Nā rula no ka hoʻonui ʻana i nā pale me nā laʻana

Ma kēia hoʻolaha, e noʻonoʻo mākou i nā lula kumu no ka wehe ʻana i nā brackets, e hele pū me lākou me nā hiʻohiʻona no ka hoʻomaopopo maikaʻi ʻana i nā mea theoretical.

Hoʻonui bracket - ka hoʻololi ʻana i kahi huaʻōlelo i loaʻa nā pale me kahi huaʻōlelo like me ia, akā ʻaʻohe pale.

maʻiʻo

Nā lula hoʻonui bracket

Māhele 1

Inā loaʻa kahi "plus" ma mua o nā pale, a laila mau nā hōʻailona o nā helu āpau i loko o nā pale.

a + (b – c – d + e) = a + b – c – d + e

Hōʻike: ʻO kēlā mau mea. Hoʻonui ka manawa hoʻohui i ka hoʻohui, a me nā manawa hoʻemi e hoʻemi.

mau laʻana:

  • 6 + (21 – 18 – 37) = 6 + 21 – 18 – 37
  • 20 + (-8 + 42 – 86 – 97) = 20 – 8 + 42 – 86 – 97

Māhele 2

Inā loaʻa kahi hōʻemi i mua o nā pale, a laila hoʻohuli ʻia nā hōʻailona o nā helu āpau i loko o nā pale.

a – (b – c – d + e) = a – b + c + d – e

Hōʻike: ʻO kēlā mau mea. ʻO ka hoʻemi ʻana o ka hoʻohui ʻana he hōʻemi ia, a ʻo ka hoʻemi ʻana he hoʻohui.

mau laʻana:

  • 65 – (-20 + 16 – 3) = 65 + 20 – 16 + 3
  • 116 – (49 + 37 – 18 – 21) = 116 – 49 – 37 + 18 + 21

Māhele 3

Inā loaʻa kahi hōʻailona "hoʻonui" ma mua a ma hope paha o nā pale, pili ia i nā hana i hana ʻia i loko o lākou:

Hoʻohui a/a unuhi

  • a ⋅ (b – c + d) = a ⋅ b – a ⋅ c + a ⋅ d
  • (b + c – d) ⋅ a = a ⋅ b + a ⋅ c – a ⋅ d

Ka Hoʻohui

  • a ⋅ (b ⋅ c ⋅ d) = a ⋅ b ⋅ c ⋅ d
  • (b ⋅ c ⋅ d) ⋅ a = b ⋅ с ⋅ d ⋅ a

mahele

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

mau laʻana:

  • 18 ⋅ (11 + 5 – 3) = 18 ⋅ 11 + 18 ⋅ 5 – 18 ⋅ 3
  • 4 ⋅ (9 ⋅ 13 ⋅ 27) = 4 ⋅ 9 ⋅ 13 ⋅ 27
  • 100 ⋅ (36 : 12) = (100 ⋅ 36) : 12

Māhele 4

Inā loaʻa kahi hōʻailona mahele ma mua a ma hope paha o nā pale, a laila, e like me ka lula ma luna, pili ia i nā hana i hana ʻia i loko o lākou:

Hoʻohui a/a unuhi

ʻO ka mua, hana ʻia ka hana i loko o nā pale, ʻo ia hoʻi ka hopena o ka huina a ʻokoʻa paha o nā helu, a laila hana ʻia ka mahele.

a : (b – c + d)

b – с + d = e

a : e = f

(b + c – d): a

b + с – d = e

e : a = f

Ka Hoʻohui

  • a : (b ⋅ c) = a : b : c = a : c : b
  • (b ⋅ c): a = (b : a) ⋅ p = (me : a) ⋅ b

mahele

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

mau laʻana:

  • 72 : (9 – 8) = 72:1
  • 160 : (40 ⋅ 4) = 160:40:4
  • 600 : (300 : 2) = (600 : 300) ⋅ 2

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