Chapter 4.5, Problem 13P

Tamar calculated 41 41 as follows:

Four 4s is 16, so four 40s is 160 and forty 40s is 1600. Then forty-one 40s is another 40 added on, which is 1640. So forty- one 41s is 41 more, which is 1681.

a. Explain briefly why it makes sense for Tamar to solve the problem the way she does. What is the idea behind her strategy?

b. Write equations that incorporate Tamar’s work and that show clearly why Tamar’s method calculates the correct answer to 41 . 41. Which properties of arithmetic did Tamar use (knowingly or not), and where? Be thorough and be specific. Write your equations in the following format:

   $\begin{array}{l}41.41=\text{someexpression}\\ =\text{some expression}\\ =:\\ =1681\end{array}$