Răspuns:
1.
[tex]\frac{7}{3} =\frac{2*3+1}{3} =2\frac{1}{3}[/tex]
[tex]\frac{35}{5} =\frac{5*7}{5} =7[/tex]
[tex]\frac{54}{17} =\frac{3*17+3}{17} =3\frac{3}{17}[/tex]
[tex]\frac{134}{23} =\frac{5*23+19}{23} =5\frac{19}{23}[/tex]
[tex]\frac{4}{3} =\frac{1*4+1}{3} =1\frac{1}{3}[/tex]
[tex]\frac{5}{2} =\frac{2*2+1}{2} =2\frac{1}{2}[/tex]
[tex]\frac{7}{4} =\frac{1*4+3}{4} =1\frac{1}{4}[/tex]
[tex]\frac{8}{7} =\frac{1*7+1}{7} =1\frac{1}{7}[/tex]
[tex]\frac{11}{9} =\frac{1*9+2}{9} =1\frac{2}{9}[/tex]
[tex]\frac{23}{4} =\frac{5*4+3}{4} =5\frac{3}{4}[/tex]
[tex]\frac{36}{5} =\frac{7*5+1}{5} =7\frac{1}{5}[/tex]
[tex]\frac{51}{6} =\frac{8*6+3}{6} =8\frac{3}{6} =8\frac{1}{2}[/tex]
[tex]\frac{54}{14} =\frac{3*14+12}{14} =3\frac{12}{14} =3\frac{6}{7}[/tex]
[tex]\frac{124}{23} =\frac{5*23+9}{23} =5\frac{9}{23}[/tex]
2. a) [tex]\frac{17}{5} =\frac{3*5+2}{5} =3\frac{2}{5}[/tex]
[tex]\frac{12}{8} =\frac{1*8+4}{8} =1\frac{4}{8} =1\frac{1}{2}[/tex]
[tex]\frac{10}{5} =\frac{2*5}{5} =2[/tex]
[tex]1\frac{1}{2} <2<3\frac{2}{5}[/tex] ⇒ [tex]\frac{12}{8} <\frac{10}{5} <\frac{17}{5}[/tex]
b) [tex]\frac{110}{10} =\frac{11*10}{10} =11[/tex]
[tex]\frac{135}{12} =\frac{11*12+5}{12} =11\frac{5}{12}[/tex]
[tex]\frac{96}{9} =\frac{10*9+6}{9} =10\frac{6}{9} =10\frac{2}{3}[/tex]
[tex]11\frac{5}{12 } >11>10\frac{2}{3}[/tex] ⇒ [tex]\frac{135}{12} >\frac{110}{10} >\frac{96}{6}[/tex]
c) [tex]\frac{54}{6} =\frac{9*6}{6} =9[/tex]
[tex]\frac{65}{6} =\frac{10*6+5}{6} =10\frac{5}{6}[/tex]
[tex]\frac{101}{9} =\frac{11*9+2}{9} =11\frac{2}{9}[/tex]
Explicație pas cu pas:
