Carmen has learned an algorithm for subtraction. She uses it to find $52$minus$16$ as follows.

$52$plus$10$equals$62$

so

$52$plus$10$equals$50$plus$12$

minus$(16$plus$10)$equalsminus$26$

so

minus$(16$plus$10)$equalsminus$(20$plus$6)$

So her answer is $30$plus$6$equals$36.$

$($a$)$ What properties does$$ Carmen's algorithm$$ use? Is her method$$ correct?

$($b$)$ Now solve another subtraction$$ problem, $74$minus$38,$ with$$ Carmen's algorithm. Use the traditional algorithm to check your work.