De retinut faptul ca impartirea la fractii devine inmultire prin inversarea celei de-a doua fractii
Un intreg se introduce in fractie prin suma dintre inmultirea intregului cu numitorul si numaratorul, iar numitorul se pastreaza in fractie
a.
[tex]1\frac{1}{4}:\frac{3}{2}-\frac{7}{12}=\frac{1\times 4+1}{4} \times \frac{2}{3} -\frac{7}{12}\\\\\frac{5}{4} \times \frac{2}{3} -\frac{7}{12}=\frac{10}{12} -\frac{7}{12} =\frac{3}{12} =\frac{1}{4}[/tex]
b.
[tex]\frac{8}{3}:3\frac{1}{5} -\frac{1}{9} =\\\\\frac{8}{3}: \frac{5\times3+1}{5} -\frac{1}{9} =\\\\\frac{8}{3}:\frac{16}{5} -\frac{1}{9}=\\\\\frac{8}{3} \times\frac{5}{16} -\frac{1}{9}=\\\\\frac{5}{6} -\frac{1}{9} =\\\\[/tex]
Aducem la acelasi numitor comun adica 18
pe prima amplificam cu 3 si pe a doua cu 2
[tex]\frac{15}{18}-\frac{2}{18} =\frac{13}{18}[/tex]
c.
[tex]\frac{3}{10}+2\frac{2}{9} :\frac{8}{3} =\\\\\frac{3}{10}+\frac{2\times9+2}{9} :\frac{8}{3} =\\\\\frac{3}{10}+\frac{20}{9} :\frac{8}{3} =\\\\\frac{3}{10}+\frac{20}{9}\times\frac{3}{8}=\\\\ \frac{3}{10}+\frac{5}{3}\times\frac{1}{2} =\\\\\frac{3}{10} +\frac{5}{6} =[/tex]
Amplificam pe prima cu 3 si pe a doua cu 5 si avem numitorul comun 30
[tex]\frac{9}{30}+ \frac{25}{30}=\frac{34}{30}[/tex]
Simplificam prin 2
[tex]\frac{17}{15}[/tex]
d.
[tex]\frac{11}{6}-\frac{4}{45}:2\frac{2}{3} =\\\\\frac{11}{6}- \frac{4}{45}:\frac{8}{3} =\\\\\frac{11}{6}-\frac{4}{45}\times\frac{3}{8}=\\\\\frac{11}{6}-\frac{1}{15\times2} =\\\\\frac{11}{6}-\frac{1}{30} =\\\\\frac{55}{30} -\frac{1}{30}=\frac{54}{30} =\frac{9}{5}[/tex] am simplificat prin 6
e.
[tex]1\frac{13}{50}:\frac{9}{2}+\frac{13}{15} =\frac{63}{50} \times\frac{2}{9} +\frac{13}{15} =\\\\\frac{7}{25} +\frac{13}{15}=\\[/tex]
Numitorul comun 75, amplificam pe prima cu 3 si a doua cu 5
[tex]\frac{21}{75} +\frac{65}{75} =\frac{86}{75}[/tex]
f.
[tex]2\frac{9}{20}:\frac{14}{5}+\frac{5}{18}=\frac{49}{20}\times\frac{5}{14}+ \frac{5}{18}=\\\\ \frac{7}{8} +\frac{5}{18}=[/tex]
Aducem la numitorul 72
amplificam pe prima cu 9 si pe a doua cu 4
[tex]\frac{63}{72} +\frac{20}{72} =\frac{83}{72}[/tex]
De retinut! numitorul comun se afla prin aflarea celui mai mic multiplu! Adica, se descompun numerele si se inmultesc toate bazele la cea mai mare putere
exemplu 8 si 18
8=2³ si 18=3²×2
cmmmc= 2³×3²=72