Expand $\frac{10.2}{5}$ by multiplying both numerator and the denominator by $10$.
$$\frac{102}{50}\times 3.125-1.14+202$$
Reduce the fraction $\frac{102}{50}$ to lowest terms by extracting and canceling out $2$.
$$\frac{51}{25}\times 3.125-1.14+202$$
Convert decimal number $3.125$ to fraction $\frac{3125}{1000}$. Reduce the fraction $\frac{3125}{1000}$ to lowest terms by extracting and canceling out $125$.
$$\frac{51}{25}\times \frac{25}{8}-1.14+202$$
Multiply $\frac{51}{25}$ times $\frac{25}{8}$ by multiplying numerator times numerator and denominator times denominator.
$$\frac{51\times 25}{25\times 8}-1.14+202$$
Cancel out $25$ in both numerator and denominator.
$$\frac{51}{8}-1.14+202$$
Convert decimal number $1.14$ to fraction $\frac{114}{100}$. Reduce the fraction $\frac{114}{100}$ to lowest terms by extracting and canceling out $2$.
$$\frac{51}{8}-\frac{57}{50}+202$$
Least common multiple of $8$ and $50$ is $200$. Convert $\frac{51}{8}$ and $\frac{57}{50}$ to fractions with denominator $200$.
$$\frac{1275}{200}-\frac{228}{200}+202$$
Since $\frac{1275}{200}$ and $\frac{228}{200}$ have the same denominator, subtract them by subtracting their numerators.
$$\frac{1275-228}{200}+202$$
Subtract $228$ from $1275$ to get $1047$.
$$\frac{1047}{200}+202$$
Convert $202$ to fraction $\frac{40400}{200}$.
$$\frac{1047}{200}+\frac{40400}{200}$$
Since $\frac{1047}{200}$ and $\frac{40400}{200}$ have the same denominator, add them by adding their numerators.
