Posted: 8/21/2014 5:14:55 PM EDT
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The wife and I are having a difference of opinion on how to evaluate a particular equation. The kids are using Saxon math this year and they teach them to evaluate the equation: -3 squared + 4 = -5. They treat the negative at the front of the equation as a separate item, so they say you should evaluate the 3 squared first, giving you 9, then make it a negative, giving you -9, and then add 4, giving you a total of -5.
Eta: problem is written as -3^2 + 4 = x. What is x? As you can see, there are no parenthesis. The way I was taught was that if a negative number was at the beginning of an equation, and it didn't have a parenthesis around the number so that it looked like -3 squared, then you should treat it as the equivalent of -3 times -3, thus giving you 9. Therefore, I was taught to evaluate -3 squared + 4 = 13. It would be the equivalent of (-3 times -3) + 4 = 13. Now, if I saw - (3 squared) + 4, with the parenthesis around the 3 squared, then I would evaluate that as -5 since the 3 squared would be done first, then a negative applied. So.... which is right? Posted Via AR15.Com Mobile |
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-3^2+4 = -5
(-3)^2+4 = 13 The base for the exponent 2 is 3, not -3. so -3^2 is -9 (-3)^2 says the whole -3 is the base. You can use wolfram alpha if you want to double check http://www.wolframalpha.com/input/?i=-3^2%2B4 |
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-3^2 + 4 = 13 -(3^2) + 4 = -5 But there's no parenthesis on the first number in the equation in their books. FWIW, if you type in -3 squared + 4 = into google and hit enter it says it's -5. Doh... But, if you type in (-3) squared + 4 = and hit enter, you get 13. |
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the negative sign in front of the base, 3, tells you its the opposite of 3 squared. or -1x3^2 you square the three, multiply by negative 1. If it were -(3^2) you would multiply by negative 1. -3^2 is (-3 x -3) Edit: at least that's how they were still teaching it when I graduated last year |
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4 - 3^2 = -5 (-3)^2 + 4 = 13 I would say presenting the formula the way you describe was sloppy, at best. It might be deliberately sloppy to create some discussion in class but to me, that would be a very BAD teaching approach. Nice way to demonstrate that saying "-3 squared + 4 = -5" is equivalent to: 0 - 3^2 + 4 which would be -5 |
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I was taught that if you wanted the result the teacher wanted, you wrote -(x2). Same here. Now, it's apparently implied that is the case (at least with Saxon math). So, if somebody asked me what -3 squared was, I'd have said 9 (-3 * -3) = 9, or I'd have asked if there were any parenthesis around the 3. If there were parenthesis around the 3, I'd have said it was -9. But, I can throw -3 squared in the calculator on my phone and it says -9. Grrrr... ETA: From the looks of the poll it looks like a LOT of folks were taught the same way I was regarding the way to treat that -3 squared without any parenthesis at the front of the equation. Interesting. (or maybe they're trolling the poll, which GD has never been known for) 
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that makes more sense. Quoted:
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the negative sign in front of the base, 3, tells you its the opposite of 3 squared. or -1x3^2 you square the three, multiply by negative 1. that makes more sense. negitive ghost rider. According to rob99rt then a negative number squared is a negative number which is impossible. A negative number squared is always a positive number. The base is negative. -3^2 =9 -(3^2)=-9 ETA: re-read your statement you are correct. |
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PEMDAS If equation is written -3squared + 4, answer is 13 if equation is written - (3squared) + 4, answer is -5 All depends on how they laid out the equation. I'd agree with your assessment based upon how I was taught math, but there are no parenthesis in the equation in the book and they say -5. Just seems odd to me. |
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Quoted: -3^2 + 4 = 13 -(3^2) + 4 = -5 ETA: Perhaps it's just my programming bend, but I parsed it as (-3)^2 + 4. If you specifically want to negate the square it should be -1 * 3^2 + 4. This my whole reason for going on random rants about the sins of implicit multiplication notation. |
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Quoted: 4 - 3^2 = -5 (-3)^2 + 4 = 13 I would say presenting the formula the way you describe was sloppy, at best. It might be deliberately sloppy to create some discussion in class but to me, that would be a very BAD teaching approach. |
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PEMDAS If equation is written -3squared + 4, answer is 13 if equation is written - (3squared) + 4, answer is -5 All depends on how they laid out the equation. In PEMDAS the E for exponent takes place before multiplication. The negative sign in front of a exponent base basically means multiple by -1 after performing the exponent. Both your examples are the exact same thing, the () are not needed. The answer to both your examples is -5 to get 13 it would have to be written as (-3)^2+4=13 Wow: I just realized 87% of GD don't know the correct answer to this 6th grade math problem. For those interested in learning here is a link to the correct way to perform exponents: Link ETA: Based on OPs request BS in Mechanical Engineering. |
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Ok, so wife and I are talking and based upon the poll results, how would this equation be solved?
10 - 5^2 = ? Because, based upon the poll, it would seem that folks would evaluate that as 35 (10 + 25) since the second operation would be treated as -5 * -5, thus giving a positive 25 to be added to the 10. However, it's actually 10-25 = -15. Therefore, it would seem based upon that, then -3^2 +4 does equal -5. BTW, Jenny's wondering what level of math folks have completed who answered one way or another, so if you wouldn't mind ETA-ing, we'd appreciate it. |
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Ok, so wife and I are talking and based upon the poll results, how would this equation be solved? 10 - 5^2 = ? Because, based upon the poll, it would seem that folks would evaluate that as 35 (10 + 25) since the second operation would be treated as -5 * -5, thus giving a positive 25 to be added to the 10. However, it's actually 10-25 = -15. Therefore, it would seem based upon that, then -3^2 +4 does equal -5. BTW, Jenny's wondering what level of math folks have completed who answered one way or another, so if you wouldn't mind ETA-ing, we'd appreciate it. 10 - 5^2 = ? 10-25 -15 |
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Quoted: -3^2+4 = -5 (-3)^2+4 = 13 The base for the exponent 2 is 3, not -3. so -3^2 is -9 (-3)^2 says the whole -3 is the base. You can use wolfram alpha if you want to double check http://www.wolframalpha.com/input/?i=-3^2%2B4 You beat me to it. I should put the OP in one of my slides for class this year.
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Ask their math teacher. He or she should agree with you. We're the teachers... Homeschooling. That's the reason we want to get it right because this evaluation of the equation is just a tad important for higher math. I've got a BA in Computer Info Systems and Accounting, and Jenny's an RN. It's just goofy that I was taught the order of operations one way and she another for the leading number of an equation if it's a negative with an exponent. That's the hitch.... |
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And what these types of problems illustrate so well, yet always seems to be lost on so many, is that ambiguity is bad.
Don't write shit that can be easily misinterpreted. Just put some parentheses (or other accepted grouping characters) to make it absolutely clear what is supposed to be evaluated. This is especially true when dealing with variables. Realize that IRL, people will make assumptions about what somebody meant, and not necessarily what they wrote, when it comes to ambiguous situations like this. That is, they think "yeah, he wrote it like that, but he probably meant this instead". So even if someone were not just misinformed as to the nuances of certain mathematical syntax, they could still make the wrong call by "correcting" something that didn't need to be fixed. So best to make it unambiguous. |
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The way I learned math (and the last math class I ever took 11 years ago was Calc IV), the answer is 13. But now I'm second guessing myself, because I can also interpret any number as 1n. So since 1n = n and -1n = -n, in order to satisfy the equation, it must be -1(3^2) + 4 = -5.
So, OP, I voted 13; But after reconsidering, I would change my answer to -5. |
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I was taught as you were OP. -3^2 would be 9 and -(3^2) would be -9. I think so long as the understanding of the underlying mathematics is there, it's fine. I wish it was that easy, but it's not... The way I was taught to use the exponent (if no parenthesis are present) was to multiply the negative number times itself that many times. However, that screws you up when it's an even exponent. So, -3^2 the way I was taught (if negative number being squared at the beginning of an equation) would give you positive 9. However, if it was -3^3, I would have evaluated it correctly as -27. So, -3^1, -3^2, -3^3, -3^4 would have evaluated the way I was taught to be -3, 9, -27, 81. However, it's in reality -3, -9, -27, and -81, respectively. So, I was taught it incorrectly according to a lot of things on the web. Funny thing is, I made A's in math in HS, so either I didn't hit that many problems like this or the text books had problems like this computed incorrectly. |