Kalkuletar Kashi
Ƙara, rage, ninka, da raba kashi tare da sauƙaƙewa ta atomatik
Yadda Ayyukan Kashi ke Aiki
Fahimtar dokokin lissafi a bayan ayyukan kashi yana taimaka maka warware matsaloli mataki-mataki da kuma tabbatar da sakamakon kalkuletar.
- Ƙarawa/Ragewa yana buƙatar ma'auni iri ɗaya: ninka da kashi masu kama
- Ninkawa yana ninka lamba ta sama tare da lamba ta sama, da lamba ta ƙasa tare da lamba ta ƙasa
- Rabawa yana amfani da dokar 'ninka da juyayyen': a/b ÷ c/d = a/b × d/c
- Sauƙaƙewa yana amfani da Mafi Girman Abin Rarrabawa na Gama Gari (GCD) don rage kashi
- Lambobi masu gauraye suna juyewa daga kashi marasa dace lokacin da lamba ta sama > lamba ta ƙasa
Menene Kalkuletar Kashi?
Kalkuletar kashi tana yin ayyukan lissafi da kashi (ƙara, rage, ninka, raba) kuma tana sauƙaƙe sakamakon ta atomatik. Kashi suna wakiltar sassa na gabaɗaya, ana rubuta su a matsayin lamba ta sama/lamba ta ƙasa. Wannan kalkuletar tana neman ma'auni iri ɗaya idan an buƙata, tana yin aikin, kuma tana rage sakamakon zuwa mafi ƙanƙanta. Hakanan tana juya kashi marasa dace zuwa lambobi masu gauraye kuma tana nuna kwatankwacin decimal, wanda ya sa ta zama cikakkiya don aikin gida, girki, gini, da duk wani aiki da ke buƙatar ingantattun lissafin kashi.
Amfani da Aka Saba
Girki & Kayan Abinci
Ƙara ko auna kayan abinci: 1/2 kofi + 1/3 kofi, ninka ma'aunin 3/4 na karamin cokali, da sauransu.
Awo & Gini
Lissafa tsawon katako, yankan zane, ko ma'aunin kayan aiki da inci na kashi da ƙafafu.
Aikin Gida na Lissafi
Duba amsoshin matsalolin kashi, koyi matakan sauƙaƙewa, da kuma tabbatar da lissafi.
Kimiyya & Aikin Dakin Gwaje-gwaje
Lissafa rabon sinadarai, narkarwa, da kuma rabon gauraye a cikin adadin kashi.
Lissafin Kuɗi
Lissafa hannun jari na kashi, kaso na mallaka, ko raba kadarori daidai gwargwado.
DIY & Sana'o'i
Lissafa adadin kayan aiki, auna zane, ko juyar da girma a cikin raka'o'in kashi.
Dokokin Ayyukan Kashi
Ƙarawa
Formula: a/b + c/d = (ad + bc)/bd
Nemi ma'auni iri ɗaya, ƙara lamba ta sama, sauƙaƙe sakamako
Ragewa
Formula: a/b - c/d = (ad - bc)/bd
Nemi ma'auni iri ɗaya, rage lamba ta sama, sauƙaƙe sakamako
Ninkawa
Formula: a/b × c/d = (ac)/(bd)
Ninka lamba ta sama tare, ninka lamba ta ƙasa tare
Rabawa
Formula: a/b ÷ c/d = a/b × d/c = (ad)/(bc)
Ninka da juyayyen kashi na biyu
Nau'o'in Kashi
Kashi Mai Kyau
Example: 3/4, 2/5, 7/8
Lamba ta sama ta fi lamba ta ƙasa ƙanƙanta, darajar ta gaza 1
Kashi Mara Kyau
Example: 5/3, 9/4, 11/7
Lamba ta sama ta fi lamba ta ƙasa girma ko daidai da ita, darajar ≥ 1
Lamba Mai Gauraye
Example: 2 1/3, 1 3/4, 3 2/5
Gabaɗayan lamba tare da kashi mai kyau, an juya daga kashi marasa kyau
Kashi na Raka'a
Example: 1/2, 1/3, 1/10
Lamba ta sama ita ce 1, tana wakiltar sashi ɗaya na gabaɗaya
Kashi Masu Kama
Example: 1/2 = 2/4 = 3/6
Kashi daban-daban da ke wakiltar daraja iri ɗaya
Yadda Ake Amfani da Wannan Kalkuletar
Mataki na 1: Shigar da Kashi na Farko
Shigar da lamba ta sama (numerator) da lamba ta ƙasa (denominator) na kashin farko.
Mataki na 2: Zaɓi Aiki
Zaɓi Ƙarawa (+), Ragewa (−), Ninkawa (×), ko Rabawa (÷) don lissafinku.
Mataki na 3: Shigar da Kashi na Biyu
Shigar da lamba ta sama da lamba ta ƙasa na kashin na biyu.
Mataki na 4: Duba Sakamako
Duba sakamakon da aka sauƙaƙe, ainihin tsari, lamba mai gauraye (idan akwai), da kwatankwacin decimal.
Mataki na 5: Fahimtar Sauƙaƙewa
Kalkuletar tana rage kashi zuwa mafi ƙanƙanta ta atomatik ta hanyar rarrabawa da mafi girman abin rarrabawa na gama gari.
Mataki na 6: Duba Decimal
Yi amfani da sakamakon decimal don tabbatar da kashinku ko don yanayin da ke buƙatar rubutun decimal.
Shawarwari kan Sauƙaƙe Kashi
Nemi GCD
Yi amfani da Mafi Girman Abin Rarrabawa na Gama Gari don rage kashi: GCD(12,18) = 6, don haka 12/18 = 2/3
Rarraba zuwa Lambobin Firamare
Raba lambobi zuwa abubuwan firamare don sauƙin nemo abubuwan rarrabawa na gama gari
Dokokin Rarrabawa
Yi amfani da gajerun hanyoyi: lambobin da ke ƙarewa da 0,2,4,6,8 ana iya raba su da 2; idan jimlar lambobin ta rabu da 3, tana nufin an raba ta da 3
Soke ta Giciye a Ninkawa
Soke abubuwan gama gari kafin ninkawa: (6/8) × (4/9) = (3×1)/(4×3) = 1/4
Yi Aiki da Ƙananan Lambobi
Koyaushe sauƙaƙe sakamakon tsakiya don kiyaye lissafi cikin sauƙi
Shawarwari kan Lissafin Kashi
Ƙarawa & Ragewa
Yana buƙatar ma'auni iri ɗaya. Kalkuletar tana neman LCD ta atomatik: 1/2 + 1/3 = 3/6 + 2/6 = 5/6.
Ninka Kashi
Ninka lamba ta sama tare da lamba ta sama, da lamba ta ƙasa tare da lamba ta ƙasa: 2/3 × 3/4 = 6/12 = 1/2 (an sauƙaƙe).
Raba Kashi
Ninka da juyayyen (juya kashi na biyu): 2/3 ÷ 1/4 = 2/3 × 4/1 = 8/3.
Sauƙaƙewa
Raba lamba ta sama da lamba ta ƙasa da GCD (mafi girman abin rarrabawa na gama gari): 6/9 = (6÷3)/(9÷3) = 2/3.
Lambobi Masu Gauraye
Kashi marasa dace (lamba ta sama > lamba ta ƙasa) suna juyewa zuwa masu gauraye: 7/3 = 2 1/3 (gabaɗaya 2, saura 1/3).
Kashi Marasa Kyau
Alamar ragi na iya zama a lamba ta sama ko a kan dukkan kashi: -1/2 = 1/(-2). Kalkuletar tana kiyaye lamba ta ƙasa a matsayin mai kyau.
Amfanin Kashi a Rayuwa ta Zahiri
Girki & Gasa
Auna kayan abinci, rabon sinadarai, kofuna da cokula na aunawa
Gini
Awo a inci (1/16, 1/8, 1/4), lissafin kayan aiki
Kuɗi
Farashin hannun jari, ribar banki, lissafin kaso
Magani
Adadin magani, rabon narkewa, kididdigar marasa lafiya
Waƙa
Darajojin noti, alamar lokaci, lissafin sautin waƙa
Wasanni
Kididdiga, rabon nasara, rabon lokaci
Abubuwan Ban Sha'awa game da Kashi
Asalin Da
Tsoffin Masarawa sun yi amfani da kashi a kusan 2000 BC, amma sun yi amfani da kashi na raka'a ne kawai (1/n).
Lissafin Pizza
Idan ka ci 3/8 na pizza kuma abokinka ya ci 1/4, tare kun ci 5/8 na pizza.
Waƙa da Kashi
Darajojin notin waƙa kashi ne: cikakken noti = 1, rabin noti = 1/2, kwata noti = 1/4.
Haɗin Decimal
Kowane kashi yana wakiltar decimal da ke ƙarewa ko maimaitawa: 1/4 = 0.25, 1/3 = 0.333...
Jerin Farey
Jerin Farey yana lissafa dukkan kashi da aka sauƙaƙe tsakanin 0 da 1 tare da lamba ta ƙasa har zuwa n.
Rabon Zinariya
Rabon zinariya φ = (1 + √5)/2 ≈ 1.618 ana iya bayyana shi a matsayin kashi mai ci gaba [1; 1, 1, 1, ...].
Kuskuren da Aka Saba Yi da Kashi
Ƙara Lamba ta Ƙasa
Ba daidai ba: 1/2 + 1/3 = 2/5. Daidai: Fara nemo ma'auni iri ɗaya: 1/2 + 1/3 = 3/6 + 2/6 = 5/6.
Ninkawa ta Giciye a Ƙarawa
Ninkawa ta giciye tana aiki ne kawai don warware lissafi, ba don ƙara kashi ba.
Manta da Sauƙaƙewa
Koyaushe rage kashi zuwa mafi ƙanƙanta: ya kamata a sauƙaƙe 6/8 zuwa 3/4.
Rikicewar Rabawa
Ka tuna 'ninka da juyayyen': a/b ÷ c/d = a/b × d/c, ba a/b × c/d ba.
Kuskuren Juyar da Lambobi Masu Gauraye
Don juya 7/3 zuwa lamba mai gauraye: 7 ÷ 3 = 2 saura 1, don haka 2 1/3, ba 2 4/3 ba.
Sifili a Lamba ta Ƙasa
Kada a taɓa barin sifili a lamba ta ƙasa - ba a san rarrabawa da sifili ba.
Cikakken Jagoran Kayan Aiki
Dukan kayan aiki 71 da ke akwai a kan UNITS