Giải Toán 7 (t1) [Chương 1] Bài 4 – THỨ TỰ THỰC HIỆN CÁC PHÉP TÍNH. QUY TẮC CHUYỂN VẾ. (bộ Kết nối tri thức với cuộc sống)

Giải

$$\mathbf{a)}\; \left(\frac{2}{3} + \frac{1}{6}\right) : \frac{5}{4} + \left(\frac{1}{4} + \frac{3}{8}\right) : \frac{5}{2}$$

$$= \left(\frac{4}{6} + \frac{1}{6} \right) : \frac{5}{4} + \left(\frac{2}{8} + \frac{3}{8}\right) : \frac{5}{2}$$

$$= \frac{5}{6} : \frac{5}{4} + \frac{5}{8} : \frac{5}{2}$$

$$= \frac{5}{6} \cdot \frac{4}{5} + \frac{5}{8} \cdot \frac{2}{5}$$

$$= \frac{2}{3} + \frac{1}{4}$$

$$= \frac{8}{12} + \frac{3}{12}$$

$$= \frac{11}{12}.$$

$$\mathbf{b)}\; \frac{5}{9} : \left(\frac{1}{11} – \frac{5}{22}\right) + \frac{7}{4} \cdot \left(\frac{1}{14} – \frac{2}{7}\right)$$

$$= \frac{5}{9} : \left(\frac{2}{22} – \frac{5}{22}\right) + \frac{7}{4} \cdot \left(\frac{1}{14} – \frac{4}{14}\right)$$

$$= \frac{5}{9} : \frac{-3}{22} + \frac{7}{4} \cdot \frac{-3}{14}$$

$$= \frac{5}{9} \cdot \frac{-22}{3} + \frac{-3}{8}$$

$$= \frac{-110}{27} – \frac{3}{8}$$

$$= \frac{-880}{216} – \frac{81}{216}$$

$$= \frac{-961}{216}.$$

Giải

$$\mathbf{a)}\; x + 7,25 = 15,75$$

$$x = 15,75 – 7,25$$

$$x = 8,5.$$

$$\mathbf{b)}\; \left(-\frac{1}{3}\right) – x = \frac{17}{6}$$

$$\left(-\frac{1}{3}\right) – \frac{17}{6} = x$$

$$x = \left(-\frac{1}{3}\right) – \frac{17}{6}$$

$$x = \frac{-2}{6} – \frac{17}{6}$$

$$x = \frac{-19}{6}.$$

Giải

Gọi $x$ là khối lượng thịt. Khi đó:

$$x + 0,5 + 0,125 + 0,04 = 0,8$$

$$x = 0,8 – 0,5 – 0,125 – 0,04$$

$$x = 0,135$$

Vậy khối lượng thịt trong mỗi cái bánh là khoảng $0,135$ kg.

Giải

$$\mathbf{a)}\; x + 0,25 = \frac{1}{2}$$

$$x = \frac{1}{2} – 0,25$$

$$x = 0,5 – 0,25$$

$$x = 0,25.$$

$$\mathbf{b)}\; x – \left(-\frac{5}{7}\right) = \frac{9}{14}$$

$$x = \frac{9}{14} + \left(-\frac{5}{7}\right)$$

$$x = \frac{9}{14} – \frac{5}{7}$$

$$x = \frac{9}{14} – \frac{10}{14}$$

$$x = \frac{-1}{14}.$$

Giải

$$\mathbf{a)}\; x – \left(\frac{5}{4} – \frac{7}{5}\right) = \frac{9}{20}$$

$$x – \left(\frac{25}{20} – \frac{28}{20}\right) = \frac{9}{20}$$

$$x – \frac{-3}{20} = \frac{9}{20}$$

$$x = \frac{9}{20} + \frac{-3}{20}$$

$$x = \frac{9}{20} – \frac{3}{20}$$

$$x = \frac{6}{20}$$

$$x = \frac{3}{10}.$$

$$\mathbf{b)}\; 9 – x = \frac{8}{7} – \left(-\frac{7}{8}\right)$$

$$9 – x = \frac{8}{7} + \frac{7}{8}$$

$$9 – x = \frac{64}{56} + \frac{49}{56}$$

$$9 – x = \frac{113}{56}$$

$$9 – \frac{113}{56} = x$$

$$x = 9 – \frac{113}{56}$$

$$x = \frac{504}{56} – \frac{113}{56}$$

$$x = \frac{391}{56}.$$

Giải

$$\mathbf{a)}\; -1,2 +(-0,8) + 0,25 + 5,75 – 2021$$

$$= [(-1,2) + (-0,8)] + (0,25 + 5,75) – 2021$$

$$= (-2) + 6 – 2021$$

$$= 4 – 2021$$

$$= -2017.$$

$$\mathbf{b)}\; -0,1 + \frac{16}{9} + 11,1 + \frac{-20}{9}$$

$$= -0,1 + 11,1 + \frac{16}{9} + \frac{-20}{9}$$

$$= (-0,1 + 11,1) + \left(\frac{16}{9} + \frac{-20}{9}\right)$$

$$= 11 + \frac{-4}{9}$$

$$= \frac{99}{9} + \frac{-4}{9}$$

$$= \frac{95}{9}$$

Giải

$$\mathbf{a)}\; \frac{17}{11} – \left(\frac{6}{5} – \frac{16}{11}\right) + \frac{26}{5}$$

$$= \frac{17}{11} – \frac{6}{5} + \frac{16}{11} + \frac{26}{5}$$

$$= \frac{17}{11} + \frac{16}{11} + \frac{26}{5} – \frac{6}{5}$$

$$= \left(\frac{17}{11} + \frac{16}{11}\right) + \left(\frac{26}{5} – \frac{6}{5}\right)$$

$$= \frac{33}{11} + \frac{20}{5}$$

$$= 3 + 4$$

$$= 7.$$

$$\mathbf{b)}\; \frac{39}{5} + \left(\frac{9}{4} – \frac{9}{5}\right) – \left(\frac{5}{4} + \frac{6}{7}\right)$$

$$= \frac{39}{5} + \frac{9}{4} – \frac{9}{5} – \frac{5}{4} – \frac{6}{7}$$

$$= \frac{39}{5} – \frac{9}{5} + \frac{9}{4} – \frac{5}{4} – \frac{6}{7}$$

$$= \left(\frac{39}{5} – \frac{9}{5}\right) + \left(\frac{9}{4} – \frac{5}{4}\right) – \frac{6}{7}$$

$$= \frac{30}{5} + \frac{4}{4} – \frac{6}{7}$$

$$= 6 + 1 – \frac{6}{7}$$

$$= 7 – \frac{6}{7}$$

$$= \frac{49}{7} – \frac{6}{7}$$

$$= \frac{43}{7}.$$

Giải

Gọi $x$ là số cốc bột cần tìm. Ta có:

$$x + 1\frac{1}{2} = 2\frac{3}{4}$$

$$x = 2\frac{3}{4} – 1\frac{1}{2}$$

$$x = \frac{11}{4} – \frac{3}{2}$$

$$x = \frac{11}{4} – \frac{6}{4}$$

$$x = \frac{5}{4}$$

$$x = 1\frac{1}{4}.$$

Vậy Lan cần thêm $1\frac{1}{4}$ cốc bột nữa để làm được một cái bánh.

Chú ý

Không cần đổi hỗn số thành phân số, ta vẫn có thể tính được giá trị của $x$ như sau:

$$x = 2\frac{3}{4} – 1\frac{1}{2}$$

$$x = \left(2 + \frac{3}{4}\right) – \left(1 + \frac{1}{2}\right)$$

$$x = 2 + \frac{3}{4} – 1 – \frac{1}{2}$$

$$x = (2 – 1) + \left(\frac{3}{4} – \frac{1}{2}\right)$$

$$x = 1 + \frac{1}{4}$$

$$x = 1\frac{1}{4}.$$