Kaʻina hana ma ka makemakika

Ma kēia paʻi ʻana, e noʻonoʻo mākou i nā lula ma ka makemakika e pili ana i ke ʻano o ka hana ʻana i nā hana helu (me nā ʻōlelo me nā brackets, e hoʻokiʻekiʻe i kahi mana a i ʻole ka unuhi ʻana i kahi kumu), e hui pū me lākou me nā laʻana no ka hoʻomaopopo maikaʻi ʻana i ka mea.

Kaʻina hana no ka hana ʻana i nā hana

Hoʻomaopopo koke mākou e noʻonoʻo ʻia nā hana mai ka hoʻomaka ʻana o ka laʻana a hiki i kona hopena, ʻo ia hoʻi mai ka hema a i ka ʻākau.

ʻO ke kānāwai holoʻokoʻa

ʻO ka mua, hana ʻia ka hoʻonui a me ka mahele, a laila ka hoʻohui a me ka unuhi ʻana i nā waiwai waena.

E nānā pono kākou i kekahi laʻana: 2 ⋅ 4 + 12 : 3.

Ma luna aʻe o kēlā me kēia hana, ua kākau mākou i kahi helu e pili ana i ke ʻano o kāna hoʻokō ʻana, ʻo ia hoʻi, ʻo ka hopena o ka laʻana he ʻekolu mau ʻanuʻu waena:

• 2 ⋅ 4 = 8
• 12:3 = 4
• 8 + 4 = 12

Ma hope o kahi hoʻomaʻamaʻa liʻiliʻi, i ka wā e hiki mai ana, hiki iā ʻoe ke hana i nā hana āpau i ke kaulahao (ma hoʻokahi / mau laina), e hoʻomau i ka ʻōlelo kumu. I kā mākou hihia, ʻike ʻia:

2 ⋅ 4 + 12 : 3 = 8 + 4 = 12.

Inā he nui nā hoʻonui a me ka mahele i ka lālani, hana ʻia lākou i ka lālani, a hiki ke hoʻohui ʻia inā makemake ʻia.

Hoʻoholo:

• 5 ⋅ 6 : 3 = 10 (e hui ana i na anuu 1 a me 2)
• 18:9 = 2
• 7 + 10 = 17
• 17 - 2 = 15

Laʻana kaulahao:

7 + 5 ⋅ 6 : 3 – 18 : 9 = 7 + 10 - 2 = 15.

Nā laʻana me nā pale

Hoʻokō mua ʻia nā hana i loko o nā pale (inā loaʻa). A i loko o ia mau mea, e hana ana ke kauoha i ʻae ʻia, i wehewehe ʻia ma luna.

Hiki ke hoʻokaʻawale ʻia ka hopena i nā ʻanuʻu ma lalo nei:

• 7 ⋅ 4 = 28
• 28 - 16 = 12
• 15:3 = 5
• 9:3 = 3
• 5 + 12 = 17
• 17 - 3 = 14

I ka hoʻonohonoho ʻana i nā hana, hiki ke ʻike ʻia ka ʻōlelo i loko o nā bracket ma ke ʻano he hoʻokahi integer / helu. No ka maʻalahi, ua hōʻike mākou iā ia ma ke kaulahao ma lalo i ka ʻōmaʻomaʻo:

15 : 3 + (7 ⋅ 4 – 16) - 9:3 = 5+ 28 - 16 - 3 = 5+ 12 - 3 = 14.

Nā pale i loko o nā pale

I kekahi manawa hiki ke loaʻa nā pale ʻē aʻe (i kapa ʻia ʻo nested ones) i loko o nā pale. Ma ia mau hihia, hana mua ʻia nā hana i loko o nā pale i loko.

ʻO ka hoʻolālā o ka laʻana ma kahi kaulahao e like me kēia:

11 ⋅ 4 + (10 : 5 + (16:2 - 12:4)) = 44 + (2+ 8 - 3) = 44 + (2+ 5) = 51.

Exponentiation / unuhi kumu

Hana ʻia kēia mau hana ma mua loa, ʻo ia hoʻi ma mua o ka hoʻonui a me ka mahele. Eia kekahi, inā pili lākou i ka ʻōlelo ma nā brackets, a laila e hana mua ʻia nā helu i loko o lākou. E noʻonoʻo i kekahi laʻana:

Ke Kaʻina Hana:

• 19 - 12 = 7
• 7² = 49
• 6² = 36
• 4 ⋅ 5 = 20
• 36 + 49 = 85
• 85 + 20 = 105

Laʻana kaulahao:

6² + 19 - 12² + 4 ⋅ 5 = 36 + 49 +20 = 105.