenhamba dzesere, tichaita kuverenga zviri nyore, kurerutsa mashandiro, uye kudzidza misoro yemasvomhu inotevera senge algebra, equation, nedzimwe nhamba.
Kana muchida, ndinogona kugadzira chinyorwa chino chepuraimari/sekondari (chiri nyore) kana chinyorwa chepamutemo senge bepa rakazara rine mibvunzo yekudzidzira nekukurukurirana.
