Find a low and high estimate for the product or quotient. (p. 748)

$31217÷218$.

To find the low estimate, round the divisor up and replace the dividend with a number that is divisible by the increased divisor and is less than the actual dividend.

To find the high estimate, round the divisor down and replace the dividend with a number that is divisible by the decreased divisor and is greater than the actual dividend.

To find the low estimate, round the divisor up and replace the dividend with a number that is divisible by the increased divisor and is less than the actual dividend.

So, the low estimate of the quotient is

$300104\begin{array}{l}31200\\ \underset{¯}{31200}\\ 0\end{array}$

Thus, the low estimate of the quotient is 104.

To find the high estimate, round the divisor down and replace the dividend with a number that is divisible by the decreased divisor and is greater than the actual dividend.

So, the high estimate of the quotient is

$200157\begin{array}{l}31400\\ \underset{¯}{31400}\\ 0\end{array}$

Thus, the high estimate of the quotient is 157.