Question

1. higher order thinking you are dividing 3,972 by 41. explain why the first digit in the quotient should be placed over the tens place of the dividend.

Explanation:

Step1: Check divisor and dividend parts

When dividing \(3972\) by \(41\), we first look at the first few digits of the dividend. The divisor is \(41\) (a two - digit number). We check the first two digits of the dividend, which is \(39\). Since \(39<41\), we can't divide \(39\) by \(41\) to get a non - zero whole number quotient.

Step2: Consider the first three digits

So we move on to the first three digits of the dividend, which is \(397\). Now we check if \(41\) can divide into \(397\). We know that when we perform long division, the digit of the quotient is placed above the digit of the dividend that we are currently dividing into. Since we are dividing into the three - digit number \(397\) (and the third digit of the dividend \(3972\) is in the tens place when we consider the place value of the digits we are using for the division at this step), the first digit of the quotient should be placed over the tens place of the dividend. Mathematically, when we do long division, for a dividend \(a = 3972\) and divisor \(b = 41\), we express \(a\) as \(a=39\times100 + 7\times10+2\). When we check \(41\) against the first two digits (\(39\)) and find it's too small, we use the first three digits (\(397\)). The digit in the dividend that is the right - most digit of the number we are dividing into (\(397\)) is the tens digit of the original dividend (\(3972\)). So the quotient digit for dividing \(41\) into \(397\) is placed above the tens place of the original dividend.

Answer:

When dividing \(3972\) by \(41\), we first check the first two digits of the dividend (\(39\)). Since \(39<41\), we cannot get a non - zero whole number quotient from dividing \(39\) by \(41\). We then use the first three digits of the dividend (\(397\)) for the division. In long division, the digit of the quotient is placed above the digit of the dividend that we are currently dividing into. The right - most digit of \(397\) (from the original dividend \(3972\)) is in the tens place of \(3972\), so the first digit of the quotient should be placed over the tens place of the dividend.