multiply in the indicated base
14
5
x 4
5
________________
4 x 4 is 16(base 10), which is 40 (base 4). Enter zero on the right and "carry the 4".
4x1 is 4 in the 4^1 column, but you have to "carry the 4", which gives you 8*4^1 (32), whis is 2*4^2 + 0*4^1.
The product must be written
200 (base 4) , which is
= 2*4^2 + 0*4 + 0*1
The multiplication is equivalent to the operation
8 x 4 = 32 (base 10)
the base should be 5 I need to redo the problem 32 was the incorrect answer per my instructor
You could make yourself a multiplication table in base 5
X 1 2 3 4
1 1 2 3 4
2 2 4 11 13
3 3 11 14 22
4 4 13 22 31
so
145
x 45
-------
1215
(4x4)5 = 315
so put down 1 and carry a 3
4x1 5 = 4
4 plus the 3 carry is 125
or
you could change to base 10
145 = 1(5) + 4 = 9
4 ---- > 4
9x4 = 3610
36 = 1(5^2) + 2(5) + 1
= 1215
so your answer is 1215
Whoops. Sorry I'm no good at that stuff
To multiply in the indicated base, follow these steps:
1. Start by multiplying the rightmost digit of the bottom number (4 in this case) by each digit of the top number (14 in this case), just like how you would in regular multiplication:
4
x 4
_______
2. Write down the result of each multiplication below, keeping the rightmost digit aligned with the rightmost digit of the top number:
4
x 4
_______
16
3. Add a placeholder zero to the right of the first result, and then multiply the second digit of the bottom number (0 in this case) by each digit of the top number (14 in this case):
4
x 4
_______
16 0
4. Write down the result of each multiplication below, keeping the rightmost digit aligned with the rightmost digit of the top number:
4
x 4
_______
16 0
14 0
5. Finally, add the two results together:
4
x 4
_______
16 0
+ 14 0
_________
19 0
So, the result of multiplying 14 in base 5 by 4 in base 5 is 190 in base 5.