Giải bài 27 trang 37 sách bài tập Toán 6 – Cánh Diều Tập 2

Đề bài

Tính các tổng sau (tính hợp lí nếu có thể):

a) $\frac{7}{{ - 27}} + \frac{{ - 8}}{{27}}$

b) $\frac{6}{{13}} + \frac{{ - 17}}{{39}}$

c) $\frac{{ - 17}}{{13}} + \frac{{25}}{{101}} + \frac{4}{{13}}$

d) $\frac{{ - 13}}{7} + \frac{3}{5} + \frac{{ - 1}}{7}$

e) $\frac{{ - 5}}{9} + \frac{8}{{15}} + \frac{4}{{ - 9}} + \frac{7}{{15}}$

Lời giải chi tiết

a) $\frac{7}{{ - 27}} + \frac{{ - 8}}{{27}} = \frac{{ - 7}}{{27}} + \frac{{ - 8}}{{27}} = \frac{{( - 7) + ( - 8)}}{{27}} = \frac{{ - 15}}{{27}} =- \frac{5}{9}$

b) $\frac{6}{{13}} + \frac{{ - 17}}{{39}} = \frac{{18}}{{39}} + \frac{{ - 17}}{{39}} = \frac{{18 + ( - 17)}}{{39}} = \frac{1}{{39}}$

c)

 $\begin{array}{l}\frac{{ - 17}}{{13}} + \frac{{25}}{{101}} + \frac{4}{{13}} = \left( {\frac{{ - 17}}{{13}} + \frac{4}{{13}}} \right) + \frac{{25}}{{101}} = \frac{{ - 17 + 4}}{{13}} + \frac{{25}}{{101}}\\ = \frac{{ - 13}}{{13}} + \frac{{25}}{{101}} =  - 1 + \frac{{25}}{{101}} = \frac{{ - 101}}{{101}} + \frac{{25}}{{101}} = \frac{{ - 101 + 25}}{{101}} = \frac{{ - 76}}{{101}}\end{array}$

d)

 $\begin{array}{l}\frac{{ - 13}}{7} + \frac{3}{5} + \frac{{ - 1}}{7} = \left( {\frac{{ - 13}}{7} + \frac{{ - 1}}{7}} \right) + \frac{3}{5} = \frac{{ - 13 + ( - 1)}}{7} + \frac{3}{5}\\ = \frac{{ - 14}}{7} + \frac{3}{5} =  - 2 + \frac{3}{5} = \frac{{ - 10}}{5} + \frac{3}{5} = \frac{{ - 7}}{5}\end{array}$

e)

 $\begin{array}{l}\frac{{ - 5}}{9} + \frac{8}{{15}} + \frac{4}{{ - 9}} + \frac{7}{{15}} = \left( {\frac{{ - 5}}{9} + \frac{4}{{ - 9}}} \right) + \left( {\frac{7}{{15}} + \frac{8}{{15}}} \right)\\ = \left( {\frac{{ - 5}}{9} + \frac{{ - 4}}{9}} \right) + \frac{{15}}{{15}} = \frac{{ - 9}}{9} + \frac{{15}}{{15}} =  - 1 + 1 = 0\end{array}$