Question

[giang nguyen]

Từ tỉ lệ thức \(\frac{a}{b}=\frac{c}{d}\). Hãy suy ra các tỉ lệ thức:

a,   \(\frac{a+b}{b}=\frac{c+d}{d}\)b,\(\frac{a}{a+b}=\frac{c}{c+d}\)

Answer 1

[Le Thi Khanh Huyen]

a) \(\frac{a}{b}=\frac{c}{d}\)

\(\frac{a}{b}+1=\frac{c}{d}+1\)

\(\frac{a}{b}+\frac{b}{b}=\frac{c}{d}+\frac{d}{d}\)

\(\frac{a+b}{b}=\frac{c+d}{d}\)

Vậy \(\frac{a+b}{b}=\frac{c+d}{d}\).

b) \(\frac{a}{b}=\frac{c}{d}\)

\(\Rightarrow\frac{b}{a}=\frac{d}{c}\)

\(\frac{b}{a}+1=\frac{d}{c}+1\)

\(\frac{b}{a}+\frac{a}{a}=\frac{d}{c}+\frac{c}{c}\)

\(\frac{a+b}{a}=\frac{c+d}{c}\)

\(\Rightarrow\frac{a}{a+b}=\frac{c}{c+d}\)

Vậy \(\frac{a}{a+b}=\frac{c}{c+d}\)

Answer 2

[Phan Thanh Tịnh]

a) \(\frac{a}{b}=\frac{c}{d}\Rightarrow\frac{a}{b}+1=\frac{c}{d}+1\Leftrightarrow\frac{a+b}{b}=\frac{c+d}{d}\)

b) \(\frac{a}{b}=\frac{c}{d}\Rightarrow\frac{b}{a}=\frac{d}{c}\Rightarrow\frac{b}{a}+1=\frac{d}{c}+1\Leftrightarrow\frac{a+b}{a}=\frac{c+d}{c}\Rightarrow\frac{a}{a+b}=\)\(\frac{c}{c+d}\)