Nā waiwai māhele helu me nā laʻana

Ma kēia paʻi ʻana, e noʻonoʻo mākou i nā waiwai kumu 8 o ka mahele ʻana i nā helu kūlohelohe, e hui pū me lākou me nā hiʻohiʻona no ka hoʻomaopopo maikaʻi ʻana i ka mea theoretical.

Waiwai mahele helu

Waiwai 1

ʻO ka puʻunaue o ka puʻunaue ʻana i kahi helu kūlohelohe iā ia iho, ua like ia me ka hoʻokahi.

a: a = 1

mau laʻana:

• 9:9 = 1
• 26:26 = 1
• 293:293 = 1

Waiwai 2

Inā puunaue ʻia kahi helu kūlohelohe i hoʻokahi, ʻo ka hopena ka helu like.

a : 1 = a

mau laʻana:

• 17:1 = 17
• 62:1 = 62
• 315:1 = 315

Waiwai 3

I ka puunaue ana i na huahelu maoli, aole hiki ke hoohana ia ke kanawai commutative, ua kupono ia no .

a : b ≠ b : a

mau laʻana:

• 84 : 21 ≠ 21 : 84
• 440 : 4 ≠ 4 : 440

Waiwai 4

Inā makemake ʻoe e puʻunaue i ka huina o nā helu me kahi helu i hāʻawi ʻia, a laila pono ʻoe e hoʻohui i ka quotient o ka puʻunaue ʻana i kēlā me kēia huina me kahi helu i hāʻawi ʻia.

(a + b): c = a : c + b : c

waiwai hoʻohuli:

c : (a + b) = c : a + c : b

mau laʻana:

• (45 + 18) : 3 = 45 : 3 + 18 : 3
• (28 + 77 + 140) : 7 = 28 : 7 + 77 : 7 + 140 : 7
• 120 : (6 + 20) = 120 : 6 + 120 : 20

Waiwai 5

I ka puunaue ana i ka okoa o na huahelu me ka helu i haawiia, pono oe e unuhi i ka huahelu mai ka puunaue ana i ka subtrahend me ka huina i haawiia mai ka puuhui mai ka puunaue ana i ka minuend me keia helu.

(a – b): c = a : c – b : c

waiwai hoʻohuli:

c : (a – b) = c : a – c : b

mau laʻana:

• (60 – 30) : 2 = 60:2-30:2
• (150 – 50 – 15) : 5 = 150 : 5 – 50 : 5 – 15 : 5
• 360 : (90 – 15) = 360:90-360:15

Waiwai 6

ʻO ka puʻunaue ʻana i ka huahelu me ka mea i hāʻawi ʻia, ua like ia me ka puʻunaue ʻana i kekahi o nā mea i kēia helu, a laila e hoʻonui i ka hopena me kekahi.

(a ⋅ b): c = (a : c) ⋅ b = (b : c) ⋅ a

Inā like ka helu i puunaue ʻia me kekahi o nā kumu:

• (a ⋅ b): a = b
• (a ⋅ b): b = a

waiwai hoʻohuli:

c : (a ⋅ b) = c : a : b = c : b : a

mau laʻana:

• (90 ⋅ 36) : 9 = (90 : 9) ⋅ 36 = (36 : 9) ⋅ 90
• 180 : (90 ⋅ 2) = 180:90:2 = 180:2:90

Waiwai 7

Inā makemake ʻoe i ka quotient o ka mahele o nā helu a и b e puunaue i ka helu c, ʻo ia hoʻi a hiki ke hoʻokaʻawale i b и c.

(a : b): c = a : (b ⋅ c)

waiwai hoʻohuli:

a : (b : c) = (a : b) ⋅ c = (a ⋅ c): b

mau laʻana:

• (16 : 4) : 2 = 16 : (4 ⋅ 2)
• 96 : (80 : 10) = (96 : 80) ⋅ 10

Waiwai 8

Ke puunaueia ka huahelu me ka helu maoli, he zero ka hopena.

0 : a = 0

mau laʻana:

• 0:17 = 0
• 0:56 = 56

'Ōlelo Aʻo: ʻAʻole hiki iā ʻoe ke puʻunaue i kahi helu me ka ʻole.