The document shows the step-by-step workings of two base conversions: 1) 302.45 + 402.55 in base 5, which equals 121045 2) 701.48 - 340.78 in base 8, which equals 34058 It breaks down each digit addition and subtraction, borrowing when needed, to get the final answers in the given bases.

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