Question

Calculati:
a)(12\25:4\5):9\35
b)(12\25:(4\5:9\35)
c)(25\36:7\16):(60\49:162\7)
d)(11\12:13\18):22\33
e)(19\45:7\30):19\21
f)(13\12:7\15):39\70

Answer 1

Cerinta-sa efectuam calcule cu fractii

Explicație pas cu pas:

a) folosim proprietatea ca $\boxed{\frac{x}{y} :\frac{z}{t} =\frac{x}{y} x\frac{t}{z}}$

$\displaystyle (\frac{12}{25} : \frac{4}{5} ):\frac{9}{35} =(\frac{12}{25} x \frac{5}{4} ):\frac{9}{35} = (\frac{\not12}{25} x \frac{5}{\not4} ):\frac{9}{35} = (\frac{3}{\not25} x \frac{\not5}{4} ):\frac{9}{35} = \frac{3}{20} : \frac{9}{35}= \frac{\not3}{20} x \frac{35}{\not9} =\frac{1}{\not20} x \frac{\not35}{3} =\frac{1}{4}x\frac{7}{3} =\frac{7}{12}$

b)

$\displaystyle \frac{12}{25} : (\frac{4}{5} :\frac{9}{35} )= \frac{12}{25} :(\frac{4}{5} x \frac{35}{9} )=\frac{12}{25} :(\frac{4}{\not5} x \frac{\not35}{9} )=\frac{12}{25} :(\frac{4}{1} x \frac{7}{9} )=\frac{12}{25} :\frac{28}{9} =\frac{\not12}{25} x \frac{9}{\not28} =\frac{3}{25} x \frac{9}{7} =\frac{27}{175}$

c)

$\displaystyle(\frac{25}{36} :\frac{7}{16} ):(\frac{60}{49}:\frac{162}{7} )=(\frac{25}{36} x\frac{16}{7} ):(\frac{60}{49}x\frac{7}{162} )=(\frac{25}{\not36} x\frac{\not16}{7} ):(\frac{60}{\not49}x\frac{\not7}{162} )=(\frac{25}{9} x\frac{4}{7} ):(\frac{60}{7}x\frac{1}{162} )=\frac{100}{63} :(\frac{\not60}{7}x\frac{1}{\not162} )=\frac{100}{63} :(\frac{10}{7}x\frac{1}{27} )==\frac{100}{63} : \frac{10}{189}= \frac{\not100}{63}x\frac{189}{\not10} = \frac{10}{\not63} x \frac{\not189}{1} = 10x3=30$

d)

$\displaystyle(\frac{11}{12} :\frac{13}{18} ):\frac{22}{33} =(\frac{11}{12} x\frac{18}{13} ):\frac{22}{33} =(\frac{11}{\not12} x\frac{\not18}{13} ):\frac{22}{33} =(\frac{11}{2} x\frac{3}{13} ):\frac{22}{33} =\frac{33}{26} :\frac{22}{33} =\frac{33}{26} x\frac{33}{22} =\frac{\not33}{26} x\frac{33}{\not22} =\frac{3}{26} x\frac{\not33}{\not11} =\frac{3}{26} x\frac{3}{1} =\frac{9}{26}$

e)

$\displaystyle(\frac{19}{45} :\frac{7}{30} ):\frac{19}{21} =(\frac{19}{45} x\frac{30}{7} ):\frac{19}{21} =(\frac{19}{\not45} x\frac{\not30}{7} ):\frac{19}{21} =(\frac{19}{3} x\frac{2}{7} ):\frac{19}{21} =\frac{38}{21} :\frac{19}{21} =\frac{38}{21} x\frac{\not21}{19} =\frac{38}{\not21} x\frac{21}{19} =\frac{\not38}{\not19} =2$

f)

$\displaystyle(\frac{13}{12} :\frac{7}{15} ):\frac{39}{70} =(\frac{13}{12} x\frac{15}{7} ):\frac{39}{70} =(\frac{13}{\not12} x\frac{\not15}{7} ):\frac{39}{70} =(\frac{13}{4} x\frac{5}{7} ):\frac{39}{70} =\frac{45}{28} : \frac{39}{70} =\frac{45}{28} x \frac{70}{39}= \frac{45}{\not28} x \frac{\not70}{39} =\frac{45}{4} x \frac{10}{39} =\frac{45}{\not4} x \frac{\not10}{39} ==\frac{45}{2} x \frac{5}{39} =\frac{225}{78}$