Masharti muhimu Sura ya 01: Misingi

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Thamani kamili: Thamani kamili ya namba ni umbali wake kutoka\(0\) kwenye mstari wa nambari. Thamani kamili ya namba\(n\) imeandikwa kama\(|n|\).

Identity ya nyongeza: Utambulisho wa nyongeza ni nambari\(0\); kuongeza\(0\) kwa nambari yoyote haibadili thamani yake.

Inverse ya kuongezea: Kinyume cha nambari ni inverse yake ya kuongezea. Nambari na inverse yake ya kuongezea huongeza\(0\).

Mgawo: Mgawo wa neno ni mara kwa mara ambayo huzidisha kutofautiana kwa muda.

Complex Fraction: Sehemu ngumu ni sehemu ambayo nambari au denominator ina sehemu.

Idadi ya Composite: Nambari ya composite ni namba ya kuhesabu ambayo si mkuu. Nambari ya composite ina mambo mengine zaidi ya 1 na yenyewe.

Mara kwa mara: Mara kwa mara ni namba ambayo thamani yake daima inakaa sawa.

Hesabu Hesabu: Nambari za kuhesabu ni namba\(1, 2, 3, …\)

Decimal: Decimal ni njia nyingine ya kuandika sehemu ambayo denominator ni nguvu ya kumi.

denominator: Denominator ni thamani kwenye sehemu ya chini ya sehemu inayoonyesha idadi ya sehemu sawa ambazo nzima imegawanywa.

Imegawanyika na Idadi: Kama idadi\(m\) ni nyingi ya\(n\), basi\(m\) ni mgawanyiko na\(n\). (Kama\(6\) ni nyingi ya\(3\), basi\(6\) ni mgawanyiko na\(3\).)

Ishara ya Usawa: Ishara “=” inaitwa ishara sawa. Tunasoma\(a=b\) kama “\(a\)ni sawa na\(b\).”

Mlinganyo: Equation ni maneno mawili yanayounganishwa na ishara sawa.

Sawa Decimals: Decimals mbili ni sawa kama wao kubadilisha kwa sehemu sawa.

Sehemu sawa: Sehemu ndogo sawa ni sehemu ndogo ambazo zina thamani sawa.

Tathmini ya Kuelezea: Kutathmini njia ya kujieleza ina maana ya kupata thamani ya kujieleza wakati kutofautiana inabadilishwa na nambari iliyotolewa.

Ufafanuzi: Maneno ni namba, kutofautiana, au mchanganyiko wa namba na vigezo kwa kutumia alama za uendeshaji.

Mambo: Ikiwa\(a·b=m\), basi\(a\) na\(b\) ni sababu za\(m\). Tangu\(3 · 4 = 12\), basi\(3\) na\(4\) ni sababu za\(12\).

Fraction: Sehemu imeandikwa\(ab\), wapi\(b≠0\)\(a\) namba na\(b\) ni denominator. Sehemu inawakilisha sehemu ya nzima. Denominator\(b\) ni idadi ya sehemu sawa ambazo zote zimegawanywa, na namba\(a\) inaonyesha sehemu ngapi zinajumuishwa.

Nambari kamili: Nambari nzima na kupinga kwao huitwa integers:\(...−3, −2, −1, 0, 1, 2, 3...\)

Idadi isiyo na maana: Nambari isiyo na maana ni namba ambayo haiwezi kuandikwa kama uwiano wa integers mbili. Fomu yake ya decimal haina kuacha na haina kurudia.

Denominator ya kawaida: denominator angalau kawaida (LCD) ya sehemu mbili ni angalau kawaida nyingi (LCM) ya denominators yao.

Angalau ya kawaida nyingi: Nambari ndogo ya kawaida ya namba mbili ni namba ndogo zaidi ambayo ni nyingi ya namba zote mbili.

Kama Masharti: Masharti ambayo ni ama constants au kuwa na vigezo sawa kukulia kwa nguvu sawa ni kuitwa kama maneno.

Nyingi ya Idadi: idadi ni nyingi ya\(n\) kama ni bidhaa ya idadi kuhesabu na\(n\).

Identity ya kuzidisha: Utambulisho wa kuzidisha ni namba\(1\); kuzidisha\(1\) kwa nambari yoyote haibadili thamani ya nambari.

Inverse ya kuzidisha: Utoaji wa nambari ni inverse yake ya kuzidisha. Nambari na inverse yake ya kuzidisha huongezeka kwa moja.

Nambari ya mstari: Mstari wa nambari hutumiwa kutazama namba. Nambari kwenye mstari wa nambari hupata kubwa kama wanaenda kutoka kushoto kwenda kulia, na ndogo kama wanaenda kutoka kulia kwenda kushoto.

Nambari: Nambari ni thamani kwenye sehemu ya juu ya sehemu inayoonyesha sehemu ngapi za jumla zinajumuishwa.

Kinyume: Kinyume cha namba ni namba ambayo ni umbali sawa kutoka sifuri kwenye mstari wa namba lakini upande wa pili wa sifuri:\(−a\) inamaanisha kinyume cha namba. Nukuu\(−a\) inasomewa “kinyume cha\(a\).”

Mwanzo: Asili ni hatua iliyoandikwa\(0\) kwenye mstari wa namba.

Asilimia: Asilimia ni uwiano ambao denominator yake ni\(100\).

Mkuu Factorization: Factorization mkuu wa idadi ni bidhaa ya idadi ya mkuu ambayo ni sawa na idadi.

Idadi ya Waziri: Nambari kuu ni namba ya kuhesabu kubwa kuliko\(1\), ambayo mambo yake pekee ni\(1\) yenyewe.

Ishara kali: Ishara kubwa ni ishara\(\sqrt{m}\) inayoashiria mizizi nzuri ya mraba.

Idadi ya busara: Nambari ya busara ni idadi ya fomu\(pq\), wapi\(p\) na\(q\) ni integers na\(q≠0\). Nambari ya busara inaweza kuandikwa kama uwiano wa integers mbili. Fomu yake ya decimal inacha au kurudia.

Nambari halisi: Nambari halisi ni namba ambayo ni ya busara au isiyo ya maana.

kurudisha nyuma: Usawa wa\(ab\) ni\(ba\). Nambari na kuongezeka kwake kwa moja:\(ab·ba=1\).

Kurudia Decimal: Decimal ya kurudia ni decimal ambayo tarakimu ya mwisho au kikundi cha tarakimu hurudia bila kudumu.

Sehemu kilichorahisishwa: Sehemu inachukuliwa kuwa rahisi ikiwa hakuna mambo ya kawaida katika nambari yake na denominator.

Kurahisisha kujieleza: Ili kurahisisha kujieleza, fanya shughuli zote katika maneno.

Mizizi ya Mraba na Mraba: Ikiwa\(n^2=m\), basi\(m\) ni mraba wa\(n\) na\(n\) ni mizizi ya mraba ya\(m\).

Muda: Neno ni mara kwa mara au bidhaa ya vigezo vya mara kwa mara na moja au zaidi.

Variable: Variable ni barua inayowakilisha namba ambayo thamani yake inaweza kubadilika.

Hesabu nzima: Nambari nzima ni namba\(0, 1, 2, 3, ...\).