Solve for: 709\times 25

Expression: $709\times 25$

Multiply the top number by the bolded digit of the bottom number

$\begin{matrix}\:\:&\bold{7}&\bold{0}&\bold{9}\\\times &\:\:&2&\bold{5}\end{matrix}$

Mutliply the bold numbers $9\times 5=45$

$\frac{\begin{matrix}\:\:&\:\:&4&\:\:\\\:\:&7&0&\bold{9}\\\times &\:\:&2&\bold{5}\end{matrix}}{\begin{matrix}\:\:&\:\:&\:\:&5\end{matrix}}$

Add the carried number to the multiplication $4+0\times 5=4$

$\frac{\begin{matrix}\:\:&\:\:&\bold{4}&\:\:\\\:\:&7&\bold{0}&9\\\times &\:\:&2&\bold{5}\end{matrix}}{\begin{matrix}\:\:&\:\:&4&5\end{matrix}}$

Mutliply the bold numbers $7\times 5=35$

$\frac{\begin{matrix}\:\:&3&\:\:&4&\:\:\\\:\:&\:\:&\bold{7}&0&9\\\times &\:\:&\:\:&2&\bold{5}\end{matrix}}{\begin{matrix}\:\:&\:\:&5&4&5\end{matrix}}$

Add the carried digit, $3$, to the result

$\frac{\begin{matrix}\:\:&3&\:\:&4&\:\:\\\:\:&\:\:&7&0&9\\\times &\:\:&\:\:&2&5\end{matrix}}{\begin{matrix}\:\:&3&5&4&5\end{matrix}}$

Multiply the top number by the bolded digit of the bottom number

$\frac{\begin{matrix}\:\:&\:\:&\bold{7}&\bold{0}&\bold{9}\\\:\:&\times &\:\:&\bold{2}&5\end{matrix}}{\begin{matrix}\:\:&3&5&4&5\end{matrix}}$

Mutliply the bold numbers $9\times 2=18$

$\frac{\begin{matrix}\:\:&\:\:&\:\:&1&\:\:\\\:\:&\:\:&7&0&\bold{9}\\\:\:&\times &\:\:&\bold{2}&5\end{matrix}}{\begin{matrix}\:\:&3&5&4&5\\\:\:&\:\:&\:\:&8&\:\:\end{matrix}}$

Add the carried number to the multiplication $1+0\times 2=1$

$\frac{\begin{matrix}\:\:&\:\:&\:\:&\bold{1}&\:\:\\\:\:&\:\:&7&\bold{0}&9\\\:\:&\times &\:\:&\bold{2}&5\end{matrix}}{\begin{matrix}\:\:&3&5&4&5\\\:\:&\:\:&1&8&\:\:\end{matrix}}$

Mutliply the bold numbers $7\times 2=14$

$\frac{\begin{matrix}\:\:&1&\:\:&1&\:\:\\\:\:&\:\:&\bold{7}&0&9\\\times &\:\:&\:\:&\bold{2}&5\end{matrix}}{\begin{matrix}\:\:&3&5&4&5\\\:\:&4&1&8&\:\:\end{matrix}}$

Add the carried digit, $1$, to the result

$\frac{\begin{matrix}\:\:&1&\:\:&1&\:\:\\\:\:&\:\:&7&0&9\\\times &\:\:&\:\:&2&5\end{matrix}}{\begin{matrix}\:\:&3&5&4&5\\1&4&1&8&\:\:\end{matrix}}$

Add the rows to get the answer. For simplicity, fill in trailing zeros

$\frac{\begin{matrix}\:\:&\:\:&7&0&9\\\:\:&\times &\:\:&2&5\end{matrix}}{\begin{matrix}0&3&5&4&5\\1&4&1&8&0\end{matrix}}$

Line up the numbers

$\begin{matrix}\:\:&7&0&9\\\times &\:\:&2&5\end{matrix}$ $=17725$