Question

Determinati raportul a supra b daca :
a) 3a = 7b
b) 0,2 inmultit cu a = 0,8 inmultit cu b
c)3 supra 5 inmultit cu b = 1 supra 4 inmultit cu a
d) b = 0,(3) inmultit cu a
e) 1 intreg si 1 supra 5b - 0,(5) inmultit cu a= 7 supra 10b

Answer 1

$a)3a = 7b \: | \div b$

$\frac{3a}{b} = 7 | \times \frac{1}{3}$

$\frac{3a}{3b} = \frac{1 \times 7}{3}$

$\frac{a}{b} = \frac{7}{3}$

$b)0.2 \times a = 0.8 \times b$

$\frac{2}{10} \times a = \frac{8}{10} \times b$

$\frac{1}{5} \times a = \frac{4}{5} \times b$

$\frac{1 \times a}{5} = \frac{4 \times b}{5}$

$\frac{a}{5} = \frac{4b}{5}$

$a = 4b$

$\frac{a}{b} = 4$

$c) \frac{3}{5} \times b = \frac{1}{4} \times a$

$\frac{3b}{5} = \frac{a}{4}$

$3b \times 4 = 5 \times a$

$12b = 5a \: | \div b$

$\frac{5a}{b} = 12 \: | \times \frac{1}{5}$

$\frac{5a}{5b} = \frac{12}{5}$

$\frac{a}{b } = \frac{12}{5}$

$d)b = 0.(3) \times a$

$b = \frac{3}{9} \times a$

$b = \frac{1}{3} \times a$

$b = \frac{a}{3}$

$3b = a \: | \div b$

$\frac{a}{b} = 3$