Giải bài 4 trang 26 SGK Toán 7 tập 1 – Cánh diều

Đề bài

Tính một cách hợp lí:

a) \(\frac{4}{{15}} – \left( {2,9 – \frac{{11}}{{15}}} \right)\);

b) \(( – 36,75) + \left( {\frac{{37}}{{10}} – 63,25} \right) – ( – 6,3)\);

c) \(6,5 + \left( { – \frac{{10}}{{17}}} \right) – \left( { – \frac{7}{2}} \right) – \frac{7}{{17}}\);

d) \(( – 39,1) \cdot \frac{{13}}{{25}} – 60,9 \cdot \frac{{13}}{{25}}\).

Lời giải chi tiết

a)

 \(\begin{array}{l}\frac{4}{{15}} – \left( {2,9 – \frac{{11}}{{15}}} \right)\\ = \frac{4}{{15}} – 2,9 + \frac{{11}}{{15}}\\ = \left( {\frac{4}{{15}} + \frac{{11}}{{15}}} \right) – 2,9\\=\frac{15}{15}-2,9 \\= 1 – 2,9 =  – 1,9\end{array}\)

b)

\(\begin{array}{l}( – 36,75) + \left( {\frac{{37}}{{10}} – 63,25} \right) – ( – 6,3)\\ = ( – 36,75) + 3,7 – 63,25 + 6,3\\ = \left( { – 36,75 – 63,25} \right) + \left( {3,7 + 6,3} \right)\\ =  – 100 + 10 =  – 90\end{array}\)

c)

\(\begin{array}{l}6,5 + \left( { – \frac{{10}}{{17}}} \right) – \left( { – \frac{7}{2}} \right) – \frac{7}{{17}}\\ = \frac{{65}}{{10}} – \frac{{10}}{{17}} + \frac{7}{2} – \frac{7}{{17}}\\ = \left( {\frac{{65}}{{10}} + \frac{7}{2}} \right) – \left( {\frac{{10}}{{17}} + \frac{7}{{17}}} \right)\\ = \left( {\frac{{65}}{{10}} + \frac{{35}}{{10}}} \right) – \frac{17}{17}\\ = \frac{100}{10}-1\\=10 – 1 = 9\end{array}\)

d)

\(\begin{array}{l}( – 39,1) \cdot \frac{{13}}{{25}} – 60,9 \cdot \frac{{13}}{{25}}\\ = \frac{{13}}{{25}}.\left( { – 39,1 – 60,9} \right)\\ = \frac{{13}}{{25}}.\left( { – 100} \right)\\ =  – 52\end{array}\).