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Giải mục I trang 12, 13, 14 SGK Toán 7 tập 1 - Cánh diều

Thực hiện các phép tính sau:...Tính:...Tính một cách hợp lí:

🍎Tổng hợp đề thi học kì 2 lớp 7 tất cả các môn - Cánh diều

Toán - Văn - Anh - Khoa học tự nhiên...
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HĐ 1

Hoạt động 1 

Thực hiện các phép tính sau: a)\(\frac{{ - 2}}{5} + \frac{3}{7}\);            b)\(0,123 - 0,234\).

Phương pháp giải:

a) Quy đồng mẫu hai phân số rồi thực hiện phép cộng hai phân số.            b) Áp dụng quy tắc trừ hai số thập phân.

Lời giải chi tiết:

a)\(\frac{{ - 2}}{5} + \frac{3}{7} = \frac{{ - 14}}{{35}} + \frac{{15}}{{35}} = \frac{1}{{35}}\)            b)\(0,123 - 0,234 =  - \left( {0,234 - 0,123} \right) =  - 0,111.\)

LT - VD 1

Luyện tập vận dụng 1

Tính: a)\(\frac{5}{7} - \left( { - 3,9} \right)\); b)\(\left( { - 3,25} \right) + 4\frac{3}{4}\).

Phương pháp giải:

-          Đưa hai số về phép cộng, trừ hai phân số. -          Quy đồng mẫu hai phân số rồi thực hiện phép cộng hai phân số.           

Lời giải chi tiết:

a)\(\frac{5}{7} - \left( { - 3,9} \right) = \frac{5}{7} + 3,9 = \frac{5}{7} + \frac{{39}}{{10}} = \frac{{50}}{{70}} + \frac{{273}}{{70}} = \frac{{323}}{{70}}\); b)\(\left( { - 3,25} \right) + 4\frac{3}{4} =  - \frac{{13}}{4} + \frac{{19}}{4} = \frac{6}{4} = \frac{3}{2}.\)

HĐ 2

Hoạt động 2

Nêu tính chất của phép cộng các số nguyên

Phương pháp giải:

Nhớ lại tính chất của phép cộng các số nguyên đã học.

Lời giải chi tiết:

Tính chất giao hoán: \(a + b = b + a.\) Tính chất kết hợp: \((a + b) + c = a + (b + c).\) Cộng với số 0: \(a + 0 = 0 + a = a\). Cộng với số đối: \(a + ( - a) = 0.\)

LT - VD 2

Luyện tập vận dụng 2

Tính một cách hợp lí: a)\(\left( { - 0,4} \right) + \frac{3}{8} + \left( { - 0,6} \right)\); b)\(\frac{4}{5} - 1,8 + 0,375 + \frac{5}{8}\).

Phương pháp giải:

Sử dụng tính chất giao hoán của các số hữu tỉ.

Lời giải chi tiết:

a)\(\left( { - 0,4} \right) + \frac{3}{8} + \left( { - 0,6} \right) = \left[ {\left( { - 0,4} \right) + \left( { - 0,6} \right)} \right] + \frac{3}{8} =  - 1 + \frac{3}{8} = \frac{{ - 5}}{8}\). b) \(\frac{4}{5} - 1,8 + 0,375 + \frac{5}{8} = (0,8 - 1,8) + (0,375 + 0,625) = ( - 1) + 1 = 0\)

HĐ 3

Hoạt động 3

a) Tìm số nguyên x, biết: \(x + 5 =  - 3.\) b) Trong tập hợp các số nguyên, nêu quy tắc tìm một số hạng của tổng hai số khi biết tổng và số hạng còn lại.

Phương pháp giải:

a) Áp dụng quy tắc tìm một số hạng của tổng hai số khi biết tổng và số hạng còn lại. b) Nhắc lại quy tắc đã được học

Lời giải chi tiết:

a)  \(\begin{array}{l}x + 5 =  - 3\\x =  - 3 - 5\\x =  - 8.\end{array}\) Vậy x=-8. b) Quy tắc: Muốn tìm một số hạng của tổng hai số khi biết tổng và số hạng còn lại, ta lấy tổng trừ đi số hạng kia.

LT - VD 3

Luyện tập vận dụng 3

Tìm x, biết: a)\(x - \left( { - \frac{7}{9}} \right) =  - \frac{5}{6}\); b)\(\frac{{15}}{{ - 4}} - x = 0,3\).

Phương pháp giải:

Sử dụng quy tắc chuyển vế.

Lời giải chi tiết:

a) \(\begin{array}{l}x - \left( { - \frac{7}{9}} \right) =  - \frac{5}{6}\\x + \frac{7}{9} =  - \frac{5}{6}\\x =  - \frac{5}{6} - \frac{7}{9}\\x =  - \frac{{15}}{{18}} - \frac{{14}}{{18}}\\x = \frac{{ - 29}}{{18}}\end{array}\) Vậy \(x = \frac{{ - 29}}{{18}}\). b) \(\begin{array}{l}\frac{{15}}{{ - 4}} - x = 0,3\\x = \frac{{15}}{{ - 4}} - 0,3\\x =  - 3,75 - 0,3\\x =  - 4,05\end{array}\) Vậy \(x =  - 4,05\).

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