Giải Bài 41 trang 54 sách bài tập toán 7 tập 1 - Cánh diều

Đề bài

Tìm số x trong mỗi tỉ lệ thức sau:

a) \(\dfrac{x}{{26}} = \dfrac{{21}}{{39}}\);

b) \(4:5,2 = x:\dfrac{2}{7}\);

c) \(\dfrac{{1,25}}{{0,1x}} = \dfrac{{1,35}}{{0,2}}\);

d*) \((3x - 2):\dfrac{7}{2} = \dfrac{4}{{21}}:\dfrac{1}{{12}}\).

Lời giải chi tiết

a) \(\dfrac{x}{{26}} = \dfrac{{21}}{{39}}\)

\(\begin{array}{l}39.x = 21.26\\39.x = 546\\x = 546:39\\x = 14\end{array}\)

Vậy \(x = 14\).

b) \(4:5,2 = x:\dfrac{2}{7}\)

\(\begin{array}{l}4:\dfrac{{26}}{5} = x:\dfrac{2}{7}\\x:\dfrac{2}{7} = 4.\dfrac{5}{{26}}\\x:\dfrac{2}{7} = \dfrac{{10}}{{13}}\\x = \dfrac{{10}}{{13}}.\dfrac{2}{7}\\x = \dfrac{{20}}{{91}}\end{array}\)

Vậy \(x = \dfrac{{20}}{{91}}\).

c) \(\dfrac{{1,25}}{{0,1x}} = \dfrac{{1,35}}{{0,2}}\)

\(\begin{array}{l}1,25.0,2 = 1,35.0,1x\\0,25 = 0,135x\\x = 0,25:0,135\\x = \dfrac{{50}}{{27}}\end{array}\)

Vậy \(x = \dfrac{{50}}{{27}}\).

d*) \((3x - 2):\dfrac{7}{2} = \dfrac{4}{{21}}:\dfrac{1}{{12}}\)

\(\begin{array}{l}(3x - 2).\dfrac{2}{7} = \dfrac{4}{{21}}.12\\\dfrac{{2.(3x - 2)}}{7} = \dfrac{{16}}{7}\\ \text{Suy ra }2.(3x - 2) = 16\\3x - 2 = 16:2 = 8\\3x = 8 + 2 = 10\\x = 10:3\\x = \dfrac{{10}}{3}\end{array}\)

Vậy \(x = \dfrac{{10}}{3}\).