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 April 12th, 2014, 12:10 PM #1 Senior Member   Joined: Nov 2013 Posts: 434 Thanks: 8 rest if we divide n by 7 rest =3 if we divide 5n+4 by 7 what the rest April 12th, 2014, 01:28 PM #2 Global Moderator   Joined: May 2007 Posts: 6,807 Thanks: 717 5x3 + 4 = 19, mod 7 = 5. April 12th, 2014, 05:37 PM   #3
Math Team

Joined: Dec 2006
From: Lexington, MA

Posts: 3,267
Thanks: 408

Hello, mared!

Quote:
 If we divide $\displaystyle n$ by 7, the remainder is 3. What is the remainder if we divide $\displaystyle 5n+4$ by 7 ?

We are told that: $\displaystyle \;n \:=\:7a+3$ for some integer $\displaystyle a.$

Then $\displaystyle \:5n+4 \;=\;5(7a+3)+4 \;=\;35a + 15 + 4 \;=\;35a + 19$

Hence: $\displaystyle \;\frac{5n+4}{7} \;=\; \frac{35a+19}{7} \;=\;5a + 2 + \frac{5}{7}$

Therefore, the remainder is $\displaystyle 5.$ Tags rest Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post mathkid Physics 9 February 1st, 2013 06:03 PM poisonpoison Algebra 0 October 15th, 2011 01:00 PM Rem700PSS Algebra 1 January 31st, 2010 05:05 PM mathkid Algebra 0 December 31st, 1969 04:00 PM

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