200 CHAPTER 4 Systems of Numeration Division Division is performed in much the same manner as long division in base 10. A detailed example of a division in base 5 is illustrated in Example 9. The same procedure is used for division in any other base. Now try Exercise 41 × = = × + × = 2 4 8 (17) (11) 11. 10 7 Record the 11. Now add in base 7 to determine the answer. Remember, in base 7, there are no digits greater than 6. × 43 25 311 116 1501 2 7 7 7 Therefore, the product is 1501 .7 7 Example 9 Dividing in Base 5 Divide ) 2 143 . 5 5 Solution Using the multiplication table for base 5, Table 4.9, we list the multiples of the divisor, 2. 2 1 2 2 2 4 2 3 11 2 4 13 5 5 5 5 5 5 5 5 5 5 5 5 × = × = × = × = Since × = 2 4 13 , 5 5 5 which is the largest product less than 14 , 2 5 5 divides into 145 four times. Record the 13. Subtract 135 from 14 .5 The difference is 1 .5 Record the 1. ) 4 2 143 13 1 5 5 Now bring down the 3 as when dividing in base 10. ) 4 2 143 13 13 5 5 We see that × = 2 4 13 . 5 5 5 Use this information to complete the problem. ) 44 2 143 13 13 13 0 5 5 5 Therefore, ÷ = 143 2 44 5 5 5 with remainder 0 .5 7 Now try Exercise 51 A division problem can be checked by multiplication. If the division was performed correctly, (quotient divisor) remainder dividend. × + = We can check Example 9 as follows. (44 2 ) 0 143 44 2 143 5 5 5 5 5 5 5 × + = × Check.
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