Giải câu 3 trang 49 toán VNEN 7 tập 1 .
a) Ta có: $\frac{a}{b}$ = $\frac{c}{d}$ $\Rightarrow$ $\frac{a}{c}$ = $\frac{b}{d}$ = $\frac{a + b}{c + d}$
Từ $\frac{b}{d}$ = $\frac{a + b}{c + d}$ $\Rightarrow$ $\frac{a + b}{b}$ = $\frac{c + d}{d}$.
b) Ta có: $\frac{a}{b}$ = $\frac{c}{d}$ $\Rightarrow$ $\frac{a}{c}$ = $\frac{b}{d}$ = $\frac{a - b}{c - d}$
Từ $\frac{b}{d}$ = $\frac{a - b}{c - d}$ $\Rightarrow$ $\frac{a - b}{b}$ = $\frac{c - d}{d}$.
c) Ta có: $\frac{a}{b}$ = $\frac{c}{d}$ $\Rightarrow$ $\frac{d}{b}$ = $\frac{c}{a}$ = $\frac{c + d}{a + b}$
Từ $\frac{c}{a}$ = $\frac{c + d}{a + b}$ $\Rightarrow$ $\frac{a + b}{a}$ = $\frac{c + d}{c}$.
d) Ta có: $\frac{a}{b}$ = $\frac{c}{d}$ $\Rightarrow$ $\frac{d}{b}$ = $\frac{c}{a}$ = $\frac{c - d}{a - b}$
Từ $\frac{c}{a}$ = $\frac{c - d}{a - b}$ $\Rightarrow$ $\frac{a - b}{a}$ = $\frac{c - d}{c}$.
e) Ta có: $\frac{a}{b}$ = $\frac{c}{d}$ $\Rightarrow$ $\frac{b}{d}$ = $\frac{a}{c}$ = $\frac{a + b}{c + d}$
Từ $\frac{a}{c}$ = $\frac{a + b}{c + d}$ $\Rightarrow$ $\frac{a}{a + b}$ = $\frac{c}{c + d}$.
f) Ta có: $\frac{a}{b}$ = $\frac{c}{d}$ $\Rightarrow$ $\frac{b}{d}$ = $\frac{a}{c}$ = $\frac{a - b}{c - d}$
Từ $\frac{a}{c}$ = $\frac{a - b}{c - d}$ $\Rightarrow$ $\frac{a}{a - b}$ = $\frac{c}{c - d}$.