$$3 \frac{ 4 }{ 5 } \times (4 \frac{ 1 }{ 3 } -2 \frac{ 2 }{ 5 } )=3 \frac{ 4 }{ 5 } \times 4 \frac{ 1 }{ 3 } -3 \frac{ 4 }{ 5 } \times 2 \frac{ 2 }{ 3 }$$
$\text{false}$
$$3\left(3\times 5+4\right)\left(\frac{4\times 3+1}{3}-\frac{2\times 5+2}{5}\right)=\left(3\times 5+4\right)\left(4\times 3+1\right)-\left(3\times 5+4\right)\left(2\times 3+2\right)$$
$$3\left(15+4\right)\left(\frac{4\times 3+1}{3}-\frac{2\times 5+2}{5}\right)=\left(3\times 5+4\right)\left(4\times 3+1\right)-\left(3\times 5+4\right)\left(2\times 3+2\right)$$
$$3\times 19\left(\frac{4\times 3+1}{3}-\frac{2\times 5+2}{5}\right)=\left(3\times 5+4\right)\left(4\times 3+1\right)-\left(3\times 5+4\right)\left(2\times 3+2\right)$$
$$57\left(\frac{4\times 3+1}{3}-\frac{2\times 5+2}{5}\right)=\left(3\times 5+4\right)\left(4\times 3+1\right)-\left(3\times 5+4\right)\left(2\times 3+2\right)$$
$$57\left(\frac{12+1}{3}-\frac{2\times 5+2}{5}\right)=\left(3\times 5+4\right)\left(4\times 3+1\right)-\left(3\times 5+4\right)\left(2\times 3+2\right)$$
$$57\left(\frac{13}{3}-\frac{2\times 5+2}{5}\right)=\left(3\times 5+4\right)\left(4\times 3+1\right)-\left(3\times 5+4\right)\left(2\times 3+2\right)$$
$$57\left(\frac{13}{3}-\frac{10+2}{5}\right)=\left(3\times 5+4\right)\left(4\times 3+1\right)-\left(3\times 5+4\right)\left(2\times 3+2\right)$$
$$57\left(\frac{13}{3}-\frac{12}{5}\right)=\left(3\times 5+4\right)\left(4\times 3+1\right)-\left(3\times 5+4\right)\left(2\times 3+2\right)$$
$$57\left(\frac{65}{15}-\frac{36}{15}\right)=\left(3\times 5+4\right)\left(4\times 3+1\right)-\left(3\times 5+4\right)\left(2\times 3+2\right)$$
$$57\times \frac{65-36}{15}=\left(3\times 5+4\right)\left(4\times 3+1\right)-\left(3\times 5+4\right)\left(2\times 3+2\right)$$
$$57\times \frac{29}{15}=\left(3\times 5+4\right)\left(4\times 3+1\right)-\left(3\times 5+4\right)\left(2\times 3+2\right)$$
$$\frac{57\times 29}{15}=\left(3\times 5+4\right)\left(4\times 3+1\right)-\left(3\times 5+4\right)\left(2\times 3+2\right)$$
$$\frac{1653}{15}=\left(3\times 5+4\right)\left(4\times 3+1\right)-\left(3\times 5+4\right)\left(2\times 3+2\right)$$
$$\frac{551}{5}=\left(3\times 5+4\right)\left(4\times 3+1\right)-\left(3\times 5+4\right)\left(2\times 3+2\right)$$
$$\frac{551}{5}=\left(15+4\right)\left(4\times 3+1\right)-\left(3\times 5+4\right)\left(2\times 3+2\right)$$
$$\frac{551}{5}=19\left(4\times 3+1\right)-\left(3\times 5+4\right)\left(2\times 3+2\right)$$
$$\frac{551}{5}=19\left(12+1\right)-\left(3\times 5+4\right)\left(2\times 3+2\right)$$
$$\frac{551}{5}=19\times 13-\left(3\times 5+4\right)\left(2\times 3+2\right)$$
$$\frac{551}{5}=247-\left(3\times 5+4\right)\left(2\times 3+2\right)$$
$$\frac{551}{5}=247-\left(15+4\right)\left(2\times 3+2\right)$$
$$\frac{551}{5}=247-19\left(2\times 3+2\right)$$
$$\frac{551}{5}=247-19\left(6+2\right)$$
$$\frac{551}{5}=247-19\times 8$$
$$\frac{551}{5}=247-152$$
$$\frac{551}{5}=95$$
$$\frac{551}{5}=\frac{475}{5}$$
$$\text{false}$$
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