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
