Giải bài 1 trang 18 SGK Toán 6 Chân trời sáng tạo

Đề bài

Tính giá trị các biểu thức sau theo hai cách (có cách dùng tính chất phép cộng):

a) \(\left( {\frac{{ – 2}}{{ – 5}} + \frac{{ – 5}}{{ – 6}}} \right) + \frac{4}{5}\)

b) \(\frac{{ – 3}}{{ – 4}} + \left( {\frac{{11}}{{ – 15}} + \frac{{ – 1}}{2}} \right)\).

Lời giải chi tiết

 a) Cách 1:

 \(\begin{array}{l}\left( {\frac{{ – 2}}{{ – 5}} + \frac{{ – 5}}{{ – 6}}} \right) + \frac{4}{5} = \frac{2}{5} + \frac{5}{6} + \frac{4}{5}\\ = \frac{{12}}{{30}} + \frac{{25}}{{30}} + \frac{{24}}{{30}} = \frac{{61}}{{30}}\end{array}\)

Cách 2:

\(\begin{array}{l}\left( {\frac{{ – 2}}{{ – 5}} + \frac{{ – 5}}{{ – 6}}} \right) + \frac{4}{5} = \left( {\frac{2}{5} + \frac{4}{5}} \right) + \frac{5}{6}\\ = \frac{6}{5} + \frac{5}{6} = \frac{{36}}{{30}} + \frac{{25}}{{30}} = \frac{{61}}{{30}}\end{array}\)

b) Cách 1:

 \(\begin{array}{l}\frac{{ – 3}}{{ – 4}} + \left( {\frac{{11}}{{ – 15}} + \frac{{ – 1}}{2}} \right) = \frac{3}{4} + \frac{{ – 11}}{{15}} + \frac{{ – 1}}{2}\\ = \frac{{45}}{{60}} + \frac{{ – 44}}{{60}} + \frac{{ – 30}}{{60}}\\ = \frac{{ – 29}}{{60}}\end{array}\).

Cách 2:

\(\begin{array}{l}\frac{{ – 3}}{{ – 4}} + \left( {\frac{{11}}{{ – 15}} + \frac{{ – 1}}{2}} \right) = \frac{3}{4} + \frac{{ – 11}}{{15}} + \frac{{ – 1}}{2}\\ = \left( {\frac{3}{4} + \frac{{ – 1}}{2}} \right) + \frac{{ – 11}}{{15}}\\ = \left( {\frac{3}{4} + \frac{{ – 2}}{4}} \right) + \frac{{ – 11}}{{15}}\\ = \frac{1}{4} + \frac{{ – 11}}{{15}}\\ = \frac{{15}}{{60}} + \frac{{ – 44}}{{60}}\\ = \frac{{ – 29}}{{60}}\end{array}\)