Matematika 1+1=2 - Zlomky - zlomky

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zlomky

29. 10. 2009

Zlomek je část celku. Zlomek se skládá ze jmenovatele (udává, na kolik částí celek dělíme), čitatele (počet částí celku) a zlomkové čáry, která představuje jen jiný zápis dělení. Zlomek v základním tvaru: čitatel a jmenovatel nemají žádného společného dělitele různého od 1. Krácení zlomku: dělení čitatele a zároveň jmenovatele stejným číslem různým od 0. Rozšiřování zlomku: vynásobení čitatele a zároveň jmenovatele stejným číslem různým od 0. Krácením a rozšiřováním se hodnota zlomku nemění, jedná se pouze o různý zápis stejné části celku. Pravý zlomek: čitatel je menší než jmenovatel. 2 7 Nepravý zlomek: čitatel je větší než jmenovatel (zlomek je větší, než celek). 7 2 Smíšené číslo: skládá se z celého čísla a pravého zlomku. Pokud je v čitateli nula, pak je zlomek roven nule. Ve jmenovateli nesmí být nula (nulou nedělíme). Převádění zlomků na společného jmenovatele: vhodně původní zlomky rozšíříme tak, aby ve jmenovateli nových zlomků bylo stejné číslo (nejmenší společný násobek jmenovatelů původních zlomků). Porovnávání zlomků: smíšená čísla převedeme na zlomky, všechny zlomky převedeme na společného jmenovatele a pak porovnáme podle velikosti čitatele. Převod desetinného čísla na zlomek: desetinné číslo je ve své podstatě už zlomek, jen je napsaný v jiném formátu. Porovnej si zápis 1,2 (čti jedna celá dvě desetiny) a (čti jeden celek dvě desetiny). Převod zlomku na desetinné číslo: vydělíme čitatele jmenovatelem nebo (když to jde) ho šikovně rozšíříme na desetiny, setiny, tisíciny... Např. máme zlomek 1 4 1 : 4 = 0,25 (žádná celá, dvacet pět setin) 1 = 25 (dvacet pět setin) 4 100 Sčítání zlomků: zlomky musí mít společného jmenovatele, pak čitatele sečteme a společného jmenovatele opíšeme. Odečítání zlomků: zlomky musí mít společného jmenovatele, pak čitatele odečteme (pozor na pořadí, nesmíme ho přehodit) a společného jmenovatele opíšeme. Násobení zlomků: všechny zlomky napřed vykrátíme. Násobíme-li celým číslem, pak násobíme pouze čitatele, jmenovatele necháme beze změny. Násobíme-li zlomkem, čitatel je součin čitatelů původních zlomků, jmenovatel součin jmenovatelů původních zlomků. Stejným způsobem se počítá zlomek ze zlomku (například polovina z poloviny je čtvrtina). Dělení zlomků: celá čísla převedeme na zlomky, všechny zlomky vykrátíme, pak vynásobíme první zlomek převrácenou hodnotou druhého zlomku. (Stejným způsobem řešíme složený zlomek.) Lomený výraz: zlomek obsahující jednu nebo více proměnných. Ve jmenovateli lomeného výrazu nesmí být nula, proto musíme uvádět podmínky, za kterých výraz existuje (má smysl).

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