Mahele. Multiplication o maʻamau hapa, kekimala, hui pu

he ka theme like o "hapa" I ka holo ana o ka waena a me ke kula kiʻekiʻe nā haumāna. Naʻe, i kēia manaʻo o ka nui ma mua o ka mea i haawiia mai ma o ka hoʻonaʻauao kaʻina. I kēia lā i ka manaʻo o ka hapa iki mea ole uncommon, a i kela kanaka keia kanaka hiki ke lawe mai i ka ho omaulia ana o ka olelo, no ka laʻana, multiplication o ka mahele.

He aha mea he hapa?

Hawaiʻi nei, ua fractional nui e noho ana ma muli o ia i ka pono, e ana. E like me ka hana pono E hoike mai, pinepine loaʻa examples ma ka wehewehena o ka lōʻihi o ka Hoʻohana, ka buke o ka huinahń parallelepiped, i ka wahi o ka rectangle.

Initially, nā haumāna loaaʻi ka ike lea i ka manaʻo o ka pehea e kaʻana. No kekahi laʻana, ina e puunaue oe i ka melon i 8 māhele, laila kēlā e kiʻi i kekahi-walu o ka watermelon. Eia kekahi hapa o ka ewalu kapaia lobes.

Share, like i ½ o ka waiwai i kapaia he hapalua; ⅓ - kolu; ¼ - hapaha. 'Ikamu hana ^{_{5/8, 4/5, 2/4}} kapaia, he pono ole hapa. Common hapa puunaueia e ka numerator a me ka denominator. Ma waena o ia mea he hapa laina, a me slashes. Slashes hiki ke unuhi i loko o ka palapala o nā ana papamoe, a me kēlā laina. Ma keia hihia, e Hōʻike ka mahele hoailona.

Ka denominator ho ehia na mahele o ka ia i kaʻana like cia'ikamu; ka numerator - ka ia me mahele ia. Ke numerator Ua palapala ma o ka hou, i ka denominator - ma lalo iho.

Ka loa kupono ala e hōʻike ano hapa ma luna o ka i kahi kūlike o Ray. Inā ka mokuna Hoʻohana ua maheleia i 4 like loa, hoike i ke kaʻana like 'ana o kēlā me kēia he Roma hua, i ka hopena hiki ia e kiʻi i ka maikai kākoʻo kiʻi. Ke'ī mai, i ka wahi A Hōʻike ka like ana e like me ^_1/4 o ka huina o ka loa o ka hui pu ia lakou, a me ka wahi B hōʻailona ka ^_2/8 o ka haawi mai Hoʻohana.

ʻano likeʻole hapa

Hapa i ole, decimals, a me ka hui helu. Eia hou, i ka mahele hiki ke maheleia i loko o ka pono a me ka hewa. Kēia Mea Maluna Ua oi pono no ka maʻamau hapa.

Ma lalo o kupono hapa maopopo helu nona ka numerator ka emi o ka denominator. Alaila, o ka kūpono hapa - ka helu ana i oi ma mua o ka numerator denominator. Ka lua oʻano Ua ana i kākau 'ia me ka hui' ano apau loa. Oia ka 'aoʻao o ua i mai ka helu a me ka fractional māhele. No ka laʻana, 1½. 1 - ka a pau loa, ½ - fractional. Eia naʻe, inā e pono e lawe mai i kekahi manipulation o ka hōʻike (mahele paha multiplication o ka mahele a me kā lākou ka ho'ēmiʻana a me ka huli ana), ua unuhi i hui helu i loko o kūpono hapa.

Pono fractional 'aoʻao o ka manawa a emi ma mua o kekahi, a me ka hewa - ua oi aku ia ma mua o paha e like me 1.

Like no na decimals, laila, ma kēia 'aoʻao o ike i ka moolelo e hōʻike i kekahi helu, ka denominator o ka fractional olelo o ka i hiki e hoike ia ma ka mokuna me he mau' Aʻohe hualoaʻa. Inā ka hapa ka pololei, alaila, o ka pau loa i loko o kekimala notation mea like me ke 'Aʻohe.

E kākau i kekahi kekimala hapa, e pono e palapala mua i ka pau hapa, e hookaawale ia, mai ka hapa iki me ka comma, a laila, e kakau i ka fractional hōʻike. Ua pono e hoomanao ia ma hope o ka wahi numerator Pono e komo i ka hookahi helu o kikohoʻe huapalapala like 'Aʻohe hualoaʻa ma ka denominator.

Laʻana. Keia pana ^₇ 21/1000 ma kekimala notation.

Translation Algorithm kūpono mahele i ka poʻe'ē he nui a me ka Hope versa

Kākau 'ia ma muli o ke kūpono hapa incorrectly hana, pela no ka mea, pono e huli ana i ka hui helu:

• puunaue i ka numerator ma ka denominator i loaʻa;
• i loko o ka mea i ho'ākāka 'kumu hoʻohālike o ka hapa puu hapa - pa alima;
• a me ke koena - ka numerator o ka fractional hapa, ka denominator koe ua hoʻololiʻia.

Laʻana. Hoohuli kūpono mahele i ka poʻe'ē he nui: ^_47/5.

Olelo hooholo. 47: 5. ka hapa puu hapa Ua like ia 9, i ke koena = 2. Nolaila, ^_47/5 = 9 ^_2/5.

I kekahi manawa, he mea pono i ka mai i kekahi poʻe'ē he helu me he kūpono mahele. A laila, e pono e hoʻohana i ka kēia algorithm:

• ka helu hapa ua hoonuiia e ka denominator o ka fractional hōʻike;
• ka mea kūpono huahana ua hou a hiki i ka numerator;
• ka hopena ua kākau i loko o ka numerator ka denominator koe ua hoʻololiʻia.

Laʻana. Ho i ka helu i ka hui ano like kūpono mahele 9 ^_8/10.

Olelo hooholo. 9 m 10 + 8 = 90 + 8 = 98 - numerator.

Pane: ^_98/10.

Multiplication o ka hapa

Ma na mahele ke hana i kekahiʻano o algebraic hana. E hoonui i ka helu elua, e pono e hoonui i ka numerator o ka numerator, a me ka denominator me ka denominator. A, i ka multiplication o ka mahele me kekahi mau denominators Ia, aole ia i oko mai o ka huina hoonui o fractional helu a me ka ia denominators.

Ua hana ia ma hope o loaa ia i nā hualoaʻa e pono e emi i ka mahele. He OAXA ia i ke Nohie i ka kūpono hōʻike. O ka holo ana, ua hiki ole ke olelo i ka mea kūpono hapa iki i loko o ka pane - ia mea he hewa, akā, ma ka pono ka pane, a kapa aku ia he paʻakikī.

Laʻana. E huli i ka huina hoonui o ka elua na hapa: ½, a me ^_20/18.

I hiki ke ike i ka hana mai, ma hope o loaa i ka huina hoonui o ka fractional huli cancellative i hoʻopaʻa 'ia. A me ka numerator, a me ka denominator ma keia hihia mea divisible ka 4, a me ka hopena lawelawe 'ana i nā pane ^_5/9.

Multiplication o kekimala hapa

Hana noʻeau decimals Ua okoa mai ano o na hana ma kona rula. Penei, multiplication o ka hapa Ua like penei:

• mau decimals e e palapala ma lalo o kekahi i kekahi, no laila, i ka rightmost huahelu, he kekahi ma luna o ka mea'ē aʻe;
• oe pono e hoonui i ka helu o ka palapala mamua commas, 'o ia hoʻi, e like me ke kino;
• helu i ka helu o ka hoailona huahelu ma hope o ka kekimala wahi i loko o kela a me keia o ka loa;
• e kiʻi ma hope o hoonui i ka hopena e pono ai, e helu i ka pono i na laulā huapalapala e like me ka mea i loaʻa ma loko o ka nui o nā multipliers ma hope o ka kekimala wahi, a kau i ka hoailona hoʻokaʻawale;
• ina ka helu i loko o ka huahana ua emi manawa ma mua o ia mau mea, e kākau i na 'Aʻohe hualoaʻa e uhi i kēia dala, au i ka comma, a wahi i ka helu' ana o 'Aʻohe.

Laʻana. E huli i ka huina hoonui o ka mau decimals: 2.25 a 3,6.

Olelo hooholo.

Multiplication o ka hui hapa

No ka ho omaulia i ka huina hoonui o nā poʻe'ē he hapa iki, e pono e hoʻohana i ka rula o ka multiplication o nā mahele:

• hoolilo helu i ka poʻe'ē he palapala i loko o ka hewa mahele;
• E huli i ka huina hoonui o ka numerators;
• huli i ka huina hoonui o ka denominators;
• Ua moʻolelo o ka hopena i loaa mai;
• e Nohie i ka hōʻike.

Laʻana. E huli i ka huina hoonui o ka 4½ a me 6 ^_2/5.

Hoonui loa ana i ka helu ma ka hapa iki (hapa iki o ka helu)

Ma waho loaa ia makou kekahi huahana o elua mahele, i hui helu loaʻa i hana kahi e pono hoonuiia e ka helu maoli i loko o ka hapa.

No laila, e 'imi hana, a me ka kekimala hapa iki o ka helu maoli, e pono e:

• palapala i ka helu ma lalo o ka pana, no laila, i ka rightmost huahelu, he kekahi ma luna o ka mea'ē aʻe;
• e imi i ka hana, ma ka naʻe o ka comma;
• ka loaa hopena, e hoʻokaʻawale i ka helu 'ana, mai ka kekimala ma ka comma, e helu i ka helu pono o huahelu ma hope o ka kekimala wahi ua aia i loko o ka mahele.

No e hoonuiia e ka helu o ke ano o hapa, ka numerator e loaʻa ka hana, a me ka kūlohelohe ololi. Inā ka pane mea cancellative hapa iki, ka mea, o huli mai lakou.

Laʻana. E huli i ka huina hoonui o ka ^_5/8 a me ka 12.

Olelo hooholo. _{^{* 12 = 5/8 (5}} * 12) / 8 = 60/8 = 30/4 = 15/2 = 7 1/2 _.

A: 7 ^_1/2.

I hiki ke ike i ka mua kumu hoʻohālike mai, ka mea, ua pono e emi i ka kūpono hoʻokūkū, a hoohuli kūpono fractional olelo i loko o ka hui helu.

No hoi, multiplication a me ka hoʻoholo 'ana e pili hapa iki o ka huina hoonui i loko o ka hui ano, a kūlohelohe ololi. E hoonui e ia i ka helu 'ana o ka poʻe'ē he ololi hoonuiia e ka helu, ka numerator hoonuiia e ka ia waiwai, a me ka denominator koe ua hoʻololiʻia kēia helu elua. Inā koi 'ia, ka mea i pono, e Nohie i ka hopena.

Laʻana. Ka mea, loaʻa i ka huina hoonui o ka 9 ^_5/6 a me 9.

Olelo hooholo. 9 ^_5/6 m 9 = 9 + 9 m ^{(5 m _{9) / 6 = 81 + 45}} /6 = 81 + 7 3/6 = 88 1/2 _.

E hai mai hoi: 88 ^_1/2.

Ua multiplication ma na multipliers 10, 100, 1000 a 0,1; 0,01; 0.001

No ka mea ma mua paukū hiki aku ai i ke kēia mau rula. No ka hoonui decimals ka 10, 100, 1000, a me ka 10000 nā kana. D. hea hana i ka neʻeʻana i ka comma ma ka akau, ma ka like na huahelu hōʻailona like 'Aʻohe hualoaʻa ma ka multiplier mokuna hope.

Kumu 1. E huli i ka huina hoonui o ka 0.065 a me ka 1,000.

Olelo hooholo. 0.065 x 1000 = 0065 = 65.

I hai mai hoi: 65.

Laʻana 2. E huli i ka huina hoonui o 3,9 a me ka 1,000.

Olelo hooholo. 3,9 m 1,000 = 3,900 m 1000 = 3900.

Pane: 3900.

Inā he mea pono e hoonui maikaʻi helu, a me 0,1; 0,01; 0,001; 0,0001, a no laila, ma luna, E., E e hoʻoneʻe i ka waiho i ka comma i loko o ka kūpono huahana i like na huahelu hōʻailona like 'Aʻohe mea i kekahi. Inā pono, ma mua o ka helu maoli i hoʻopaʻa 'Aʻohe hualoaʻa ma ka ai lawa ku.

Kumu 1. Ka mea, loaʻa i ka huina hoonui o ka 56 a me 0,01.

Olelo hooholo. 56 m 0,01 = 0056 = 0,56.

Pane: 0,56.

Laʻana 2. E huli i ka huina hoonui o ka 4 a me ka 0.001.

Olelo hooholo. 4 x 0,001 = 0004 = 0,004.

Au e pane aku: 0.004.

No laila, i loaa i ka huina hoonui o kekahi mau mahele e e straightforward, koe wale no i ka i ka ho omaulia hopena; ma keia hihia me ka me ka m'kini helu pono e e hana ai.