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 235: 55


The numbers are subtracted in the same way as in the ten base. When a larger number is subtracted from a smaller number in the same column, then the value equal to the given base (base-5 in this case) is carried over from the adjacent column is carried over.

Work Step by Step

Also, take the numbers such that the sum of the numbers is bigger than the base. \[\begin{align} & \text{ 6 7 } \\ & \text{ 72} \\ & -\text{ 53} \\ & \text{ }\begin{matrix} \text{ 1 4 } \\ \end{matrix} \\ \end{align}\] The above calculation is done as: For the last column: Since 3 cannot be subtracted from 2, 5 from the adjacent column is carried over to 2, which makes it: \[{{7}_{five}}-{{3}_{five}}={{4}_{ten}}=(4\times 1)={{4}_{five}}\] For the first column: \[{{6}_{five}}-{{5}_{five}}={{1}_{ten}}=(1\times 1)={{1}_{five}}\]
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