Chapter 11.5, Problem 46PPS

(a)

To determine

To calculate: To find the quotient and remainder for $6^2÷7$

Answer to Problem 46PPS

The quotient is $5$ and remainder isy $1$

Explanation of Solution

Given information: Expression is1 $6^2÷7$

Formula Used:

Long division is the division of whole number in a systematic procedure to derive the answer.

Calculation:

Expression is given as follows:

  $6^2÷7$

Dividing the expression with the divisor to derive the quotient and remainder:

  $7\begin{array}{c}\hfill 5\\ \hfill \overline{)\begin{array}{l}36\\ 35\\ -\\ --\\ 1\end{array}}\end{array}$

Thus, quotient is $5$

Remainder is $1$

Conclusion:

Hence, quotient is $5$ and remainder is $1$

(b)

To determine

To calculate: To draw the figures for $3^2÷4$ and $2^2÷3$

Explanation of Solution

Given information: Figure that models $6^2÷7$ is

  

Calculation:

Given below the figure that models $6^2÷7$

  

Using the above figure, figure that models $3^2÷4$ is created as follows:

  

Using the above figure, figure that models $2^2÷3$ is created as follows:

  

Conclusion:

Hence, figure is drawn for expressions $3^2÷4$ and $2^2÷3$

(c)

To determine

To calculate: To find the pattern in the previous exercises

Answer to Problem 46PPS

Pattern is $x^2÷\left(x+1\right)$

Explanation of Solution

Given information: Figure that models $6^2÷7$ is

  

Calculation:

Expressions are as follows:

  $6^2÷7$

  $3^2÷4$

  $2^2÷3$

Common pattern in above expressions is:

Square of a number is divided by one more than the number.

Thus, mathematically,

  $x^2÷\left(x+1\right)$

Conclusion:

Hence, pattern is $x^2÷\left(x+1\right)$

(d)

To determine

To calculate: To find $x^2÷\left(x+1\right)$ using log division method

Answer to Problem 46PPS

The quotient is $\left(x-1\right)$ and remainder is $1$

Explanation of Solution

Given information: Expression is $x^2÷\left(x+1\right)$

Formula Used:

Long division is the division of whole number in a systematic procedure to derive the answer.

Calculation:

Expression is given as follows:

  $x^2÷\left(x+1\right)$

Dividing the expression with the divisor to derive the quotient and remainder:

  $x+1\begin{array}{c}\hfill x-1\\ \hfill \overline{)\begin{array}{l}{x}^2\\ x^2+x\\ --\\ ----\\ -x\\ -x-1\\ ++\\ -----\\ 1\\ -----\end{array}}\end{array}$

Thus, quotient is $\left(x-1\right)$

Remainder is $1$

Conclusion:

Hence, quotient is $\left(x-1\right)$ and remainder is $1$