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June 1st, 2016, 10:01 AM  #1 
Member Joined: Mar 2016 From: NJ Posts: 48 Thanks: 2  Multiplication signed numbers question
Hi, I'm reading Dan Hamilton's Mastering Algebra (introduction) and on page 7 he has the following rule for multiplying a negative and positive: a * (b) = a * b = ab He gives examples, such as: 2 * (5) = 2 *5 = 10 and 40 * (9) = 40 * 9 = 360 I don't understand why the negative is being moved to the first number and feel like it's going to confuse me and lead to errors with harder problems in the future. Thanks, Ryan 
June 1st, 2016, 12:27 PM  #2 
Senior Member Joined: May 2016 From: USA Posts: 1,310 Thanks: 551 
Think back to multiplication of two positive numbers. Rule # 1 is $a * b = b * a.$ For example $3 * 7 = 21 = 7 * 3.$ That is a handy rule to know, right. You hardly have to memorize it: you are so used to it that you just think it natural. Now think back to multiplication of three positive numbers. Rule #2 is ${(a * b) * c} = {a * (b * c)}.$ For example {(3 * 5) * 2} = (15 * 2) = 30 = {3 * (5 * 2)} = (3 * 10). Another handy rule. When we get to negative numbers, Rule 3 is $\ a\ MEANS\ + {(\ 1) * a}.$ Understanding that equivalency will let you avoid many problems. Now $\{b * (\ a)\} = \{b * [(\ 1) * a]\}. $ Rule 3 $So\ \{b * (\ a)\} = \{[b * (\ 1)] * a\}.$ Rule 2 $So\ \{b * (\ a)\} = \{[ (\ 1) * b ] * a\}.$ Rule 1 $So\ \{b * (\ a)\} = \{(\ 1) * (b * a)\}.$ Rule 2 $So\ \{b * (\ a)\} = \{(\ (b * a)\}.$ Rule 3 Now see if you can prove to yourself that $\{b * (\ a)\} = \{(\ b) * a\}.$ Last edited by skipjack; June 1st, 2016 at 01:59 PM. 
June 2nd, 2016, 05:43 AM  #3 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 
He is simply trying to tell you that it doesn't matter where the negative sign is.

June 2nd, 2016, 07:53 AM  #4 
Member Joined: Mar 2016 From: NJ Posts: 48 Thanks: 2 
Thanks for the responses. I just thought it was odd he switched the negative to the first number with no explanation. I understand it ends up the same but thought maybe I was missing something. Thanks again, especially for the equivalency examples. 
June 2nd, 2016, 10:48 PM  #5 
Newbie Joined: Jun 2016 From: Cyprus Posts: 2 Thanks: 2 
Anyone here who knows where I can ask questions?

June 2nd, 2016, 10:59 PM  #6 
Senior Member Joined: Apr 2014 From: UK Posts: 955 Thanks: 342 
Church?

June 3rd, 2016, 01:26 AM  #7 
Senior Member Joined: Dec 2015 From: holland Posts: 162 Thanks: 37 Math Focus: tetration  
June 3rd, 2016, 08:50 AM  #8 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902  

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