Question

Calculați produsul extremilor din următoarele propoziții:
a) a/7=11/b
b) a/8=5/b
c) a/0,(3)=15/b
d) a/20=0,3(6)/9​

Answer 1

Răspuns:

Explicație pas cu pas:

a)

$\frac{a}{7} = \frac{11}{b}$

$a \times b = 7 \times 11 = \boxed{77}$

b)

$\frac{a}{8} = \frac{5}{b}$

$a \times b = 8 \times 5 = \boxed{40}$

c)

$\frac{a}{0,(3)} = \frac{15}{b}$

$a \times b = 15 \times 0,(3) = 15 \times \frac{3}{9} = \frac{45}{9} = \boxed{5}$

d)

$\frac{a}{20} = \frac{0,3(6)}{9}$

$a = \frac{0,3(6) \times 20}{9} = \frac{ \frac{36 - 3}{90} \times 20 }{9} = \frac{ \frac{ 33^{(3}}{90} \times 20 }{9}$

$= \frac{ \frac{11}{30} \times 20}{9} = \frac{ \frac{220}{30} }{9} = \frac{220}{30} \times \frac{1}{9} = \frac{ 220^{(10}}{270} = \boxed{\frac{22}{27}}$