SOLUTION: When Z is divided by 8, the remainder is 5. What is the remainder when 4Z is divided by 8?

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Question 396628: When Z is divided by 8, the remainder is 5. What is the remainder when 4Z is divided by 8?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
When Z is divided by 8, the remainder is 5.
What is the remainder when 4Z is divided by 8?
:
Let r = the remainder
%28%28z-5%29%29%2F8 = %28%284z-r%29%29%2F4%288%29
%28%28z-5%29%29%2F8 = %28%284z-r%29%29%2F32
Cross multiply
8(4z-r) = 32(z-5)
32z - 8r = 32z - 160
Subtract 32z from both sides
-8r = -160
r = %28-160%29%2F%28-8%29
r = +20 is the remainder, when you divide by 32, but when you divide by 8; 20/8 = 2 with a remainder of 4
Therefore, the remainder when 4Z is divided by 8 is 4