Converting Words to NumbersDate: 06/03/98 at 21:18:26 From: Cambree Subject: Integers Can you solve this problem? Tell me an integer to describe each situation: 1. 5 degrees below zero 2. a loss of 7 pounds 3. a gain of 10 yards 4. positive twelve 5. 3 feet below sea level 6. 2 degrees above zero Tell me the opposite of each integer: 7. -8 8. 9 9. -15 Date: 06/11/98 at 19:57:26 From: Doctor Peterson Subject: Re: Integers Hi, Cambree, The first set of questions deals with what we call "conventions"; that is, people who use math have generally agreed that certain "directions" should be "conventionally" thought of as "positive." Anything that is "up" or "forward" or "increasing" or "more" is positive, and anything that is "down" or "backward" or "decreasing" or "less" is negative. For example, if I make a profit of 5 dollars in my business, I would call that +5, and if I lose 5 dollars, that would be -5. Why? Because then whichever happens, I can add that number to my bank account to find out how much I have now. Similarly, if a mountain's base is 2 miles below sea level and its peak is 3 miles above sea level, then the altitude of its base is -2 and the altitude of its peak is +3, so the total height is (+3) - (-2) = 5 miles. On the other hand, as I said, these are just conventions, and they really depend on what you're measuring. If I were in a submarine measuring depth, I would say my depth is +2 miles, because when I think about "depth" I mean something that increases as I go deeper. So a depth of +2 means the same thing as an altitude of -2. Therefore, the answer to these questions should include some sort of label. For instance, I would say "altitude = -3" for problem 5. You could also say "depth = +3" if you want to confuse your teacher, but then you'd have to bring me in to testify on your behalf, so maybe you'd better stick with -3. You should be able to do the rest by looking for words like "below" or "loss" to indicate a negative number. Or look on your thermometer and see what they call a temperature below zero. As for the last three questions, "opposite" just means to flip the number line around (stick a pin at the zero and give it a spin) and see where you land. The opposite of -3 is +3, and the opposite of +3 is -3: ------------------+----------+----------+-------------------> -3 0 +3 flips around to give: <-----------------+----------+----------+-------------------- +3 0 -3 so that -3 is where +3 belongs. I hope this helps. Negative numbers aren't hard, but if you're confused, just remember that a few hundred years ago people thought mathematicians who talked about negative numbers were crazy. Let me know if you need more help. -Doctor Peterson, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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