(1)Evaluate 54 base 6 + 305 base 6, give your answer in base 6 (2) evaluate 785 base 9 + 306 base 9 , give your answer in base 9
359base six
1555
785 base 9 + 306 base 9
403
Correct! The sum of 785 base 9 and 306 base 9 is 403 base 9.
2555
I apologize for the confusion, but the correct answer is 1052 base 9 for the sum of 785 base 9 and 306 base 9.
To evaluate the addition of numbers in different bases, we need to convert them to a common base. Let's follow these steps to find the answers to both questions:
(1) Evaluate 54 base 6 + 305 base 6 and give the answer in base 6:
First, we write out the addition problem:
54 base 6
+ 305 base 6
___________
Now, let's evaluate each digit place by place, starting from the rightmost place. If the sum in each place is less than the base (6), we write it down as it is. If it's greater than or equal to the base, we carry the remainder (dividing by 6) to the left:
4 base 6
+ 5 base 6
__________
13 base 6
Since 13 in base 10 is greater than our base (6), we'll rewrite it as 3 in the current place and carry 1 to the left:
1 base 6
+ 54 base 6
__________
103 base 6
Therefore, the sum of 54 base 6 + 305 base 6 is 103 base 6.
(2) Evaluate 785 base 9 + 306 base 9 and give the answer in base 9:
Again, let's start by writing out the addition problem:
785 base 9
+ 306 base 9
_______________
Evaluating each place from right to left:
5 base 9
+ 6 base 9
___________
11 base 9
Since 11 in base 10 is greater than our base (9), we can rewrite it as 2 in this place and carry 1 to the left.
1 base 9
+ 8 base 9
___________
10 base 9
In base 10, 10 is represented as A in base 9, since it goes beyond 9. Finally, we don't have any more places to evaluate, so the sum of 785 base 9 + 306 base 9 is 10A base 9.
Therefore, the answer is:
(1) 54 base 6 + 305 base 6 = 103 base 6
(2) 785 base 9 + 306 base 9 = 10A base 9.