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Giải Bài 54 trang 57 sách bài tập toán 7 tập 1 - Cánh diều

Cho tỉ lệ thức

𒈔Tổng 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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Đề bài

Cho tỉ lệ thức \(\dfrac{a}{b} = \dfrac{c}{d}\), hãy chứng tỏ mỗi tỉ lệ thức sau: a) \(\dfrac{{a + b}}{b} = \dfrac{{c + d}}{d}\);                                                          b) \(\dfrac{{a - b}}{b} = \dfrac{{c - d}}{d}\).

Phương pháp giải - Xem chi tiết

Ta chứng minh các tỉ lệ thức dựa vào việc cộng thêm vào hoặc trừ bớt đi một đại lượng tương ứng ở hai vế của tỉ lệ thức.

Lời giải chi tiết

a) Ta có: \(\dfrac{a}{b} = \dfrac{c}{d} \Rightarrow \dfrac{a}{b} + 1 = \dfrac{c}{d} + 1 \Rightarrow \dfrac{a}{b} + \dfrac{b}{b} = \dfrac{c}{d} + \dfrac{d}{d}\) hay \(\dfrac{{a + b}}{b} = \dfrac{{c + d}}{d}\);                                                                                b) Ta có: \(\dfrac{a}{b} = \dfrac{c}{d} \Rightarrow \dfrac{a}{b} - 1 = \dfrac{c}{d} - 1 \Rightarrow \dfrac{a}{b} - \dfrac{b}{b} = \dfrac{c}{d} - \dfrac{d}{d}\) hay \(\dfrac{{a - b}}{b} = \dfrac{{c - d}}{d}\).

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