An example of adding in base 5 and subtracting in base 8

1. Complete the following computation in base
5.
3 0 2 45
+ 4 0 2 35

2. Complete the following computation in base
5.
3 0 2 45
+ 4 0 2 55
First, we add 4 + 5.
This gives 9, which is larger than our
base (5).
Therefore, we have to convert:
4 + 5 = 9 = ( __ × 5) + ( __ × 1)

3. Complete the following computation in base
5.
3 0 2 45
+ 4 0 2 55
There is one set of 5 and 4 sets of 1 in
9.
4 + 5 = 9 = ( 1 × 5) + ( 4 × 1) = 145
So, we write the 4 and carry the 1

4. Complete the following computation in base
5.
1
3 0 2 45
+ 4 0 2 55
45

5. Complete the following computation in base
5.
1
3 0 2 45
+ 4 0 2 55
45
Now, we add 1 + 2 + 2.
This gives 5, which is equal to our base
(5).
Therefore, we have to convert:
1 + 2 + 2 = 5 = ( __ × 5) + ( __ × 1)

6. Complete the following computation in base
5.
1
3 0 2 45
+ 4 0 2 55
45
There is one set of 5 and 0 sets of 1 in
5.
1 + 2 + 2 = 5 = ( 1 × 5) + ( 0 × 1) = 105
So, we write the 0 and carry the 1

7. Complete the following computation in base
5.
1 1
3 0 2 45
+ 4 0 2 55
0 45

8. Complete the following computation in base
5.
1 1
3 0 2 45
+ 4 0 2 55
1 0 45
Then, we add 1 + 0 + 0.
This gives 1, which is less than our
base (5).
Therefore, we can just write the 1.

9. Complete the following computation in base
5.
1 1
3 0 2 45
+ 4 0 2 55
1 0 45
Finally, we add 3 + 4.
This gives 7, which is larger than our
base (5).
Therefore, we have to convert:
3 + 4 = 7 = ( __ × 5) + ( __ × 1)

10. Complete the following computation in base
5.
1 1
3 0 2 45
+ 4 0 2 55
1 2 1 0 45
There is one set of 5 and 2 sets of 1 in
5.
3 + 4 = 7 = ( 1 × 5) + ( 2 × 1) = 125
Since this is the last computation, we
just write 1 and 2.

11. Complete the following computation in base
5.
1 1
3 0 2 45
+ 4 0 2 55
1 2 1 0 45
Our final answer is
121045

12. Complete the following computation in base
8.
7 0 1 48
̶ 3 4 0 78

13. Complete the following computation in base
8.
7 0 1 48
̶ 3 4 0 78
First, we subtract 4 ̶ 7.
Since 7 is bigger than 4, we will have
to borrow.

14. Complete the following computation in base
8.
0 12
7 0 1 48
̶ 3 4 0 78
58
We borrow from the 1. Remember
that when you borrow, you borrow
the base.
So, the 1 becomes a 0 and the 4
becomes 4 + 8 = 12.

15. Complete the following computation in base
8.
0 12
7 0 1 48
̶ 3 4 0 78
0 58
Now, 0 – 0 = 0

16. Complete the following computation in base
8.
0 12
7 0 1 48
̶ 3 4 0 78
0 58
Now, we subtract 0 ̶ 4.
Since 4 is bigger than 0, we will have
to borrow.

17. Complete the following computation in base
8.
6 8 0 12
7 0 1 48
̶ 3 4 0 78
4 0 58
We borrow from the 7. Remember
that when you borrow, you borrow
the base.
So, the 7 becomes a 6 and the 0
becomes 0 + 8 = 8.

18. Complete the following computation in base
8.
6 8 0 12
7 0 1 48
̶ 3 4 0 78
3 4 0 58
Finally, 6 – 3 = 3

19. Complete the following computation in base
8.
6 8 0 12
7 0 1 48
̶ 3 4 0 78
3 4 0 58
Our final answer is
34058