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Daughter's math homework (1 Viewer)
- Thread starter MrPack
- Start date
The "-" I am referring to is the stand alone "-" that is often found at the beginning of numerals and expressions such as "-5", "-5x", "-5^2", etc.The "-" you are referring to in your reply is commonly called a "subtraction" sign. By definition, subtracting is merely "adding the opposite". In your "3 - 2" example, we can rewrite it as "3 + (-2)" which can be read as "three plus negative two" or "three plus the opposite of two".
This must be a slow Friday
You could write it like that or "-(-1)" or "+1" or simply use the conventional notation of "1".
Well let him know.
That's a longer way to write it, but sure.
Yes I is a math teacher. Below 50 is cold to me.
Buckychudd
Footballguy
So the negative apple thing didn't get you?
Paper Lions
Footballguy
He made an assumption and then answered it correctly pursuant to his assumption. He just doesn't know the convention. He must have been advanced in Junior High tooWell let him know.
Buckychudd
Footballguy
Not even remotely.
rolyaTy
You're Heinous
I'd explain it this way
retty much all math, from basic 2+2=4 up to differential calculus, is based on the addition of numbers. To understand addition, you have to understand what is actually being done to the two values in question.Take 2 and 2. Both of these are magnitudes of an arbitrary unit. They could represent houses, planes, or internet geeks who post too much on silly topics. The best way to conceptualize what is happening when you add two and two, is to draw a number line. On the number line, you start with your pencil tip at zero, and draw a line from zero to two. Your new origin is 2 now and you go two more to the right (default direction). The total displacement is the answer, and you have traveled across 4 units.When you want to move to subtraction, the concept of direction comes in and it can be taught a number of different ways. You can introduce negative numbers and positive numbers, and show that negative is the left direction and positive is the right direction.So if you want to subtract 1 from 2, (2-1), you start at 0, draw a line from 0 to 2, and then draw a line ONE unit in the negative direction from 2, or left from 2. Your total displacement from 0 is 1 unit. This is absolutely the same as saying (2+(-1)), as the sign only indicates the direction you travel on the number line. The important thing is the value, and the total displacement. On the number line, you cannot have a negative distance traveled (as you can't have a negative length of your line from 0 to your end point), but you can have a distance traveled in the negative or positive direction.So when someone says -5, and you look at it with respect to the number line, it is simply saying that you travel five units in the negative direction. The negative sign tells direction, and the 5 tells distance. The two are clearly separate entities.This becomes an issue in multiplication (which is really fancy addition). So, you have 2*5. Start on the line at 0, and go five in the positive direction, twice. Total displacement is 10 units.Now try -2*5. You can do this another way, by going 2 in the negative direction 5 times, or 5 in the negative direction twice. Clearly, the direction is detached from the values.So now you have (-5)^2. You factor it out to (-5)(-5) and it looks confusing because you have two direction components. But just like double negatives, they cancel each other out because they are SEPARATE from the numerical values themselves. Two neg's make a positive, and you have (5)(5) and you go 5 units in the positive direction five times.So, basically, it should be obvious that the sign and the value are separate entities UNLESS they are explicitly grouped together.-5^2 is basically the negative direction of the result of 5^2, or (5)(5).
retty much all math, from basic 2+2=4 up to differential calculus, is based on the addition of numbers. To understand addition, you have to understand what is actually being done to the two values in question.Take 2 and 2. Both of these are magnitudes of an arbitrary unit. They could represent houses, planes, or internet geeks who post too much on silly topics. The best way to conceptualize what is happening when you add two and two, is to draw a number line. On the number line, you start with your pencil tip at zero, and draw a line from zero to two. Your new origin is 2 now and you go two more to the right (default direction). The total displacement is the answer, and you have traveled across 4 units.When you want to move to subtraction, the concept of direction comes in and it can be taught a number of different ways. You can introduce negative numbers and positive numbers, and show that negative is the left direction and positive is the right direction.So if you want to subtract 1 from 2, (2-1), you start at 0, draw a line from 0 to 2, and then draw a line ONE unit in the negative direction from 2, or left from 2. Your total displacement from 0 is 1 unit. This is absolutely the same as saying (2+(-1)), as the sign only indicates the direction you travel on the number line. The important thing is the value, and the total displacement. On the number line, you cannot have a negative distance traveled (as you can't have a negative length of your line from 0 to your end point), but you can have a distance traveled in the negative or positive direction.So when someone says -5, and you look at it with respect to the number line, it is simply saying that you travel five units in the negative direction. The negative sign tells direction, and the 5 tells distance. The two are clearly separate entities.This becomes an issue in multiplication (which is really fancy addition). So, you have 2*5. Start on the line at 0, and go five in the positive direction, twice. Total displacement is 10 units.Now try -2*5. You can do this another way, by going 2 in the negative direction 5 times, or 5 in the negative direction twice. Clearly, the direction is detached from the values.So now you have (-5)^2. You factor it out to (-5)(-5) and it looks confusing because you have two direction components. But just like double negatives, they cancel each other out because they are SEPARATE from the numerical values themselves. Two neg's make a positive, and you have (5)(5) and you go 5 units in the positive direction five times.So, basically, it should be obvious that the sign and the value are separate entities UNLESS they are explicitly grouped together.-5^2 is basically the negative direction of the result of 5^2, or (5)(5).
That's possible. Or his teacher was wrong. Or his teacher didn't teach him well. Or he didn't pay attention. Or he forgot.He made an assumption and then answered it correctly pursuant to his assumption. He just doesn't know the convention. He must have been advanced in Junior High tooWell let him know.
I have created no new Clayton Theory in this thread.
Paper Lions
Footballguy
Maybe you were caught passing a note and had your head down?(Man I miss that.
)
poopdawg
Footballguy
Simple. By definition, a negative number is formed by multiplying that number by -1. Since multiplication is involved, you would first perform the exponential part first, therefore arriving at -25. If -5 had been in parenthesis, then the answer would be 25. -1x5^2 + 4x2^3 = 7. I cant believe there has been this many posts about this.
Paper Lions
Footballguy
Let's just blame Smoo's teacher. And mine. And most everyone's teacher.
The Iguana
Footballguy
WOW! I'm glad work kept me busy today... I can't believe this has grown all the way to 27 pages!I wrote down the equations and gave them to a guy here at work that is the ultimate math geek, so much so that he has actually written a couple of math books for educational use. He quickly, without thinking twice, rattled off the answers as -7 and 18. I gave him a brief synopsis of this thread and he just kind of chuckled. The only way you answer this any other way is to make up your own rules for calculating the value of expressions or making assumptions that aren't in the equation.
Paper Lions
Footballguy
No one is disputing that this is the current convention. Smoo doesn't like the convention.
Buckychudd
Footballguy
He probably wrote the textbook that this trick question appeared in.
More specifically, negative five is a self-contained number, and you can represent negative just fine by writing "-5" since -5 = (-5) = -(5) = (-1)(5) = "negative five".The problem comes when you write "-5" as part of a larger expression, combining it with other characters. When you do that, you have to apply rules about what the other characters mean and what happens when you combine them.
In the same way, twenty-three can be represented just fine by writing "23". But when you combine that with other characters so as to write, for example, "1,236" now the "23" no longer means twenty-three.
Similarly, when you write "-5^2," now the "-5" no longer means negative five.
My experience is that some very advanced math students are deficient in some basic math operations.Your theory was that some people went to some advanced math class and missed the dummy math class where they covered this stuff.
Paper Lions
Footballguy
I've been torn if I think that this is a stupid math question or not to give a kid. On one hand, it's not even testing the order of operation, it's testing math convention in the absense of clear instruction. On the other hand, I apparently needed to be taught this and was not.I presently think it's a great math question and the teacher should win some sort of teacher award, provided she explains it clearly.
How is that mysterious? Negative means opposite and the opposite of a negative is a positive, so a negative negative is a positive.
Buckychudd
Footballguy
Go ahead defy convention, use your base 50 system.
rolyaTy
You're Heinous
It's a pure logic problem. -5 times -2 consists of four important parts. 2 directions and 2 values. Since direction and values are independent, you can separate them logically into (--) direction and (5*2) value. (--) direction is the same thing as "Not Not" something, and as we all know, double negatives cancel each other out, as does reversing a direction twice.So a negative basically reverses the default direction, which is positive. Two negatives reverse the direction twice, which basically results in you going the default direction. Then you are left with simply going the correct distance in the proper direction.
Smoo
Fear the Beaver
It was mysterious in the context of the framework world he constructed. He was carefully explaining how everything was represented on his number line model, but then just pulled "oh, and two negatives cancel each other out" from nowhere, without explaining it within the context of his framework.
A lot of people were disputing it until Shick! and Clayton got here. Some people were ridiculing anybody who went along with the (apparently) standard convention.
Paper Lions
Footballguy
Following the convention, I don't see the problem.(-25)^.5 = (-25)^.5
If you wrote ((-5)^2)^.5 = (-25)^.5 you would have changed the problem, no?
Smoo, you tried to hack at this, but tell me what else is wrong here:
Geez, didn't think the concept was that difficult to require explanation. Negatives reverse the direction on a number line. That should answer the problems.Think in Grammar. This is not not an easy problem.
