Question

Bài 12 : THực hiện phép tính một cách hợp lý

a) \(\frac{6}{7}+\frac{5}{7}:5-\frac{8}{9}\)                                b) \(\frac{-5}{7}.\frac{2}{11}+\frac{5}{7}.\frac{9}{11}\)                    c) \(\frac{5}{9}.\frac{7}{13}+\frac{5}{9}.\frac{9}{13}-\frac{5}{9}.\frac{3}{13}\)

 

Answer 1

a)\(\frac{6}{7}+\frac{5}{7}:5-\frac{8}{9}=\frac{6}{7}+\frac{1}{7}-\frac{8}{9}=1-\frac{8}{9}=\frac{1}{9}\)

b)\(\frac{-5}{7}.\frac{2}{11}+\frac{5}{7}.\frac{9}{11}=\frac{5}{7}.\frac{2}{11}-\frac{5}{7}.\frac{9}{11}=\frac{5}{7}.\left(\frac{2}{11}-\frac{9}{11}\right)=\frac{5}{7}.\frac{-7}{11}=\frac{-5}{11}\)

c)\(\frac{5}{9}.\frac{7}{13}+\frac{5}{9}.\frac{9}{13}-\frac{5}{9}.\frac{3}{13}=\frac{5}{9}.\left(\frac{7}{13}+\frac{9}{13}-\frac{3}{13}\right)=\frac{5}{9}.1=\frac{5}{9}\)

Answer 2

a) \(\frac{6}{7}+\frac{5}{7}:5-\frac{8}{9}\)
\(\Rightarrow\frac{6}{7}+\frac{1}{7}-\frac{8}{9}\)
\(\Rightarrow1-\frac{8}{9}=\frac{1}{9}\)
b) \(\frac{-5}{7}.\frac{2}{11}+\frac{5}{7}.\frac{9}{11}\)
\(\Rightarrow\frac{5}{7}.\frac{-2}{11}+\frac{5}{7}.\frac{9}{11}\)
\(\Rightarrow\frac{5}{7}.\left(\frac{-2}{11}+\frac{9}{11}\right)\)
\(\Rightarrow\frac{5}{7}.\frac{7}{11}=\frac{5}{11}\)
c) \(\frac{5}{9}.\left(\frac{7}{13}+\frac{9}{13}-\frac{3}{13}\right)=\frac{5}{9}.1=\frac{5}{9}\)

Answer 3

a ) \(\frac{6}{7}+\frac{5}{7}:5-\frac{8}{9}\)

\(=\frac{6}{7}+\frac{5}{7}.\frac{1}{5}-\frac{8}{9}\)

\(=\frac{6}{7}+\frac{1}{7}-\frac{8}{9}\)

\(=\frac{6+1}{7}-\frac{8}{9}\)

\(=\frac{7}{7}-\frac{8}{9}\)

\(=\frac{1}{9}\)

b ) \(-\frac{5}{7}.\frac{2}{11}+\frac{5}{7}.\frac{9}{11}\)

\(=\frac{-5.2}{7.11}+\frac{5.9}{7.11}\)

\(=-\frac{10}{77}+\frac{45}{77}\)

\(=\frac{-10+45}{77}\)

\(=\frac{35}{77}=\frac{5}{11}\)

c ) \(\frac{5}{9}.\frac{7}{13}+\frac{5}{9}.\frac{9}{13}-\frac{5}{9}.\frac{3}{13}\)

\(=\frac{5}{9}.\left(\frac{7}{13}+\frac{9}{13}+\frac{3}{13}\right)\)

\(=\frac{5}{9}.1\)

\(=\frac{5}{9}\)