Hoʻololi ʻike i nā ʻōlelo

Ma kēia paʻi ʻana, e noʻonoʻo mākou i nā ʻano nui o ka hoʻololi like ʻana o nā hōʻike algebraic, me ka hui pū ʻana me nā ʻōkuhi a me nā laʻana e hōʻike i kā lākou noi ma ka hana. ʻO ke kumu o ia hoʻololi ʻana, ʻo ia ke hoʻololi i ka ʻōlelo kumu me kahi ʻano like.

Hoʻonohonoho hou i nā huaʻōlelo a me nā kumu

I kēlā me kēia huina, hiki iā ʻoe ke hoʻonohonoho hou i nā huaʻōlelo.

a + b = b + a

I kēlā me kēia huahana, hiki iā ʻoe ke hoʻonohonoho hou i nā kumu.

a ⋅ b = b ⋅ a

mau laʻana:

• 1 + 2 = 2 + 1
• 128 ⋅ 32 = 32 ⋅ 128

Nā huaʻōlelo pūʻulu (mea hoʻonui)

Inā ʻoi aku ma mua o 2 mau huaʻōlelo i ka huina, hiki ke hui pū ʻia e nā pale. Inā pono, hiki iā ʻoe ke hoʻololi mua iā lākou.

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

I ka huahana, hiki iā ʻoe ke hui pū i nā kumu.

a ⋅ b ⋅ c ⋅ d = (a ⋅ d) ⋅ (b ⋅ c)

mau laʻana:

• 15 + 6 + 5 + 4 = (15 + 5) + (6 + 4)
• 6 ⋅ 8 ⋅ 11 ⋅ 4 = (6 ⋅ 4 ⋅ 8) ⋅ 11

Hoʻohui, unuhi, hoʻonui a mahele paha me ka helu like

Inā hoʻohui a unuhi ʻia ka helu hoʻokahi i nā ʻāpana ʻelua o ka ʻike, a laila mau nō ia.

If a + b = c + dalaila, (a + b) ± e = (c + d) ± e.

Eia kekahi, ʻaʻole e uhaki ʻia ke kaulike inā hoʻonui a puʻunaue ʻia nā ʻāpana ʻelua i ka helu like.

If a + b = c + dalaila, (a + b) ⋅/: e = (c + d) ⋅/: e.

mau laʻana:

• 35 + 10 = 9 + 16 + 20 ⇒ (35 + 10) + 4 = (9 + 16 + 20) + 4
• 42 + 14 = 7 ⋅ 8 ⇒ (42 + 14) ⋅ 12 = (7 ⋅ 8) ⋅ 12

Hoʻololi i kahi ʻokoʻa me kahi huina (pinepine i kahi Huahana)

Hiki ke hōʻike ʻia kekahi ʻokoʻa ma ke ʻano he huina o nā huaʻōlelo.

a – b = a + (-b)

Hiki ke hoʻohana ʻia ka hoʻopunipuni like i ka mahele, ʻo ia hoʻi e hoʻololi pinepine me ka huahana.

a : b = a ⋅ b^-1

mau laʻana:

• 76 – 15 – 29 = 76 + (-15) + (-29)
• 42 : 3 = 42 ⋅ 3^-1

Hana i nā hana helu

Hiki iā ʻoe ke maʻalahi i ka ʻōlelo makemakika (kekahi manawa nui) ma ka hana ʻana i nā hana helu (hoʻohui, unuhi, hoʻonui a me ka mahele), me ka noʻonoʻo ʻana i ka mea i ʻae ʻia. kauoha o ka hooko ana:

• ʻO ka mua mākou e hoʻokiʻekiʻe i kahi mana, unuhi i nā aʻa, helu i nā logarithms, trigonometric a me nā hana ʻē aʻe;
• a laila hana mākou i nā hana ma nā brackets;
• hope - mai ka hema a i ka ʻākau, e hana i nā hana i koe. ʻO ka hoʻonui a me ka mahele ma mua o ka hoʻohui a me ka unuhi. Pili kēia i nā ʻōlelo i loko o nā pale.

mau laʻana:

• 14 + 6 ⋅ (35 – 16 ⋅ 2) + 11 ⋅ 3 = 14 + 18 + 33 = 65
• 20 : 4 + 2 ⋅ (25 ⋅ 3 – 15) – 9 + 2 ⋅ 8 = 5 + 120 – 9 + 16 = 132

Hoʻonui bracket

Hiki ke hoʻoneʻe ʻia nā pale ma ka ʻōlelo helu helu. Hana ʻia kēia hana e like me kekahi - e pili ana i nā hōʻailona ("plus", "minus", "multiply" a i ʻole "puʻunaue") aia ma mua a ma hope paha o nā pale.

mau laʻana:

• 117 + (90 – 74 – 38) = 117 + 90 – 74 – 38
• 1040 – (-218 – 409 + 192) = 1040 + 218 + 409 – 192
• 22⋅(8+14) = 22 ⋅ 8 + 22 ⋅ 14
• 18 : (4 – 6) = 18:4-18:6

Hoʻopaʻa i ke kumu maʻamau

Inā he kumu maʻamau nā huaʻōlelo a pau, hiki ke lawe ʻia i waho o nā brackets, kahi e mau ai nā huaʻōlelo i puʻunaue ʻia e kēia helu. Hoʻohana pū kēia ʻenehana i nā loli maoli.

mau laʻana:

• 3 ⋅ 5 + 5 ⋅ 6 = 5⋅(3+6)
• 28 + 56 – 77 = 7 ⋅ (4 + 8 – 11)
• 31x + 50x = x ⋅ (31 + 50)

Ka hoʻohana ʻana i nā ʻano hoʻonui hoʻonui

Hiki iā ʻoe ke hoʻohana no ka hana ʻana i nā hoʻololi like o nā ʻōlelo algebraic.

mau laʻana:

• (31 + 4)² = 31² + 2 ⋅ 31 ⋅ 4 + 4² = 1225
• 26² - 7² = (26 – 7) ⋅ (26 + 7) = 627