a)
[tex]4 \frac{1}{2} \div \frac{2}{3} = \frac{4 \times 2 + 1}{2} \div \frac{2}{3} = \\ \frac{9}{2} \div \frac{2}{3} = \frac{9}{2} \times \frac{3}{2} = \frac{9 \times 3}{2 \times 2} = \frac{27}{4} [/tex]
b)
[tex] \frac{7}{12} \div 3 \frac{1}{16} = \frac{7}{12} \div \frac{3 \times 16 + 1}{16} = \\ \frac{7}{12} \div \frac{49}{16} = \frac{7}{12} \times \frac{16}{49} (simplifici) = \\ \frac{1}{3} \times \frac{4}{7} = \frac{1 \times 4}{3 \times 7} = \frac{4}{21} [/tex]
c)
[tex]5 \div 1 \frac{1}{4} = 5 \div \frac{1 \times 4 + 1}{4} = \\ 5 \div \frac{5}{4} = 5 \times \frac{4}{5} = 4[/tex]
d)
[tex]2 \frac{2}{3} \div 2 \frac{1}{3} = \frac{2 \times 3 + 2}{3} \div \frac{2 \times 3 + 1}{3} = \\ \frac{8}{3} \div \frac{7}{3} = \frac{8}{3} \times \frac{3}{7} = \frac{8}{7} [/tex]
e)
[tex]4 \frac{1}{2} \div 3 \frac{1}{2} = \frac{4 \times 2 + 1}{2} \div \frac{3 \times 2 + 1}{2} = \\ \frac{9}{2} \div \frac{7}{2} = \frac{9}{2} \times \frac{2}{7} = \frac{9}{7} [/tex]
f)
[tex]5 \frac{1}{6} \div 6 \frac{8}{9} = \frac{5 \times 6 + 1}{6} \div \frac{6 \times 9 + 8}{6} = \\ \frac{31}{6} \div \frac{62}{6} = \frac{31}{6} \times \frac{6}{62} = \frac{31}{62} = \frac{1}{2} [/tex]
g)
[tex]16 \div 9 \frac{3}{5} = 16 \div \frac{9 \times 5 + 3}{5} = \\ 16 \div \frac{48}{5} = 16 \times \frac{5}{48} = \frac{5}{3} [/tex]
h)
[tex]3 \frac{3}{4} \div 1 \frac{1}{4} = \frac{3 \times 4 + 3}{4} \div \frac{1 \times 4 + 1}{4} = \\ \frac{15}{4} \div \frac{5}{4} = \frac{15}{4} \times \frac{4}{5} = \frac{15}{5} = 3[/tex]
