## Thinking Mathematically (6th Edition)

Published by Pearson

# Chapter 4 - Number Representation and Calculation - 4.3 Computation in Positional Systems - Concept and Vocabulary Check - Page 233: 4

#### Answer

Fill the blanks with ... 7 ... 7 ... 10 ... 5 ... 10 ... 5 ... 3 ... 1 ... 15

#### Work Step by Step

Rightmost column: 3 is less than 5 in any base, borrow one group of 7, giving (7+3$)=10_{ten}$. Then subtract 5 from 10, obtaining a difference of 5 Record the 5 (we have borrowed one 7) $\begin{array}{lll} & & \\ & 4 & 3_{seven}\\ - & 2 & 5_{seven}\\ -- & -- & --\\ & & 5_{seven} \end{array}$ Move onto the next column. We subtract 2 from 3 (not 4, one was borrowed) and obtain 1. Record the one, the answer is $15_{seven}$ $\begin{array}{lll} & & \\ & 4 & 3_{seven}\\ - & 2 & 5_{seven}\\ -- & -- & --\\ & 1 & 5_{seven} \end{array}$ Fill the blanks with ... 7 ... 7 ... 10 ... 5 ... 10 ... 5 ... 3 ... 1 ... 15

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