Jeleppi-vinkki
Murtoluvun käänteisluku saadaan vaihtamalla osoitajan ja nimittäjän paikkoja,
esim. luvun [[$\dfrac{5}{6}$]] käänteisluku on [[$\dfrac{6}{5}$]]
Käänteislukujen tulo on yksi:
[[$\dfrac{5}{6}$]] ∙ [[$\dfrac{6}{5}$]] = [[$\dfrac{5 ∙ 6}{6 ∙ 5}$]] = [[$\dfrac{30}{30}$]] = 1
Murtoluku jaettuna murtoluvulla:
[[$\dfrac{3}{4}$]] : [[$\dfrac{2}{5}$]] voidaan merkitä myös jakoviivalla
[[$\dfrac{\dfrac{3}{4}}{\dfrac{2}{5}}$]]
Lavennetaan nimittäjä luvuksi 1 kertomalla nimttäjä sen käänteisluvulla [[$\dfrac{5}{2}$]]
eli [[$\dfrac{2}{5}$]] ∙ [[$\dfrac{5}{2}$]] = [[$\dfrac{2 ∙ 5}{5 ∙ 2}$]] = [[$\dfrac{10}{10}$]] = 1
silloin osoittaja on myös lavennettava samalla luvulla
[[$\dfrac{3}{4}$]] : [[$\dfrac{2}{5}$]] = [[$\dfrac{\dfrac{3}{4}}{\dfrac{2}{5}}$]] = [[$^{\dfrac{5}{2})}\dfrac{\dfrac{3}{4}}{\dfrac{2}{5}}$]]
= [[$\dfrac{\dfrac{3}{4} ∙ \dfrac{5}{2}}{\dfrac{2}{5} ∙ \dfrac{5}{2}}$]] = [[$\dfrac{\dfrac{3}{4} ∙ \dfrac{5}{2}}{1}$]]
= [[$\dfrac{3}{4}$]] ∙ [[$\dfrac{5}{2}$]]
Siis [[$\dfrac{3}{4}$]] : [[$\dfrac{2}{5}$]] = [[$\dfrac{3}{4}$]] ∙ [[$\dfrac{5}{2}$]]
Murtoluku jaetaan murtoluvulla siten, että jaettava kerrotaan jakajan käänteisluvulla.
Esim. [[$\dfrac{2}{7}$]] : [[$\dfrac{4}{7}$]] = [[$\dfrac{2}{7}$]] ∙ [[$\dfrac{7}{4}$]] = [[$\dfrac{2 ∙ 7}{7 ∙ 4}$]]
= [[$\dfrac{14}{28}$]] = [[$\dfrac{14}{28}^{(14}$]] = [[$\dfrac{1}{2}$]]
esim. luvun [[$\dfrac{5}{6}$]] käänteisluku on [[$\dfrac{6}{5}$]]
Käänteislukujen tulo on yksi:
[[$\dfrac{5}{6}$]] ∙ [[$\dfrac{6}{5}$]] = [[$\dfrac{5 ∙ 6}{6 ∙ 5}$]] = [[$\dfrac{30}{30}$]] = 1
Murtoluku jaettuna murtoluvulla:
[[$\dfrac{3}{4}$]] : [[$\dfrac{2}{5}$]] voidaan merkitä myös jakoviivalla
[[$\dfrac{\dfrac{3}{4}}{\dfrac{2}{5}}$]]
Lavennetaan nimittäjä luvuksi 1 kertomalla nimttäjä sen käänteisluvulla [[$\dfrac{5}{2}$]]
eli [[$\dfrac{2}{5}$]] ∙ [[$\dfrac{5}{2}$]] = [[$\dfrac{2 ∙ 5}{5 ∙ 2}$]] = [[$\dfrac{10}{10}$]] = 1
silloin osoittaja on myös lavennettava samalla luvulla
[[$\dfrac{3}{4}$]] : [[$\dfrac{2}{5}$]] = [[$\dfrac{\dfrac{3}{4}}{\dfrac{2}{5}}$]] = [[$^{\dfrac{5}{2})}\dfrac{\dfrac{3}{4}}{\dfrac{2}{5}}$]]
= [[$\dfrac{\dfrac{3}{4} ∙ \dfrac{5}{2}}{\dfrac{2}{5} ∙ \dfrac{5}{2}}$]] = [[$\dfrac{\dfrac{3}{4} ∙ \dfrac{5}{2}}{1}$]]
= [[$\dfrac{3}{4}$]] ∙ [[$\dfrac{5}{2}$]]
Siis [[$\dfrac{3}{4}$]] : [[$\dfrac{2}{5}$]] = [[$\dfrac{3}{4}$]] ∙ [[$\dfrac{5}{2}$]]
Murtoluku jaetaan murtoluvulla siten, että jaettava kerrotaan jakajan käänteisluvulla.
Esim. [[$\dfrac{2}{7}$]] : [[$\dfrac{4}{7}$]] = [[$\dfrac{2}{7}$]] ∙ [[$\dfrac{7}{4}$]] = [[$\dfrac{2 ∙ 7}{7 ∙ 4}$]]
= [[$\dfrac{14}{28}$]] = [[$\dfrac{14}{28}^{(14}$]] = [[$\dfrac{1}{2}$]]