Chapter 4.5, Problem 15P

a. Lindsay calculates two-fifths of 1260 by using the following strategy: First, she finds half of 1260, which is 630. Then she subtracts one tenth of 1260, which is 126, from 630 and gives the answer, 504. Discuss the ideas behind Lindsay’s strategy. Then write a string of equations that incorporate this strategy and that show why the strategy is valid. What property of arithmetic is involved? Write your equations in the following form:
   $\begin{array}{l}\begin{array}{l}\\ \frac{2}{5}.1260=someexpression\end{array}\hfill \\ \begin{array}{l}=someexpression\\ =:\\ =504\end{array}\hfill \end{array}$

b. Terrell calculates $\frac{2}{5}$ of 1260 in the following way: First he multiplies 1260 by 2 to get 2520. Then he multiplies 2520 by 2 to get 5040 and divides this by 10 to get 504. Discuss the idea behind Terrell’s strategy. Then write a string of equations that incorporate Terrell’s strategy, and that show why the strategy is valid. Write your equations in the form shown previously.