Chapter 1 - Problem Solving and Critical Thinking - 1.3 Problem Solving - Exercise Set 1.3 - Page 41: 51

\[\begin{align} & 28\overset{156}{\overline{\left){4368}\right.}} \\ & \,\,\,\,\,\,\,\,\underline{28\,} \\ & \,\,\,\,\,\,\,\,\,156 \\ & \,\,\,\,\,\,\,\,\underline{\,140} \\ & \,\,\,\,\,\,\,\,\,\,\,\,168 \\ & \,\,\,\,\,\,\,\,\,\underline{\,\,\,168} \\ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,0 \\ \end{align}\]

First, see that first digit of quotient is one, so divisor will be same as the number below first two digits of dividend, that is, \[28\]. Thus, divisor is \[28\]. \[\begin{align} & 28\overset{1**}{\overline{\left){4***}\right.}} \\ & \,\,\,\,\,\,\,\,\underline{\,28\,} \\ & \,\,\,\,\,\,\,\,\,*56 \\ & \,\,\,\,\,\,\,\,\underline{\,***} \\ & \,\,\,\,\,\,\,\,\,\,\,\,*** \\ & \,\,\,\,\,\,\,\,\,\underline{\,\,\,***} \\ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,0 \\ \end{align}\] Now, to calculate the second digit of dividend, add eight and five, which gives \[13\], so second digit is three. \[\begin{align} & 28\overset{1**}{\overline{\left){43**}\right.}} \\ & \,\,\,\,\,\,\,\,\underline{\,28\,} \\ & \,\,\,\,\,\,\,\,\,*56 \\ & \,\,\,\,\,\,\,\,\underline{\,***} \\ & \,\,\,\,\,\,\,\,\,\,\,\,*** \\ & \,\,\,\,\,\,\,\,\,\underline{\,\,\,***} \\ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,0 \\ \end{align}\] Further,\[43-28=15\], so write one before five below\[28\]. \[\begin{align} & 28\overset{1**}{\overline{\left){43**}\right.}} \\ & \,\,\,\,\,\,\,\,\underline{\,28\,} \\ & \,\,\,\,\,\,\,\,\,156 \\ & \,\,\,\,\,\,\,\,\underline{\,***} \\ & \,\,\,\,\,\,\,\,\,\,\,\,*** \\ & \,\,\,\,\,\,\,\,\,\underline{\,\,\,***} \\ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,0 \\ \end{align}\] Then, follow the usual division method to find the rest of the blanks. Hence, result is \[\begin{align} & 28\overset{156}{\overline{\left){4368}\right.}} \\ & \,\,\,\,\,\,\,\,\underline{28\,} \\ & \,\,\,\,\,\,\,\,\,156 \\ & \,\,\,\,\,\,\,\,\underline{\,140} \\ & \,\,\,\,\,\,\,\,\,\,\,\,168 \\ & \,\,\,\,\,\,\,\,\,\underline{\,\,\,168} \\ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,0 \\ \end{align}\]