SOLUTION: Divide 1423 By 24 In Base 5

Algebra ->  Test -> SOLUTION: Divide 1423 By 24 In Base 5      Log On


   



Question 1119094: Divide 1423 By 24 In Base 5
Found 2 solutions by math_helper, greenestamps:
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!

One way to do it is to do the division in base 10, then convert the answer to base 5:
1423/24 (base 5) = +%281%2A125%2B4%2A25%2B2%2A5%2B3%29%2F%282%2A5%2B4%29+ (base 10) = +238+%2F+14+=+17+ (base 10)
17 (base 10) = +highlight%28matrix%281%2C4%2C+%22+%22%2C+32%2C+%22+%28base+%22%2C+%22+5%29%22%29+%29+


Answer by greenestamps(13199) About Me  (Show Source):
You can put this solution on YOUR website!


You can do the division in base 5; you just need to know how to do addition and subtraction in base 5.

Since you are not familiar with base 5, it helps to start by making a list of the multiples of 24 in base 5. Of course the work must be done in base 5; you can use either addition or multiplication to make the list. As a check of your work, you can show that in base 5 "24" times "5" is "240".

24*1 = 24
24*2 = 24+24 = 103
24*3 = 103+24 = 132
24*4 = 132+24 = 211
24*4 = 211+24 = 240

Now you have a list of all the multiples, in base 5, of the divisor, 24. Do the long division just as in base 10, remembering that the subtractions are in base 5.

         32
     ------
  24 ) 1423
       132
       ----
        103
        103
        ---
          0

1423 divided by 24 in base 5 is 32.