2*5=10, carry the 1; move to the tens; 2*3+1=7 == 70
Add an X to increment the second value
1*5=5; move to the hundreds; 1*3 =3 == 350
sum the two values; 350+70=420
You're adding four numbers instead of 2, but don't need to keep track of carried values.
Parents' problems with CC: I was embarrassed when I couldn't help my kid with their home work but I'm sure not going to admit that maybe I didn't learn math very well, it's the book that's wrong.
Believe it or not, the point of a math class is to learn math, not to crank out some answers at the answer factory.