Question

If 451 in base6 - P in base7 = 301 in base6, find d. value of P

Answer 1

451 base 6
1*6^0 + 5*6^1 + 4*6^2
= 1 + 30 + 144
= 175 in base 10

301 base 6
1*10^0 + 0*6^1 + 3*6^2
= 1 + 0 + 108
= 109 in base 10

so in base 10
175 - x = 109
x = 66 in base 10
put that in base 7
7^2 = 49
17 left
2*7^1 = 14
3 left
so
1^7^2 + 2*7^1 + 3*7^0
or
P = 123 in base 7

Answer 2

By the way, I just did that by common sense. I do not know what routine you are really supposed to know. You may have a better way to shift back and forth.

Answer 3

301 base 6
1*10^0 + 0*6^1 + 3*6^2
should be
301 base 6
1*6^0 + 0*6^1 + 3*6^2
= 109

Answer 4

You could just do the subtraction in base 6 and then convert the answer to base 7:

451-301 = 150
150₆ = 123₇

Answer 5

good point :)