He aha nā helu kūpono

Ma kēia paʻi ʻana, e noʻonoʻo mākou i ke ʻano o nā helu rational, pehea e hoʻohālikelike ai kekahi i kekahi, a me nā hana helu helu e hiki ke hana me lākou (hoʻohui, unuhi, hoʻonui, māhele a me ka hoʻonui). E hele pū mākou me nā mea manaʻo me nā hiʻohiʻona kūpono no ka hoʻomaopopo maikaʻi ʻana.

Wehewehe ʻana o kahi helu kūpono

Manaʻo kūpono he helu i hiki ke hoike ia . He notation kūikawā ko ka hoʻonohonoho o nā helu rational - Q.

Nā rula no ka hoʻohālikelike ʻana i nā helu kaulike:

1. ʻOi aku ka nui o ka helu kūpono ma mua o ka ʻole. Hōʻike ʻia e ka hōʻailona kūikawā "nui aʻe". ">".

   ʻo kahi laʻana: 5>0, 12>0, 144>0, 2098>0, etc.

2. ʻAʻole ʻoi aku ka ʻole o ka helu kuhi hewa ʻole. Hōʻike ʻia e ka hōʻailona "emi iho". "<".

   ʻo kahi laʻana: -3<0, -22<0, -164<0, -3042<0 etc.

3. ʻO nā huahelu hoʻohālikelike maikaʻi ʻelua, ʻoi aku ka nui o ka mea me ka waiwai piha.

   ʻo kahi laʻana: 10>4, 132>26, 1216<1516 a me т.д.

4. ʻO nā helu kūpono ʻole ʻelua, ʻo ka mea nui ka mea me ka waiwai kūʻokoʻa liʻiliʻi.

   ʻo kahi laʻana: -3>-20, -14>-202, -54<-10 a me т.д.

Nā hana helu me nā helu kaulike

Eia hou kekahi

1. No ka huli 'ana i ka huina o na huina kupono me na hoailona like, e houluulu wale ia lakou, a laila e kau i ko lakou hoailona ma ke alo o ka hopena.

ʻo kahi laʻana:

• 5 + 2 = + (5 + 2) = +7 = 7
• 13 + 8 + 4 = + (13 + 8 + 4) = +25 = 25
• -9 + (-11) = – (9 + 11) =-20
• -14 + (-53) + (-3) = – (14 + 53 + 3) =-70

'Ōlelo Aʻo: Inā ʻaʻohe hōʻailona ma mua o ka helu, ʻo ia hoʻi "+", ʻo ia hoʻi he maikaʻi. Eia kekahi ma ka hopena "he mea hoʻohui" hiki ke hoohaahaa.

2. I mea e loaa ai ka huina o na huina kupono me na hoailona like ole, e hoonui kakou i ka helu me ka modulus nui i ka mea nona ka hoailona i ku like me ia, a e unuhi i na huahelu me na hoailona kue (e lawe kakou i na waiwai paa). A laila, ma mua o ka hopena, kau mākou i ka hōʻailona o ka helu i unuhi mākou i nā mea āpau.

ʻo kahi laʻana:

• -6 + 4 = – (6 – 4) =-2
• 15 + (-11) = + (15 - 11) = +4 = 4
• -21 + 15 + 2 + (-4) = – (21 + 4 – 15 – 2) =-8
• 17 + (-6) + 10 + (-2) = + (17 + 10 – 6 – 2) = 19

Lawe ʻia

No ka ʻike ʻana i ka ʻokoʻa ma waena o ʻelua mau helu kūpono, hoʻohui mākou i ka helu kūʻē i ka helu e unuhi ʻia.

ʻo kahi laʻana:

• 9 – 4 = 9 + (-4) = 5
• 3 – 7 = 3 + (-7) = – (7 – 3) =-4

Inā nui nā subtrahends, a laila e hoʻohui mua i nā helu maikaʻi a pau, a laila nā helu maikaʻi ʻole (me ka helu hoʻemi ʻia). No laila, loaʻa iā mākou nā helu helu ʻelua, ʻo ka ʻokoʻa a mākou e ʻike ai me ka hoʻohana ʻana i ka algorithm ma luna.

ʻo kahi laʻana:

• 12 – 5 – 3 = 12 – (5 + 3) = 4
• 22 – 16 – 9 = 22 – (16 + 9) = 22 - 25 = – (25 – 22) =-3

Ka Hoʻohui

No ka loaʻa ʻana o ka huahana o ʻelua mau helu hoʻohālikelike, e hoʻonui wale i kā lākou mau modula, a laila e kau i mua o ka hopena:

• hoailona "+"inā he hōʻailona like nā mea ʻelua;
• hoailona "-"inā loaʻa nā hōʻailona like ʻole.

ʻo kahi laʻana:

• 3 7 = 21
• -15 4 = -60

Inā ʻoi aku ma mua o ʻelua mau kumu, a laila:

1. Inā maikaʻi nā helu a pau, a laila e pūlima ʻia ka hopena. "he mea hoʻohui".
2. Inā loaʻa nā helu maikaʻi a maikaʻi ʻole, a laila helu mākou i ka helu o ka hope:
   • he helu like ka hopena me "hou aku";
   • helu ʻokoʻa - hopena me “emi”.

ʻo kahi laʻana:

• 5 (-4) 3 (-8) = 480
• 15 (-1) (-3) (-10) 12 = -5400

mahele

E like me ka hoʻonui ʻana, hana mākou i kahi hana me nā modula o nā helu, a laila kau mākou i ka hōʻailona kūpono, e noʻonoʻo ana i nā lula i wehewehe ʻia ma ka paukū ma luna.

ʻo kahi laʻana:

• 12:4 = 3
• 48 : (-6) = -8
• 50 : (-2) : (-5) = 5
• 128 : (-4) : (-8) : (-1) = -4

Exponentiation

Hoʻonui i kahi helu kūpono a в n ua like ia me ka hoonui ana i keia huina me ia iho nka helu o na manawa. Spelled like a ⁿ.

I loko o:

• ʻO kēlā me kēia mana o ka helu maikaʻi ka hopena i ka helu maikaʻi.
• ʻO ka mana like o ka helu ʻino he maikaʻi, ʻo ka mana ʻokoʻa he ʻino.

ʻo kahi laʻana:

• 2⁶ = 2 2 2 2 2 2 = 64
• -3⁴ = (-3) · (-3) · (-3) · (-3) = 81
• -6³ = (-6) · (-6) · (-6) = -216