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 May 10th, 2010, 03:52 PM #1 Member   Joined: Apr 2010 Posts: 33 Thanks: 0 Integers: Subtracting Negative Numbers I need help with the idea of subtracting negative numbers. I'm reading this Algebra book, and the author provides a real-life example of subtracting negative numbers. Here it is: He says, "Here's a real-life situation where the idea of subtracting a negative number makes pretty good sense. Suppose the people in your town are trying to reduce their driving because of high gasoline prices. They've started a support group. People go to meetings once a month to share information about how much less they've driven in the past month compared with the last month before that. One after another, the members of the group tell their stories. William says, "I drove 45 fewer miles." Anna says, "I cut back by 65 miles." Maria says, "I drove 200 miles less last month!" Then it comes to you. You have not done so well. The group leader asks, "How much did you cut back? Go on, don't be afraid to tell us." You blush, clear your throat, hold your head up, and declare, "I reduced my driving last month by negative 80 miles."" The author doesn't provide a mathematical expression or equation of the real-life example. I know they're subtracting the two months, to end up with the difference, or the "Saved gas mileage." But I don't understand the last guys difference (Saved gas mileage). Did he gain more mileage than the month before the past month. Meaning he done poorly in saving gas. Can someone provide a mathematical expression for the last guy and maybe the other people. Also, can you explain the reason why it makes sense for the last guy to have a driving mileage of -80.
 May 10th, 2010, 04:14 PM #2 Global Moderator     Joined: Nov 2009 From: Northwest Arkansas Posts: 2,766 Thanks: 4 Re: Integers: Subtracting Negative Numbers "saved" has some subtle connotations. If I say, "I saved some money this month on my food expenses", then you would assume that I spent LESS than I did last month. The guy's "driving mileage" being -80 doesn't mean that he drove -80 miles; it means that (last month's mileage) - (this month's mileage) = -80. You see, when you subtract positive numbers, you don't always get a positive number. Consider finding the difference in age between me and my brother. How would you do it... subtract our ages? Maybe an appropriate equation would be: (his age) - (my age) = difference in ages. But as it turns out, I am older, so subtracting my age from his will result in a negative number. One way that you can think of subtraction is "moving left on the number line". So subtracting 6 from a number means going 6 units left from the number. What would subtracting -7 look like? What does it mean to go -7 units to the left??? That would be going RIGHT seven units, which is the same as adding seven!
 May 10th, 2010, 04:50 PM #3 Member   Joined: Apr 2010 Posts: 33 Thanks: 0 Re: Integers: Subtracting Negative Numbers This reply is for "The Chaz" Firstly, your equation "(last month's mileage) - (this month's mileage) = -80," should be (last month's mileage) - (last month's mileage before the last month)=-80, hence the fact that he said, "People go to meetings once a month to share information about how much less they've driven in the past month compared with the last month before that. Lastly, "The author says, "Here's a real-life situation where the idea of subtracting a negative number makes pretty good sense." Where in our equation, do we provide the subtraction of a negative number. As far as I understand, were subtracting positives. That's where I get lost. For instance, take one of the characters in the author's example. Let's take William. Say William drove 90 miles last month, and 45 miles the month before the last month. His saved gas mileage would be 45 miles. In that example we subtracted positives. But for the last character how do you subtract a negative number, and end up with a difference of -80? We have to subtract a negative number because the author said, "Here's a real-life situation where the idea of subtracting a negative number makes pretty good sense." Unless the last character had negative mileage for the last month, and a positive mileage for the month before the last month. Something like, -120 - (-40) = -80. But that wouldn't make sense right? Do you understand. By the author saying, "Here's a real-life situation where the idea of subtracting a negative number makes pretty good sense.", we would have to minus a negative number for all the characters right?
 May 10th, 2010, 05:39 PM #4 Global Moderator   Joined: Dec 2006 Posts: 20,927 Thanks: 2205 There's nothing in the illustration to suggest that -80 is what you end up with. The "last guy" said "I reduced my driving last month by negative 80 miles." Since "reduced" implies subtraction, the implied equation is "miles I drove last month" = "miles I drove in month before that" - "negative 80 miles". As The Chaz pointed out, subtracting a negative value means adding the corresponding positive value. Hence the statement meant that their mileage in the last month was 80 miles greater than their mileage in the month before that. They tried to make the fact that their mileage had increased less noticeable by referring to the increase as a reduction by a negative amount. For each member of the group, "miles driven in month before last" - "miles driven in last month" gives the reduction achieved. In the "last guy"'s case, this subtraction would give -80 miles. I think an easier to understand example would be a statement such as "The temperature was -2 degrees Celsius last night and 6 degrees Celsius this morning; though last night's temperature was 8 degrees lower than this morning's (since 6 - (-2) = 8), it still felt quite chilly this morning."
 May 10th, 2010, 06:31 PM #5 Member   Joined: Apr 2010 Posts: 33 Thanks: 0 Re: Integers: Subtracting Negative Numbers This reply is for "The Chaz" I apologize. You were right for the most part, but the only thing I point out is that "skipjack" said, the equation would be "miles driven in month before last - miles driven in last month" gives the number you use as a negative in the subtraction problem," which is correct. Not "(last month's mileage) - (this month's mileage) = -80."
 May 10th, 2010, 06:41 PM #6 Global Moderator     Joined: Nov 2009 From: Northwest Arkansas Posts: 2,766 Thanks: 4 Re: Integers: Subtracting Negative Numbers "month--"
 May 10th, 2010, 06:47 PM #7 Member   Joined: Apr 2010 Posts: 33 Thanks: 0 Re: Integers: Subtracting Negative Numbers This reply is for the "skipjack". You are 100% right. It's so clear now. They used their "increase as a reduction by a negative amount," to make it seem unnoticeable.
 May 11th, 2010, 04:29 AM #8 Global Moderator   Joined: Dec 2006 Posts: 20,927 Thanks: 2205 Actually, Mighty Mouse Jr, the equation posted by The Chaz was mathematically correct, but easily misinterpreted as it used "last month" to mean the month preceding what the author referred to as the "past month", and "this month" to refer to what the author called the "past month". However, your correction did get the terms the wrong way round.

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