Step-by-step answer:
Since the question can be solved easily with a calculator, it is assumed that no calculators are allowed.
13*379 is the same as (10+3)*379
Applying distributive law, we then solve
10*379 = 3790
3*379 = 1137
Adding the two, we get
4927
Alternatively, we can calculate the product by long multiplication to get also 4927.
To check for mistakes, we use casting out nines
13 * 379 (add the digits, 1+3, 3+7+9)
4 * 19 (add the digits)
4*10 (multiply)
40 (add digits)
4
Add digits of 4927
4+9+2+7 = 22
add digits again
2+2 =4
the two match, so the likelihood of make arithmetic error is very low.
Note: using a calculator, the value is indeed 4927.