Given 577 x 423 with grade school algorithm you calculate
577 x 3 = 1731
577 x 2 = 1154
577 x 4 = 2308
These are 3 multiplications of a number by a single digit.
Then, you go on and add
1731 + 11540 = 13271
13271 + 230800 = 244071 to get the result
These are 2 additions.
At the bottom line, this makes ~ 5 operations (of course depending on the number of digits you take, e.g., if you conceive the whole operation, it is just one multiplication, but this set aside).
In my copy of CC by Arora and Barak (you can have a look at page xx) it says for this "3 multiplications of a number by a single digit and 3 additions". Is this an error? Thank you.