Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 4 - Number Representation and Calculation - 4.3 Computation in Positional Systems - Exercise Set 4.3 - Page 234: 38

Answer

The quotient of the provided expression is, \[{{21}_{\text{five}}}\].

Work Step by Step

Consider the expression, \[{{4}_{\text{five}}}\overline{\left){{{134}_{\text{five}}}}\right.}\] Start to divide the expression same as base ten but in this take base as five. So, starts divide\[13\]by\[4\], Use the multiplication table that is given above, find the column represented by \[2\] and the row represented by \[4\]that is less than or equal to\[13\]. As \[{{4}_{\text{five}}}\times {{2}_{\text{five}}}={{13}_{\text{five}}}\] from the table, then it is purely divisible not getting any remainder, further its quotient is \[{{2}_{\text{five}}}\]; the division is represented below: \[{{4}_{\text{five}}}\overset{2}{\overline{\left){\begin{align} & \ \ {{134}_{\text{five}}} \\ & \underline{-13} \\ & \ \ \ 0 \\ \end{align}}\right.}}\] Take down the further digit in the dividend, that is\[{{4}_{\text{five}}}\] \[{{4}_{\text{five}}}\overset{2}{\overline{\left){\begin{align} & \ \ {{134}_{\text{five}}} \\ & \underline{-13} \\ & \ \ \ \ 04 \\ \end{align}}\right.}}\] Then, again use the table and find the column represented by \[1\] and row represented by \[4\]that is less than or equal to\[4\]. As \[{{4}_{\text{five}}}\times {{1}_{\text{five}}}={{4}_{\text{five}}}\]from the table, then it is purely divisible not getting any remainder, further its quotient is \[{{1}_{\text{five}}}\]; the division is represented below: \[{{4}_{\text{five}}}\overset{{{21}_{\text{five}}}}{\overline{\left){\begin{align} & \ \ {{134}_{\text{five}}} \\ & \underline{-13} \\ & \ \ \ \ 04 \\ & \underline{\ -04} \\ & \ \ \ \ \ 0 \\ \end{align}}\right.}}\] So, \[{{21}_{\text{five}}}\] is the quotient of the \[{{4}_{\text{five}}}\overline{\left){{{134}_{\text{five}}}}\right.}\] Hence, the quotient of the provided expression is, \[{{21}_{\text{five}}}\].
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