Răspuns:
Explicație pas cu pas:
b)
[tex]\Big( \frac{ {}^{3)} 5}{8} + \frac{ {}^{2)} 1}{12} \Big) \div \frac{34}{27} \\ [/tex]
[tex] = \frac{15 + 2}{24} \times \frac{27}{34} \\ [/tex]
[tex] = \frac{ \not17}{ \not24} \times \frac{ \not27}{ \not34} \\ [/tex]
[tex] = \frac{1}{8} \times \frac{9}{2} = \boxed{ \frac{9}{16} } \\ [/tex]
c)
[tex] \frac{ \not12}{ \not11} \times \frac{ \not33}{ \not30} - \frac{10}{9} \div \frac{20}{21} \\ [/tex]
[tex] = 2 \times \frac{3}{5} - \frac{ \not10}{9} \times \frac{21}{ \not20} \\ [/tex]
[tex] = \frac{6}{5} - \frac{1}{3} \times \frac{7}{2} \\ [/tex]
[tex] \frac{ {}^{6)} 6}{5} - \frac{ {}^{5)} 7}{6} = \frac{36 - 35}{30} = \boxed{ \frac{1}{30} } \\ [/tex]
d)
[tex]\Big( \frac{ {}^{4)} 4}{15} - \frac{ {}^{3)} 3}{20} \Big) \div \frac{49}{30} \\ [/tex]
[tex] = \frac{16 - 9}{60} \times \frac{30}{49} \\ [/tex]
[tex] = \frac{ \not7}{ \not60} \times \frac{ \not30}{ \not49} = \frac{1}{2} \times \frac{1}{7} = \boxed{ \frac{1}{14} }\\ [/tex]
f)
[tex] \frac{12}{15} + \frac{16}{25} \div \frac{8}{10} \\ [/tex]
[tex] = \frac{12}{15} + \frac{ \not16}{ \not25} \times \frac{ \not10}{ \not8} \\ [/tex]
[tex] = \frac{12}{25} + \frac{2}{5} \times 2 \\ [/tex]
[tex] = \frac{ {}^{3)} 12}{25} + \frac{4}{5} = \frac{4}{5} + \frac{4}{5} = \boxed{\frac{8}{5} } \\ [/tex]
g)
[tex]2 \frac{5}{12} - 4 \frac{1}{12} \div 3 \frac{8}{9} \\ [/tex]
[tex] = \frac{2 \times 12 + 5}{12} - \frac{4 \times 12 + 1}{12} \div \frac{3 \times 9 + 8}{9} \\ [/tex]
[tex] = \frac{29}{12} - \frac{49}{12} \div \frac{35}{9} \\ [/tex]
[tex] = \frac{29}{12} - \frac{ \not49}{ \not12} \times \frac{ \not9}{ \not35} \\ [/tex]
[tex] = \frac{29}{12} - \frac{7}{4} \times \frac{3}{5} \\ [/tex]
[tex] = \frac{ {}^{5)} 29}{12} - \frac{ {}^{3)} 21}{20} = \frac{145 - 63}{60} = \frac{82 {}^{(2} }{60} = \boxed{ \frac{41}{30}} \\ [/tex]
h)
[tex]\Big( \frac{ {}^{4)} 7}{6} + \frac{ {}^{3)} 7}{8} \Big) \div \Big(1 \frac{7}{18} - \frac{5}{12} \Big) \\ [/tex]
[tex] = \frac{28 + 21}{24} \div \Big( \frac{1 \times 18 + 7}{18} - \frac{5}{12} \Big) \\ [/tex]
[tex] = \frac{49}{24} \div \Big( \frac{ {}^{2)} 25}{18} - \frac{ {}^{3)} 5}{12}\Big) \\ [/tex]
[tex] = \frac{49}{24} \div \frac{50 - 15}{36} \\ [/tex]
[tex] = \frac{49}{24} \div \frac{35}{36} = \frac{ \not49}{ \not24} \times \frac{ \not36}{ \not35} = \frac{7}{2} \times \frac{3}{5} = \boxed{\frac{21}{10} } \\ [/tex]
