Final answer:
To simplify (3310₅ - 1425₅) in base 5, subtract each digit while following base 5 rules. We borrow as needed from the adjacent higher place. The simplified result is 1330₅.
Step-by-step explanation:
To simplify the expression (3310₅ - 1425₅) in base 5, we perform subtraction similarly to how we would in base 10, but with base 5 rules. Subtract each digit starting from the rightmost digit, remembering that in base 5, we can only have digits 0 through 4.
- We start with the ones place. Since the top digit is 0 and the bottom digit is 5, we need to borrow from the next digit to the left in the top number. Borrowing one from 1 in the tens place of 3310₅, we change it to 0, and the 0 in the ones place becomes 5 (since 1 in base 5 is equivalent to 5 in base 10).
- Now we subtract the ones place: 5 minus 5 is 0.
- In the tens place of 3310₅, it was changed to 0 when we borrowed, and we're subtracting 2 from it. We need to borrow again, this time from the 3 in the hundreds place. That 3 becomes 2, and the 0 in the tens place becomes 5.
- Subtract the tens place next: 5 minus 2 gives us 3.
- Moving on to the hundreds place, we have the modified 2 from borrowing, and we subtract the 4 from 1425₅. Again, we must borrow, turning the 3 in the thousands place of 3310₅ into 2 and the 2 in the hundreds place into 7 (in base 5).
- Subtract in the hundreds place: 7 minus 4 equals 3.
- Finally, subtract the thousands place, where no borrowing is needed: 2 minus 1 equals 1.
Therefore, the simplified result of the subtraction (3310₅ - 1425₅) is 1330₅.