7.S: Mali ya Hesabu Halisi (Muhtasari)

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Masharti muhimu

Identity ya nyongeza	Utambulisho wa kuongezea ni 0. Wakati sifuri imeongezwa kwa nambari yoyote, haibadili thamani.
Kuongeza Inverse	Kinyume cha namba ni inverse yake ya kuongezea. Inverse ya nyongeza ya a ni -a.
Idadi isiyo ya maana	Nambari ambayo haiwezi kuandikwa kama uwiano wa integers mbili. Fomu yake ya decimal haina kuacha na haina kurudia.
Identity ya kuzidisha	utambulisho multiplicative ni 1. Wakati mtu huzidisha namba yoyote, haibadili thamani.
Inverse ya kuzidisha	Utoaji wa nambari ni inverse yake ya kuzidisha. Inverse multiplicative ya ni$\dfrac{1}{a}$.
Nambari ya busara	Nambari ambayo inaweza kuandikwa kwa fomu$\dfrac{p}{q}$, ambapo p na q ni integers na q ∙ 0. Fomu yake ya decimal inacha au kurudia.
Nambari halisi	Nambari ambayo ni ya busara au isiyo ya maana.

Dhana muhimu

7.1 - Idadi ya busara na isiyo ya kawaida

Nambari halisi

$Picha inaonyesha mstatili mkubwa unaoitwa “Hesabu halisi”. Mstatili umegawanyika kwa nusu kwa wima. Nusu ya haki inaitwa “Hesabu zisizo na maana”. Nusu ya kushoto inaitwa “Hesabu za busara” na ina rectangles tatu za makini. Mstatili wa nje zaidi huitwa “Integers”, mstatili unaofuata ni “Hesabu Nzima” na mstatili wa ndani zaidi ni “Hesabu za Asili”.$

7.2 - Mali ya Kubadilisha na Associative

Mali ya kubadilisha
- Mali ya Kubadilisha ya Kuongezea: Ikiwa a, b ni namba halisi, basi a + b = b + a
- Mali ya Kubadilisha ya Kuzidisha: Ikiwa a, b ni namba halisi, basi • b = b • a
Associative Mali
- Mali ya Ushirikiano wa Kuongezea: Ikiwa, b, c ni namba halisi basi (a + b) + c = a + (b + c)
- Associative Mali ya Kuzidisha: Kama, b, c ni namba halisi basi (a • b) • c = a • (b • c)

7.3 - Mali ya Kusambaza

Mali ya kusambaza:
- Ikiwa, b, c ni namba halisi basi
  - a (b + c) = ab + ac
  - (b + c) a = ba + ca
  - a (b - c) = ab - ac

7.4 - Mali ya Identity, Inverses, na Zero

Mali ya Identity
- Identity Mali ya Aidha: Kwa idadi yoyote halisi a: a + 0 = a, 0 + a = a
  - 0 ni utambulisho wa kuongezea
- Identity Mali ya Kuzidisha: Kwa idadi yoyote halisi a: a • 1 = a, 1 • a = a
  - 1 ni utambulisho wa kuzidisha
Mali Inverse
- Inverse Mali ya Aidha: Kwa idadi yoyote halisi a: a + (- a) = 0
  - - ni inverse livsmedelstillsats ya
- Inverse Mali ya Kuzidisha: Kwa idadi yoyote halisi a: (a ∙ 0) a •$\dfrac{1}{a}$ = 1
  - $\dfrac{1}{a}$ni inverse multiplicative ya
Mali ya Zero
- Kuzidisha kwa Zero: Kwa idadi yoyote halisi a, a • 0 = 0, 0 • a = 0
  - Bidhaa ya namba yoyote na 0 ni 0.
- Idara ya Zero: Kwa yoyote ya kweli idadi a,$\frac{0}{a} = 0$,$0 \div a = 0$
  - Zero imegawanywa na idadi yoyote halisi, isipokuwa yenyewe, ni sifuri.
- Idara na Zero: Kwa idadi yoyote halisi a,$\dfrac{a}{0}$ haijulikani na a ÷ 0 haijulikani.
  - Idara na sifuri haijulikani.

Wachangiaji na Majina

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