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10 Apr 2013, 18:02
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hi, this question is from the number properties book, 4th edition, ch. 10 q. 23
apologies if this is in the wrong thread
you're given background info, integer x has a remainder of 5 when divided by 9, integer y has a remainder of 7 when divided by 9
question: what is the remainder when 5x - y is divided by 9?
i solved this by picking numbers, but i think that it's probably inefficient.
i did 2 examples and made sure i got the same number
taking info from above, x has remainder of 5 so:
x = 14, remainder is 5
5x = 70, remainder is 7
x = 23, remainder is 5
5x = 115, remainder is 7
i recall in chapter 10, it only mentions that if you multiply the remainders of x and y, it is equivalent to finding the remainder of xy, but i dont recall it saying that multiplying x by 5 is the same as multiplying Rx by 5 (remainder of x multiplied by 5)
could someone provide the explanation/proof/algebra of why this works?
apologies if this is in the wrong thread
you're given background info, integer x has a remainder of 5 when divided by 9, integer y has a remainder of 7 when divided by 9
question: what is the remainder when 5x - y is divided by 9?
i solved this by picking numbers, but i think that it's probably inefficient.
i did 2 examples and made sure i got the same number
taking info from above, x has remainder of 5 so:
x = 14, remainder is 5
5x = 70, remainder is 7
x = 23, remainder is 5
5x = 115, remainder is 7
i recall in chapter 10, it only mentions that if you multiply the remainders of x and y, it is equivalent to finding the remainder of xy, but i dont recall it saying that multiplying x by 5 is the same as multiplying Rx by 5 (remainder of x multiplied by 5)
could someone provide the explanation/proof/algebra of why this works?
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10 Apr 2013, 20:36
Kudos
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integer x has a remainder of 5 when divided by 9, integer y has a remainder of 7 when divided by 9
question: what is the remainder when 5x - y is divided by 9?
Let x = 9p+5 and y = 9q+7 where p and q are integers.
5x - y = 45p +25 - 9q - 7 = 45p - 9q + 18 = 9 ( 5p - q + 2 ) which is a multiple of 9.
So,the remainder will be zero.
I've explained more algebraically. Since we are dividing all the numbers by 9,we can easily find the remainder in the following way :
x gives remainder => 5
y gives remainder => 7.
5x-y gives remainder => 5 * 5 - 7 = 25 - 7 = 18.
18 when divided by 9,gives remainder 0.
---------------------------------------------------------------------------
Please press +1 KUDOS if my post helps you.
question: what is the remainder when 5x - y is divided by 9?
Let x = 9p+5 and y = 9q+7 where p and q are integers.
5x - y = 45p +25 - 9q - 7 = 45p - 9q + 18 = 9 ( 5p - q + 2 ) which is a multiple of 9.
So,the remainder will be zero.
I've explained more algebraically. Since we are dividing all the numbers by 9,we can easily find the remainder in the following way :
x gives remainder => 5
y gives remainder => 7.
5x-y gives remainder => 5 * 5 - 7 = 25 - 7 = 18.
18 when divided by 9,gives remainder 0.
---------------------------------------------------------------------------
Please press +1 KUDOS if my post helps you.
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
