4.4 Perform Computations in Other Bases 201 Example 10 Dividing in Base 6 Divide ) 5 3410 6 6 Solution The multiples of 5 in base 6 are × = 5 1 5 6 6 6 × = 5 2 14 6 6 6 × = 5 3 23 6 6 6 × = 5 4 32 6 6 6 × = 5 5 41 6 6 6 ) 423 5 3410 32 21 14 30 23 3 6 6 6 Thus, the quotient is 423 ,6 with remainder 3 .6 CHECK: Does (423 5 ) 3 3410 ? 6 6 6 6 × + = 423 5 3403 3403 3 3410 6 6 6 6 6 ? 6 × + = True 7 Now try Exercise 53 Timely Tip Be careful when subtracting in bases other than base 10! In the Example 10 division problem, we had to borrow when subtracting two different times. In each case, since we are working in base 6, we must borrow a group of 6 from the preceding column. Instructor Resources for Section 4.4 in MyLab Math Exercises SECTION 4.4 Warm Up Exercises In Exercises 1– 6, fill in the blanks with an appropriate word, phrase, or symbol(s). 1. In base + = 5, 3 4 5 5 ________. 125 2. In base + = 6, 2 5 6 6 ________. 116 3. When subtracting in base 5, when we borrow, we must borrow one group of ________ from the preceding column. 5 4. When subtracting in base 8, when we borrow, we must borrow one group of ________ from the preceding column. 8 5. In base × = 5, 3 4 5 5 ________. 225 6. In base × = 9, 3 7 9 9 ________. 239 Practice the Skills In Exercises 7–18, add in the indicated base. 9. 132 34 5 5 + 2215 10. 254 15 6 6 + 3136 13. 1011 1110 2 2 + 110012 14. 1110 1111 2 2 + 111012 11. 654 463 7 7 + 14507 12. + 727 564 8 8 15138 15. A434 128B 12 12 + B70312 16. B293 486A 12 12 + 13B4112 17. A737 128B 16 16 + B9C216 18. B299 486A 16 16 + FB0316 In Exercises 19–30, subtract in the indicated base. 19. − 201 120 3 3 113 20. − 342 261 6 6 416 21. − 338 274 9 9 549 22. 1221 202 3 3 − 10123 7. 22 20 3 3 + 1123 8. 23 13 4 4 + 1024 • Objective-Level Videos 4.4 • Animation: Addition and Multiplication in Base 5 • PowerPoint Lecture Slides 4.4 • MyLab Exercises and Assignments 4.4
RkJQdWJsaXNoZXIy NjM5ODQ=