Question

5. Efectuați înmulțirea:
Dau coroana
​

Answer 1

$\displaystyle a)~\frac{2}{5} \cdot 2\frac{1}{2} =\frac{2}{5} \cdot \frac{2 \cdot 2+1}{2} =\frac{2}{5} \cdot \frac{4+1}{2} =\frac{\not2_1}{\not5_1} \cdot \frac{\not5_1}{\not2_1} =1$

$\displaystyle b)~\frac{5}{12} \cdot 1\frac{1}{5} =\frac{5}{12} \cdot \frac{1 \cdot 5+1}{5} =\frac{5}{12} \cdot \frac{5+1}{5} =\frac{_1\not5}{_2\not12} \cdot \frac{\not6_1}{\not5_1} =\frac{1}{2}$

$\displaystyle c)~10\frac{2}{3} \cdot \frac{3}{8} =\frac{10 \cdot 3+2}{3} \cdot \frac{3}{8} =\frac{30+2}{3} \cdot \frac{3}{8} =\frac{_4\not32}{_1\not3} \cdot \frac{\not3_1}{\not8_1} =4$

$\displaystyle d)~2\frac{1}{7} \cdot 2\frac{4}{5} =\frac{2\cdot 7+1}{7} \cdot \frac{2 \cdot 5+4}{5} =\frac{14+1}{7} \cdot \frac{10+4}{5} =\frac{_3\not15}{_1\not7} \cdot \frac{_2\not14}{\not5_1} =3\cdot 2=6$

$\displaystyle e)~4\frac{1}{5} \cdot 2\frac{1}{7} =\frac{4 \cdot 5+1}{5} \cdot \frac{2 \cdot 7+1}{7} =\frac{20+1}{5} \cdot \frac{14+1}{7} =\frac{_3\not21}{\not5_1} \cdot \frac{_3\not15}{\not7_1} =3\cdot3=9$

$\displaystyle f)~1\frac{1}{4} \cdot 1\frac{1}{10}= \frac{1\cdot4+1}{4} \cdot \frac{1\cdot10+1}{10}=\frac{4+1}{4} \cdot \frac{10+1}{10}=\frac{\not5_1}{4} \cdot \frac{11}{_2\not10} =\frac{11}{4\cdot2} =\frac{11}{8}$