Question

Bài 4: THực hiện phép tính một cách hợp lý:

a) \(\frac{7}{19}.\frac{8}{11}+\frac{3}{11}.\frac{7}{19}+\frac{-12}{19}\)           b) \(\frac{-7}{25}.\frac{39}{-14}.\frac{50}{78}\)                                  c) \(\left(\frac{3}{8}+\frac{-3}{4}+\frac{7}{12}\right):\frac{5}{6}+\frac{1}{2}\)

Answer 1

a ) \(\frac{7}{19}.\frac{8}{11}+\frac{3}{11}.\frac{7}{19}+\frac{-12}{19}\)

\(=\frac{7}{19}.\left(\frac{8}{11}+\frac{3}{11}\right)+\frac{-12}{19}\)

\(=\frac{7}{19}.\frac{11}{11}+\frac{-12}{19}\)

\(=\frac{7}{19}.1+\frac{-12}{19}\)

\(=\frac{7}{19}+\frac{-12}{19}\)

\(=\frac{7+\left(-12\right)}{19}\)

\(=-\frac{5}{19}\)

b ) \(\frac{-7}{25}.\frac{39}{-14}.\frac{50}{78}=\frac{-7.39.50}{25.-14.78}=\frac{-1.1.2}{1.-2.2}=\frac{-2}{-4}=\frac{1}{2}\)

c ) \(\left(\frac{3}{8}+\frac{-3}{4}+\frac{7}{12}\right):\frac{5}{6}+\frac{1}{2}\)

\(=\frac{5}{24}:\frac{5}{6}+\frac{1}{2}\)

\(=\frac{5}{24}.\frac{6}{5}+\frac{1}{2}\)

\(=\frac{1}{4}+\frac{1}{2}\)

\(=\frac{3}{4}\)

Answer 2

a)\(\frac{7}{19}.\frac{8}{11}+\frac{3}{11}.\frac{7}{19}+\frac{-12}{19}=\frac{7}{19}.\frac{8}{11}+\frac{3}{11}.\frac{7}{19}+\frac{7}{19}.\frac{-12}{7}=\frac{7}{19}.\left(\frac{8}{11}+\frac{3}{11}+-\frac{12}{7}\right)=\frac{7}{19}.\left(\frac{-5}{7}\right)=-\frac{5}{19}\)

b)\(\frac{-7}{25}.\frac{39}{-14}.\frac{50}{78}=\frac{\left(-7\right).39.50}{25.\left(-14\right).78}=\frac{\left(-7\right).3.13.2.5.5}{5.5.\left(-7\right).2.2.13.3}=\frac{1}{2}\)

c)\(\left(\frac{3}{8}+\frac{-3}{4}+\frac{7}{12}\right):\frac{5}{6}+\frac{1}{2}=\frac{5}{24}:\frac{5}{6}+\frac{1}{2}=\frac{2}{7}+\frac{1}{2}=\frac{11}{14}\)

Answer 3

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