Hacho. Chokuwanziridza zvavo zvikamu zviduku, grade, hwakakanyiwa

vaiva dingindira "Zvikamu Zviduku" Pane nepakati uye vokusekondari. Zvisinei, pfungwa iyi yakakura zvikuru kupfuura kuti anopiwa hwekudzidza. Nhasi pfungwa zvikamu kunowanzoitika, uye havasi vose vangaita kukarukureta ane mashoko Somuenzaniso, chokuwanziridza zvikamu zviduku zveropa.

Chii chikamu?

Kare, kuti fractional nhamba zvaiva nokuda kudiwa kuyera. Sezvo tsika inoratidza kakawanda mienzaniso yezvinorehwa nokureba chidimbu, bhuku rimwe rectangular parallelepiped, nzvimbo yacho rectangle.

Pakutanga, vadzidzi tinyatsoziva pfungwa sei kugoverana. Somuenzaniso, kana iwe zviparadzanise vise kupinda 8 zvikamu, ipapo mumwe achawana mumwe-wechisere visi. Heino imwe masere anonzi lobes.

Mugove, zvakaenzana ½ ane ukoshi inonzi nehafu; ⅓ - wechitatu; ¼ - kota. Entries vanoumba ^{_{5/8, 4/5, 2/4}} inonzi nevakawanda zvikamu zviduku. Common nezvikamu yakakamurwa nokuda numerator uye dhinomineta. Pakati pavo chikamu mutsetse, kana slashes. Slashes zvinogona kumbokweva chimiro zvose zvido zvevanhu uye oblique nemitsetse. Muchiitiko chino, inoratidza kupesana chiratidzo.

The dhinomineta rinomiririra migove vangani zvakafanana vaiita ukoshi chinhu; uye numerator - iroro nhamba migove yatorwa. The numerator zvakanyorwa pamusoro yokutema miti, iro dhinomineta - pasi.

The zvikuru yokuita nzira yokuratidza zvakajairika zvikamu zviduku kutungamirira danda. Kana chikwata chidimbu rakakamurwa 4 yakaenzana mativi, anoratidza mugove tsamba neimwe Latin, zvinogona kuti yakanaka chinooneka. Saka, pfungwa A anoratidza nhamba yakaenzana ^_1/4 of zvachose kureba chikwata, uye pfungwa B unoratidza ^_2/8 ari kupiwa chidimbu.

mhando zvikamu zviduku

Zvikamu zviduku hazvizivani, decimals, uye vakavhengana nhamba. Mukuwedzera, chikamu chiduku inogona kukamurwa nezvakaipa. kupatsanura Iri nani kuti zvavo zvikamu zviduku.

Under zvakakodzera chakapatsanurwa kunzwisisa nhamba vane numerator idukusa ari dhinomineta. Nokudaro, chikamu chiduku emunhu - nhamba kuti ane kupfuura numerator dhinomineta. Chechipiri mhando Kazhinji zvakanyorwa sezvo neveMamwe siyana. Yakadaro mashoko rinoumbwa integer uye fractional nhengo. Somuenzaniso, 1½. 1 - yose chikamu, ½ - fractional. Zvisinei, kana uchida kuita chero kuchinja rokuti (weboka kana chokuwanziridza zvikamu zviduku zveropa vavo rutapudzo kana kutendeuka), zvakavhenganiswa nhamba iri akashandurirwa kukodzera zvikamu zviduku.

Kwakakodzera fractional mashoko anogara asingasviki mumwe, uye nezvakaipa - mukuru kana kuenzana 1.

Kana decimals, zvadaro aya kunzwisisa nhoroondo unoratidza chero nhamba, ari dhinomineta ari fractional okuti izvo zvinogona kutaurwa chikwata ane zeros shoma. Kana rugwaro wakarurama, ipapo rose chikamu grade notation akaenzana razero.

Kunyora grade chakapatsanurwa, unofanira kutanga kunyora yose chikamu, kusiyanisa kubva chikamu chiduku chete koma, uye ipapo kunyora fractional okuti. Zvinofanira kurangarirwa kuti pashure zvokusvika numerator anofanira zvine chete nhamba digitaalinen vatambi sezvo zeros ari dhinomineta.

Example. Present bara ^₇ 21/1000 mu grade notation.

Translation Algorithm kukodzera zvikamu zviduku kuti vakavhengana nhamba ndiEzekieri

Rakanyorwa pakupindura kukodzera zvikamu zviduku zvisiri dambudziko, saka rinofanira kuchinjwa kuti zvakavhenganiswa nhamba:

• vagovane numerator kubudikidza dhinomineta kuwanikwa;
• ari muenzaniso chaiyo iri rushoma quotient - chikwata;
• uye vakasara - the numerator of fractional kacho dhinomineta anoramba kuzochinja.

Example. Change kukodzera zvikamu zviduku kuti vakavhengana nhamba: ^_47/5.

Decision. 47: 5. The haasaruri quotient akaenzana 9, vakasara = 2. Saka, ^_47/5 = 9 ^_2/5.

Dzimwe zvakafanira yokusuma zvakavhenganiswa nhamba sezvo hacho chinhu kukodzera. Zvino unofanira kushandisa inotevera algorithm:

• ari integer chikamu zvikawanda kubudikidza dhinomineta of fractional okuti;
• kunoguma chigadzirwa inowedzerwa numerator;
• mugumisiro makanyorwei numerator, dhinomineta anoramba kuzochinja.

Example. Kumiririra nhamba makawanda muchimiro sezvo kukodzera zvikamu zviduku: 9 ^_8/10.

Decision. 9 x 10 + 8 = 90 + 8 = 98 - numerator.

Pindura: ^_98/10.

Chokuwanziridza zvikamu zviduku zveropa

On zvakafanana zvikamu zviduku zvinogona kuita siyana algebraic kushandiswa. Kuwanda nhamba mbiri, unofanira vawande pamusoro numerator pamwe numerator uye dhinomineta pamwe dhinomineta. Uyezve chokuwanziridza zvikamu zviduku zveropa vane denominators zvakasiyana Hazvina kusiyana zvibereko fractional nhamba pamwe chete denominators.

Zvinoitika kuti awana migumisiro unofanira kuderedza hacho. Zviri fanira kuva kurerutsa kunoguma okuti. Chokwadi, hatigoni kutaura kuti chikamu chiduku kukodzera iri mhinduro - ndiko kukanganisa, asi anonziwo mhinduro wazvo kuoma.

Example. Find zvinobikwa zviviri nevakawanda zvikamu zviduku: ½, uye ^_20/18.

Sezvinogona kuoneka kubva muenzaniso, pashure kuwana zvibereko fractional akatendeuka cancellative yakarekodwa. Zvino numerator uye dhinomineta hazvisi divisible kubudikidza 4, uye mugumisiro anoshanda norudaviro ^_5/9.

Chokuwanziridza pamusoro grade zvikamu zviduku

Artwork decimals rakasiyana zvavo mabasa nokuda kwayo musimboti. Saka, chokuwanziridza zvikamu zviduku zveropa riri sezvinotevera:

• decimals maviri kuti zvakanyorwa pasi mumwe, saka kuti rightmost digits vaiva mumwe pamusoro pomumwe;
• unofanira vawande uwandu akanyorwa pasinei nezvitura befu, kuti kutori chibarirwo;
• nhamba digits mushure grade pfungwa chiratidzo nechimwe nhamba;
• kuti mushure vachiwedzera mugumisiro unofanira kuverenga kurudyi sezvo vakawanda Numeric vatambi sezvo iri huri uwandu zvose multipliers mushure grade pfungwa, uye akaisa chiratidzo anoparadzanisa;
• kana nhamba dziri chigadzirwa yaiva shoma pamberi pavo nguva kunyora zeros dzakawanda kufukidza mari iyi, akaisa koma uye zvakabatanidzwa integer ndechokuti razero.

Example. Change zvinobikwa decimals maviri: 2.25 uye 3.6.

Decision.

Chokuwanziridza zvakavhenganiswa zvikamu zviduku

Kuti ngaaverenge chigadzirwa zvakavhenganiswa zvikamu zviduku maviri, unofanira kushandisa mutemo chokuwanziridza zvikamu zviduku zveropa,

• uchatamisa nhamba makawanda muchimiro nenzira isiri chikamu chiduku;
• Kuwana zvibereko numerators;
• kuwana zvibereko denominators;
• kurekodha mugumisiro yapihwa;
• kurerutsa mashoko.

Example. Find zvinobikwa 4½ uye 6 ^_2/5.

Vachiwedzera nhamba nechidimbu hacho (chakapatsanurwa nhamba)

Kuwedzera yokuwana zvinobikwa zvikamu zviviri, vakavhengana nhamba akamisidzana mabasa apo zvakafanira kane ane dzinongoitika nhamba iri chikamu.

Saka, kuti kuwana basa uye grade chakapatsanurwa dzinongoitika nhamba, unofanira:

• kunyora nhamba pasi bara, zvokuti rightmost digits vaiva mumwe pamusoro pomumwe;
• kuwana basa, pasinei koma;
• kuti vakawana mugumisiro kusiyanisa integer chikamu kubva grade pedyo koma, kuverenga rworudyi nhamba digits mushure grade pfungwa iri muna hacho.

Kuti ngazviwande maererano nokuwanda zvavo chikamu chiduku, kuti numerator vanofanira kuwana basa uye dzinongoitika chinhu. Kana mhinduro iri cancellative chakapatsanurwa, izvozvo vatendeuke.

Example. Change zvinobikwa ^_5/8 uye 12.

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

A: July ^_1/2.

Sezvinogona kuoneka kubva rapfuura muenzaniso, zvakanga zvakakodzera kuti kuderedza zvichiguma nei uye exchange kukodzera fractional mashoko ari yakavhenganiswa nhamba.

Uyewo, chokuwanziridza uye kuwanikwa chokuita zvikamu zviduku zvibereko mune vakavhengana tsika uye dzinongoitika chinhu. Kuwedzera nhamba mbiri idzi inofanira kuva integer chikamu zvakavhenganiswa chinhu kane nokuwanda, iyo numerator kane chete kukosha, uye dhinomineta akasiya kuchinja. Kana waida, zvinokosha kurerutsa mugumisiro.

Example. Find zvinobikwa 9 ^_5/6 uye 9.

Decision. 9 ^_5/6 X 9 = 9 + 9 X ^{(5 x _{9) / 6 = 81 + 45}} /6 = 81 + 7 3/6 = 88 1/2 _.

Pindura: 88 ^_1/2.

Chokuwanziridza kubudikidza multipliers 10, 100, 1000 kana 0.1; 0.01; 0.001

Of yapfuura ndima zvinotungamirira zvinotevera mutemo. Nokuti anowedzera decimals kubudikidza 10, 100, 1000, 10000, uye zvichingodaro. D. Need kutamisira koma kurudyi akawanda digits sezviratidzo zeros ari multiplier chikwata pashure.

Muenzaniso 1. Find zvinobikwa 0.065 uye 1,000.

Decision. 0.065 x 1000 = 0065 = 65.

Pindura: 65.

Muenzaniso 2. Find zvinobikwa 3.9 uye 1,000.

Decision. 3.9 X 1000 = 3,900 X 1000 = 3900.

Pindura: 3900.

Kana zvakafanira kuwanda zvakanaka integer, uye 0.1; 0.01; 0,001; 0,0001 nezvimwewo. E., CHINOFANIRA akatamira kune vakasiya koma iri zvichiguma chigadzirwa kupinda sezvo zhinji digits sezviratidzo zeros ndiko kubatana. Kana zvakakodzera, pamberi yepanyama nhamba yakanyorwa zeros yakakwana kwazvo.

Muenzaniso 1. Find zvinobikwa 56 uye 0.01.

Decision. 56 X 0,01 = 0056 = 0,56.

Pindura: 0.56.

Muenzaniso 2. Find zvinobikwa 4 uye 0.001.

Decision. 4 X 0,001 = 0004 = 0,004.

Pindura: 0.004.

Saka, kuwana zvibereko zvikamu zvakasiyana-siyana anofanira yakananga, asi kuti dzemaitirwe mugumisiro; kana ichi pasina karukureta chete haazoiti.