SOLUTION: MAT 145: Topics In Contemporary Math QUESTION Subtract the following base-9 numbers: 1) 41802(9) - 23745(9) Add the following base-3 numbers: 2) 20112(3)

Algebra.Com
Question 1192793: MAT 145: Topics In Contemporary Math
QUESTION
Subtract the following base-9 numbers:
1) 41802(9) - 23745(9)
Add the following base-3 numbers:
2) 20112(3) + 11021(3)

Found 2 solutions by Edwin McCravy, Alan3354:
Answer by Edwin McCravy(20064)   (Show Source): You can put this solution on YOUR website!

Do these analogous to the base ten methods you learned in 
elementary school.  Just remember how to count in base 9.
You count: 1,2,3,4,5,6,7,8,10,11,12,13,14,15,16,17,18,20.
Every time you get to 8, you skip to 10. For there is no
9 in base 9.  9 in base 9 is written just like ten is
written in base ten, as 10.

Subtract the following base-9 numbers:
1) 41802(9) - 23745(9)
Start as you would in 2nd grade lol:

 4 1 8 0 2
-2 3 7 4 5
----------
          
You can't subtract 5 from 2, so you have to borrow. You can't 
borrow from the 0, so borrow 1 from the 8.  Scratch the 8 and
put a 7 above it.  Now you leave the 0 an 8, (not a 9). 
Why an 8? Think what you'd do if it were base ten.  You'd 
leave the 0 with a 9 (which is 1 less than ten).  So you leave 
the zero with 1 less than 9, or 8.  So you have this:

     7 8
 4 1 8 0¹2
-2 3 7 4 5
----------

Now you need to subtract 5 from 12.  Count it out on your fingers.

To subtract 12-5, count on your fingers from 5 (not including 5) to 12
(including 12), but skip from 8 to 10.  Like this. On your fingers count
6,7,8,10,11,12. That takes 6 fingers, so put 6 under the 5:

     7 8
 4 1 8 0¹2
-2 3 7 4 5
----------
         6


To subtract 8-4, count on your fingers from 4 (not including 4) to 8 
(including 8), but you won't have to skip from 8 to 10 this time 
because we only get to 8.  Like this. On your fingers count 5,6,7,8. 
That takes 4 fingers, so put 4 under the 4.
[That was exactly the same as in base 10, 8-4=4. Bases are all the 
same as long as you are in digits less than the base number.]  

     7 8
 4 1 8 0¹2
-2 3 7 4 5
----------
       4 6

The next is easy 7-7=0, so put a 0 under the 7. In any base 
when you subtract a digit from itself you always get 0.

     7 8
 4 1 8 0¹2
-2 3 7 4 5
----------
     0 4 6

Next, you can't subtract 3 from 1, so you have to borrow. You 
borrow 1 from the 4, scratch the 4 and put a 3 above it
 
 3   7 8
 4¹1 8 0¹2
-2 3 7 4 5
----------
     0 4 6

Now you need to subtract 3 from 11.  So you count on your
fingers. 

To subtract 11-3, count on your fingers from 3 (not including 5) 
to 11 (including 11), but skip from 8 to 10.  Like this. On your 
fingers count 4,5,6,7,8,10,11. That takes 7 fingers, so put 7 
under the 3:
 
 3   7 8
 4¹1 8 0¹2
-2 3 7 4 5
----------
   7 0 4 6

The rest is simply 3-2=1, because the digits are less than 9.
Put a 1 under the 2 and you're done.
 
 3   7 8
 4¹1 8 0¹2
-2 3 7 4 5
----------
 1 7 0 4 6

-------------------------------------------------

Add the following base-3 numbers:
2) 20112(3) + 11021(3)

  2 0 1 1 2
 +1 1 0 2 1
 ----------

Here we skip all the way from 2 to 10, because 3
is written as 10.  2+1=3 but there is no 3 in base 
three. so we skip from 2 to 10.  We put 0 under
the 1 and carry 1 to the next column, like this:

        1
  2 0 1 1 2
 +1 1 0 2 1
 ----------
          0

Now you have to add 1+1+2. Count on your fingers:
1+1=2 but since you are at 2 (1 less than the base number)
you must skip up to 10 and count 10,11. So in base three
1+1+2=11, so you put 1 under the 2 and carry 1 to the
next column.

      1 1
  2 0 1 1 2
 +1 1 0 2 1
 ----------
        1 0

Now you have to add 1+1+0.  That's easy because we don't
have to skip to 10.  So 1+1+0=2 just as in base ten. So
we put a 2 under the 0, and there's nothing to carry.

      1 1
  2 0 1 1 2
 +1 1 0 2 1
 ----------
      2 1 0

The next is also easy. 0+1=1. Put a 1 under the 1 and
there's nothing to carry:

      1 1
  2 0 1 1 2
 +1 1 0 2 1
 ----------
    1 2 1 0

Finally we have 2+1.  That would be 3, but there is no
3 in base 3, so we skip to 10, which gives us an extra 
digit on the left:

      1 1
  2 0 1 1 2
 +1 1 0 2 1
 ----------
1 0 1 2 1 0

Edwin

Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
Edwin, this person just wants to get the answers, not learn anything.
RELATED QUESTIONS

MAT 145: Topics In Contemporary Math QUESTION 6 Add the following... (answered by ikleyn)
QUESTION 6 Add the following base-3 numbers: 1) 20112(3) + 11021(3) Subtract the (answered by Alan3354)
MAT 145: Topics In Contemporary Math QUESTION 8 Find the number 85... (answered by ikleyn)
Name: MAT 145: Topics In Contemporary Math Bases Covert each of... (answered by MathLover1)
MAT 145: Topics In Contemporary Math Argument Forms Identify the logical fallacy... (answered by Alan3354,ikleyn)
MAT 145: Topics In Contemporary Math Probability 3) Suppose we roll a... (answered by math_tutor2020)
MAT 145: Topics In Contemporary Math Probability 3) Suppose we roll a pair (answered by math_tutor2020)
Name: MAT 145: Topics In Contemporary Math Bases Convert each of (answered by MathLover1,greenestamps)
MAT 145: Topics In Contemporary Math More Modular Arithmetic Find each of... (answered by Edwin McCravy,greenestamps)