Hallo ich bräuchte Hilfe bei folgenden Aufgaben

1. 4/15x2 1/7=

2. 14 21/27x2 5/38x1/42=

3. (3 4/15:7/8)x39/56=

4. 3 1/2x 2 3/7-2 5/8:3/4+2/3=

5. 3/4x4+5/8x3/9+27 1/2:16/17-4 1/6:2/9=

zu 1.

\(2\frac{1}{7}={\large \color{blue}\frac{7\cdot 2+1}{7}}=\frac{15}{7}\)

2.

\(\color{red}14\frac{21}{27} \times 2 \frac{5}{38}\times\frac{1}{42}\\ =\frac{14\times27+21}{27}\times\frac{2\times 38+5}{38}\times\frac{1}{42}\\ =\frac{399}{27}\times\frac{81}{38}\times\frac{1}{42}\\ =\frac{3\cdot7\cdot 19}{3^3} \times \frac{3^4}{2 \cdot 19} \times \frac{1}{2\cdot 3\cdot 7}\\ =\frac{3^5\cdot 7\cdot 19}{2^2\cdot 3^4\cdot7\cdot19}=\frac{3}{2^2}\\ \color{blue} =\frac{3}{4}\)

3.

\(\color{red}(3\frac{4}{15}:\frac{7}{8})\times\frac{39}{56}\\ =\frac{49}{15}\times\frac{8}{7}\times\frac{39}{56}\\ =\frac{7^2}{3\cdot 5}\times \frac{2^3}{7}\times \frac{3\cdot 13}{2^3\cdot 7}=\frac{13}{5}\\ \color{blue}=2\frac{3}{5}\)

4.

\({\color{red}3\frac{1}{2}\times 2\frac{3}{7}-2\frac{5}{8}:\frac{3}{4}+\frac{2}{3}}\\ =\frac{2\cdot 3+1}{2} \times \frac{2\cdot 7+3}{7}-\frac{2\cdot 8+5}{8} \times \frac{4}{3} +\frac{2}{3}\\ =\frac{7}{2} \times \frac{17}{7}-\frac{3\cdot 7}{2^3} \times \frac{2^2}{3}+\frac{2}{3} \\ =\frac{17}{2}-\frac{7}{2} +\frac{2}{3} \\ \color{blue}=5\frac{2}{3}\)

5.

\(\color{red}\frac{3}{4}\times 4+\frac{5}{8}\times\frac{3}{9}+27\frac{1}{2}:\frac{16}{17}-4\frac{1}{6}:\frac{2}{9}\\ =3+\frac{5}{24}+\frac{55}{2}\times\frac{17}{16}-\frac{25}{6}\times\frac{9}{2}\\ =\frac{144+10}{48}+\frac{935}{32}-\frac{225}{12}\\ =\frac{308}{96}+\frac{2805}{96} -\frac{1800}{96}\\ =\frac{1313}{96}\\ \color{blue}=13\frac{65}{96}\)

Habe mal nachgerechnet. Natürlich stimmt alles.

  !