$$\frac { 12 } { 5 } \div \frac { 26 } { 15 } = \frac { 26 } { 15 } \div \frac { 12 } { 5 } \quad ( 15 \times 6 )$$
$\text{false}$
$$\frac{12}{5}\times \frac{15}{26}=\frac{\frac{26}{15}}{\frac{12}{5}}\times 15\times 6$$
$$\frac{12\times 15}{5\times 26}=\frac{\frac{26}{15}}{\frac{12}{5}}\times 15\times 6$$
$$\frac{180}{130}=\frac{\frac{26}{15}}{\frac{12}{5}}\times 15\times 6$$
$$\frac{18}{13}=\frac{\frac{26}{15}}{\frac{12}{5}}\times 15\times 6$$
$$\frac{18}{13}=\frac{26}{15}\times \frac{5}{12}\times 15\times 6$$
$$\frac{18}{13}=\frac{26\times 5}{15\times 12}\times 15\times 6$$
$$\frac{18}{13}=\frac{130}{180}\times 15\times 6$$
$$\frac{18}{13}=\frac{13}{18}\times 15\times 6$$
$$\frac{18}{13}=\frac{13\times 15}{18}\times 6$$
$$\frac{18}{13}=\frac{195}{18}\times 6$$
$$\frac{18}{13}=\frac{65}{6}\times 6$$
$$\frac{18}{13}=65$$
$$\frac{18}{13}=\frac{845}{13}$$
$$\text{false}$$
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