Chapter 6.3, Problem 22P

a. Suppose you want to estimate $459÷38$ By rounding 38 up to 40. Both $440÷40$ and $480÷40$ are easy to calculate mentally. Use reasoning about division to determine which division problem, $440÷40$ or $480÷40$ should give you a better estimate to $459÷38.$ Then check your answer by solving the division problems.
b. Suppose you want to estimate $459÷42$
by rounding 42 down to 40. As before, both $440÷40$ and $480÷40$ are easy to calculate mentally. Use reasoning about division to determine which division problem, $440÷40$ or $480÷40$ , should give you a better estimate to $459÷42$ . Then check your answer by solving the division problems.
c. Suppose you want to estimate $632÷58.$ What is a good way to round the numbers 632 and 58 so that you get an easy division problem which will give a good estimate to $632÷58?$ Explain, drawing on what you learned from parts (a) and (b).
d. Suppose you want to estimate $632÷62.$ What is a good way to round the numbers 632 and 62 so that you get an easy division problem which will give a good estimate to $632÷62?$ Explain, drawing on what you learned from parts (a) and (b).