Thinking Mathematically (6th Edition)

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

Chapter 4 - Number Representation and Calculation - Chapter Summary, Review, and Test - Review Exercises - Page 245: 29


The difference in the indicated base is \[{{5}_{\text{six}}}\].

Work Step by Step

Start by subtracting the numbers in the right-hand column:\[{{4}_{\text{six}}}-{{5}_{\text{six}}}\]. \[{{5}_{\text{six}}}\]is greater than \[{{4}_{\text{six}}}\]. So, we need to borrow from the preceding column. Now, borrow one group of 6 because in the provided question we are working in base six. This gives a sum of \[4+6\] or 10 in base ten. Now, subtract 5 from 10: \[\begin{align} & \text{ 2} \\ & \begin{matrix} \text{ 3}{{\text{4}}_{\text{six}}} \\ -{{25}_{\text{six}}} \\ 5 \\ \end{matrix} \\ \end{align}\] Now, perform the subtraction in the second column from the right. That is, subtract 2 from 2: \[\begin{align} & \text{ 2} \\ & \begin{matrix} \text{ 3}{{\text{4}}_{\text{six}}} \\ -{{25}_{\text{six}}} \\ {{05}_{\text{six}}} \\ \end{matrix} \\ \end{align}\] The difference in the indicated base is \[{{5}_{\text{six}}}\].
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