Bài 4: Thứ tự thực hiện các phép tính. Quy tắc chuyển vế

Chương 1 – Bài 4: Thứ tự thực hiện các phép tính. Quy tắc chuyển vế trang 18 sách bài tập toán lớp 7 tập 1 NXB Kết nối tri thức với cuộc sống.

1.27. Tính giá trị của biểu thức sau khi bỏ dấu ngoặc:

a) \(A=(5,1-3,4)-(-3,4+5,1);\)

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

Giải

a) \(A=(5,1-3,4)-(-3,4+5,1)\)

\(A=5,1-3,4+3,4-5,1\)

\(A=(5,1-5,1)+(-3,4+3,4)\)

\(A=0+0=0.\)

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

\(D=-\displaystyle\frac{5}{7}-\displaystyle\frac{7}{9}+\displaystyle\frac{7}{9}-\displaystyle\frac{2}{7}\)

\(D=\left(-\displaystyle\frac{5}{7}-\displaystyle\frac{2}{7}\right)+\left(\displaystyle\frac{7}{9}-\displaystyle\frac{7}{9}\right)\)

\(D=-1+0=-1.\)

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1.28. Tìm x, biết:

a) \(-x+\displaystyle\frac{7}{4}=\displaystyle\frac{6}{5}-\displaystyle\frac{3}{4};\)

b) \(1-2x=\displaystyle\frac{9}{8}+\displaystyle\frac{7}{5}:\displaystyle\frac{2}{5}.\)

Giải

a) \(-x+\displaystyle\frac{7}{4}=\displaystyle\frac{6}{5}-\displaystyle\frac{3}{4}\)

\(-x=\displaystyle\frac{6}{5}-\displaystyle\frac{3}{4}-\displaystyle\frac{7}{4}\)

\(-x=\displaystyle\frac{24}{20}-\displaystyle\frac{15}{20}-\displaystyle\frac{35}{20}\)

\(-x=\displaystyle\frac{-26}{20}=\displaystyle\frac{-13}{10}\)

\(x=\displaystyle\frac{13}{10}.\)

b) \(1-2x=\displaystyle\frac{9}{8}+\displaystyle\frac{7}{5}:\displaystyle\frac{2}{5}\)

\(1-2x=\displaystyle\frac{9}{8}+\displaystyle\frac{7}{5}.\displaystyle\frac{5}{2}\)

\(1-2x=\displaystyle\frac{9}{8}+\displaystyle\frac{7}{2}\)

\(1-2x=\displaystyle\frac{9}{8}+\displaystyle\frac{28}{8}\)

\(1-2x=\displaystyle\frac{37}{8}\)

\(2x=1-\displaystyle\frac{37}{8}\)

\(2x=\displaystyle\frac{8}{8}-\displaystyle\frac{37}{8}\)

\(x=\displaystyle\frac{-29}{8}:2\)

\(x=\displaystyle\frac{-29}{8}.\displaystyle\frac{1}{2}=\displaystyle\frac{-29}{16}.\)

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1.29. Tính: \(A= \left[\left(\displaystyle\frac{1}{81}-\displaystyle\frac{3}{162}\right).\displaystyle\frac{81}{17}+\displaystyle\frac{35}{34}\right]\) \(:\left[\left(\displaystyle\frac{9}{51}+\displaystyle\frac{7}{102}\right).\displaystyle\frac{102}{5}+2017\right].\)

Giải

\(A= \left[\left(\displaystyle\frac{1}{81}-\displaystyle\frac{3}{162}\right).\displaystyle\frac{81}{17}+\displaystyle\frac{35}{34}\right]\) \(:\left[\left(\displaystyle\frac{9}{51}+\displaystyle\frac{7}{102}\right).\displaystyle\frac{102}{5}+2017\right]\)

\(A= \left[\left(\displaystyle\frac{1}{81}.\displaystyle\frac{81}{17}-\displaystyle\frac{3}{162}.\displaystyle\frac{81}{17}\right)+\displaystyle\frac{35}{34}\right]\) \(:\left[\left(\displaystyle\frac{9}{51}.\displaystyle\frac{102}{5}+\displaystyle\frac{7}{102}.\displaystyle\frac{102}{5}\right)+2017\right]\)

\(A= \left[\displaystyle\frac{1}{17}-\displaystyle\frac{3}{34}+\displaystyle\frac{35}{34}\right]:\left[\displaystyle\frac{18}{5}+\displaystyle\frac{7}{5}+2017\right]\)

\(A= \left(\displaystyle\frac{2}{34}-\displaystyle\frac{3}{34}+\displaystyle\frac{35}{34}\right):\left(\displaystyle\frac{25}{5}+2017\right)\)

\(A= \displaystyle\frac{34}{34}:(5+2017)=1:2022=\displaystyle\frac{1}{2022}.\)

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1.30. Tìm x, biết:

a) \((0,5)^2+2.x=(0,7)^2;\)

b) \(x-\left(\displaystyle\frac{1}{3}+\displaystyle\frac{1}{5}-\displaystyle\frac{1}{7}\right)=\displaystyle\frac{1}{7}-\displaystyle\frac{1}{3}.\)

Giải

a) \((0,5)^2+2.x=(0,7)^2\)

\(2.x=(0,7)^2-(0,5)^2\)

\(2.x=0,49-0,25\)

\(2.x = 0,24\)

\(x = 0,24 : 2\)

\(x = 0,12.\)

b) \(x-\left(\displaystyle\frac{1}{3}+\displaystyle\frac{1}{5}-\displaystyle\frac{1}{7}\right)=\displaystyle\frac{1}{7}-\displaystyle\frac{1}{3}\)

\(x-\displaystyle\frac{1}{3}-\displaystyle\frac{1}{5}+\displaystyle\frac{1}{7}=\displaystyle\frac{1}{7}-\displaystyle\frac{1}{3}\)

\(x=\displaystyle\frac{1}{7}-\displaystyle\frac{1}{3}-\displaystyle\frac{1}{7}+\displaystyle\frac{1}{5}+\displaystyle\frac{1}{3}\)

\(x=\left(\displaystyle\frac{1}{7}-\displaystyle\frac{1}{7}\right)+\left(\displaystyle\frac{1}{3}-\displaystyle\frac{1}{3}\right)+\displaystyle\frac{1}{5}\)

\(x=0+0+\displaystyle\frac{1}{5}\)

\(x=\displaystyle\frac{1}{5}.\)

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1.31. Hãy viết một đẳng thức để mô tả tình trạng khi cân thăng bằng rồi tính khối lượng của quả bí đỏ (H.14).