Math Problems!........share It Here!

[predictable]

my niece is a freshman high school student, and his teacher tells him that a fraction may not have a negative number for its denominator [eg, in 1/(-4), the negative sign should be moved up to align with the fraction bar or with the numerator 1].

 

for some reason, none in his class had the guts to ask the teacher "WHY?" and everyone just accepted it as dogmatic fact, and along with it accepted the fate of their widely similar answers, which were all marked wrong coz they didn't move up the negative sign.

 

i always thought there was an underlying reason (or proof) for everything in math. can anybody shed light on this?

Why 1/(-4) moved up the sign?because if we did not move it u cannot divide the 2 numbers!

 

1/(-4) right? and make it a whole numbers

 

Just get the reciptrocal of 1/(-4)

 

ans? -4/1 why? because if we use reciptrocal we get -4/1 then we can divide it ans? -4

 

1/(-4) equal to -4 the reason is to divide it!

 

 

Im not so sure this answer try to need help in others mtc members!! :sick:

[predictable]

I have a one question

 

divide (x-2) ÷ (3x³-4x²+10x) = __________

 

Post your sulution and answer 2 this question!!

[The_Blade]

Why 1/(-4) moved up the sign?because if we did not move it u cannot divide the 2 numbers!

 

1/(-4) right? and make it a whole numbers

 

Just get the reciptrocal of 1/(-4)

 

ans? -4/1 why? because if we use reciptrocal we get -4/1 then we can divide it ans? -4

 

1/(-4) equal to -4 the reason is to divide it!

Im not so sure this answer try to need help in others mtc members!! :sick:

 

 

but the answer should be -0.25 (if you use the calculator) or -1/4 (move the neg sign up)

 

 

i dont know the answer why should the negative sign be on top of the fraction. but if you ask some proof to prove that 1/(-4) = -1/4 here's one

 

1/(-4) = [1/(-4)] * [-1/(-1)] = 1*(-1)/ (-4)*(-1) = -1/4

[predictable]

It's because of the simple rule in division / multiplication : - / - = +; + / + = +; - / + = - ; + / - = -

 

e.g. 1 / -4 = -1/4 or -.25 ;

-1 / 4 = -1/4;

-1 / -4 = 1/4

gets?

 

 

di nmn yun yung question eh ang question bkit ndi pwedeng lagyan ng negative sign yung

 

denaminator anung piipost nyo dyan explain nyo na lng yun!

[Grimace]

my niece is a freshman high school student, and his teacher tells him that a fraction may not have a negative number for its denominator [eg, in 1/(-4), the negative sign should be moved up to align with the fraction bar or with the numerator 1].

 

for some reason, none in his class had the guts to ask the teacher "WHY?" and everyone just accepted it as dogmatic fact, and along with it accepted the fate of their widely similar answers, which were all marked wrong coz they didn't move up the negative sign.

 

i always thought there was an underlying reason (or proof) for everything in math. can anybody shed light on this?

 

 

It is actually a rule in Mathematics, blue boy..fractions are also called nonnegative rational numbers, its just the rule..a sign, which is either + or - a numerator, which may be any non-negative integer ,a denominator, which may be any positive integer (not zero, not negative). Take it or leave it...ewan ko ba..

 

The denominator cannot be zero or negative! (But the numerator can)

If the numerator is zero, then the whole fraction is just equal to zero. If I have zero thirds or zero fourths, than I don’t have anything. However, it makes no sense at all to talk about a fraction measured in “zeroths.”

 

Fractions can be numbers smaller than 1, like 1/2 or 3/4 (called proper fractions), or they can be numbers bigger than 1 (called improper fractions), like two-and-a-half, which we could also write as 5/2

All integers can also be thought of as rational numbers, with a denominator of 1:

 

and thats the cause of Mathophobia! i hope this helped!

Edited August 20, 2006 by uchisy

[predictable]

kaya nga po.... actually it doesn't matter kung nasa numerator o denominator yung negative sign... pareho lang....

 

-1/4 or 1/-4 or +(-1/4) or +(1/-4) ---> actually there are 3 signs for this fraction... one for the whole fraction; one for the numerator and another for the denominator.

 

to simplify further; we can use the negative sign for the whole fraction and have positive signs for the numerator and denominator ---> -(1/4) or simply -1/4

 

ganun ka simple.

 

Ha? actually i think therr are 2 sign only for any fraction that u have counter because the deminator

have no negative sign in math the denominator positive integer not to be 0 or negative it can be a whole number

 

therefore the numerator and whole number have a sign only if denominator have a sign get the reciptrocal of those

fraction! why in your school? use calculator!!

[predictable]

therefore 2 gays = :evil:

 

therefore 2gays = women

 

2gays is equal to 1 women :boo:

[blueboy]

whoa there! didn't mean to open up the can of worms here, but hey, thanks for the party!

 

 

It is actually a rule in Mathematics, blue boy..fractions are also called nonnegative rational numbers, its just the rule..a sign, which is either + or - a numerator, which may be any non-negative integer ,a denominator, which may be any positive integer (not zero, not negative). Take it or leave it...ewan ko ba..

 

 

 

this is precisely what stumps me, uchisy. can't leave it (as dogma) for now, but i'll take it anytime i see proof or at least a sensible explanation why a denominator can not be a negative integer. i had a similar experience kasi in college, or 'uni' if you will, when the prof marked wrong those answers (mine included) that were not rationalized, ie, 1 / (square root of 2) instead of (square root of 2) / 2. so i asked why. and her answer to my question was a question...

 

prof: sir, what is a fraction?

 

me: a part of a whole, sister (she's a nun)

 

prof: is "square root of 2" a whole?

 

me: aaah, ehhh, i, o, u...?

 

prof: there you go!!

[blueboy]

kaya nga po.... actually it doesn't matter kung nasa numerator o denominator yung negative sign... pareho lang....

 

 

 

that's also what i told my niece off the hip, tina. pareho lang yun! i'll have to ask him again though if they were given explicit instructions to simplify their final answers.

[Guest wackeen]

not all teachers realize that they have to explain 'when to stop' when reducing an algebraic expression. the usual convention is:

 

all fractions should be combined (i.e. greatest common denominator)

 

fractions should be simplified (no common multiples that can 'cancel')

 

negative sign, if any, is at level of fraction bar ('outside' of the fraction, and not part of numerator or worse-denominator)

 

no negative exponents (put in denominator) or fractional exponents/radicals in the denominator (e.g. 1/sqrt(2) should be sqrt(2)/2))

 

trigonometric functions should have an 'angle' between 0 and pi.

 

 

the reason is actually quite antiquated.. but the expression is supposed to be left in a form most easily evaluated. nowadays scientific calculators allow us to evaluate (reduce to a single number) more complicated expressions.

 

otherwise, one can argue that 'it doesn't matter'. in this case it is better to think of following these rules as part of proper grammar and usage. otherwise parang 'barok' ang sagot mo.

Edited August 22, 2006 by wackeen

[Guest wackeen]

to those of you who are bored out there try this:

 

pick a number

 

if it is even, divide it by 2

 

if it is odd, multiply by 3 then add 1

 

whatever the new number is, do the same

 

 

no matter what number you will always seem to end up in a 'loop' of 4,2,1,4,2,1,...

 

it hasn't been proven that this is always the case but it sure feels like it.

 

you'll be surprised how long it takes some numbers to converge. try #27!

[lohengrimtams]

this thread is stimulating. keep it coming. :cool: :mtc:

[encounter_doc]

to those of you who are bored out there try this:

 

pick a number

 

if it is even, divide it by 2

 

if it is odd, multiply by 3 then add 1

 

whatever the new number is, do the same

no matter what number you will always seem to end up in a 'loop' of 4,2,1,4,2,1,...

 

it hasn't been proven that this is always the case but it sure feels like it.

 

you'll be surprised how long it takes some numbers to converge. try #27!

 

The general term for this is the Hailstone number sequence. There is a conjecture (Collatz) that the sequence will always reach 1, no matter what the starting number is. Its just a conjecture, because no mathematical proof has been developed as of yet. Of course, you can always write a program to verify that this is the case, but computer programs dont constitute a proof.

 

Some numbers would take only a few steps before it reaches 1, e.g.

3: 10 5 16 8 4 2 1

 

while some would require quite a bit of iterations but it would still reach 1, e.g.

31: 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1

 

(for those who are really bored, try to find the number of iterations it will take if you start with 77671)

 

anybody can write a simple program that generates this sequence of numbers

 

input n

while n <> 1

if n mod 2 = 0

then n = n div 2

else n = n * 3 + 1

end while

 

But the more general question is, will this algorithm always terminate for any positive integer n (i.e. will it go into an infinite loop for some value of n)? The answer is its impossible to know, because the Halting problem (any computer science graduate who took up a course in automata would know this) is "undecidable", i.e. we cant generate an algorithm that would determine whether the above pseudocode halts or not

 

This what makes math (and theoretical computer science) interesting - there are still lots of conjectures, which at first thought are quite "obviously" correct, but no proof (either to prove or disprove) has been found so far. It's like f*cking your FUBU ... she can't / won't admit whether what she's doing is right nor wrong :-)

[rich_girl]

uh oh! mahina ako sa math

[blueboy]

not all teachers realize that they have to explain 'when to stop' when reducing an algebraic expression. the usual convention is:

 

all fractions should be combined (i.e. greatest common denominator)

 

fractions should be simplified (no common multiples that can 'cancel')

 

negative sign, if any, is at level of fraction bar ('outside' of the fraction, and not part of numerator or worse-denominator)

 

no negative exponents (put in denominator) or fractional exponents/radicals in the denominator (e.g. 1/sqrt(2) should be sqrt(2)/2))

 

trigonometric functions should have an 'angle' between 0 and pi.

the reason is actually quite antiquated.. but the expression is supposed to be left in a form most easily evaluated. nowadays scientific calculators allow us to evaluate (reduce to a single number) more complicated expressions.

 

otherwise, one can argue that 'it doesn't matter'. in this case it is better to think of following these rules as part of proper grammar and usage. otherwise parang 'barok' ang sagot mo.

 

 

well, it turns out my niece's teacher gave her class a similar response--a so-called "negative denominator rule" seemingly pulled out of thin air as she never taught that rule to the class beforehand, but has to be followed nonetheless coz it's the convention.

 

i always thought i had good math teachers back in school, but i dunno why these "conventions" look alien to me. if these are "actually quite antiquated" then perhaps they're now obsolete. i mean why must an expression "be left in a form most easily evaluated" if we're gonna make our calculators/computers/pdas do the evaluating anyway? or, using the above program as an example...

 

input n

while n <> 1

if n mod 2 = 0

then n = n div 2

else n = n * 3 + 1

end while

 

...if the 5th line were:

 

else n = n * (-3/-1) + 1

 

...what is worst possible effect on the result? 26 trillionth of a nanosecond for the extra evaluation to be processed by the cpu before the next line is executed?

 

also, i can't see how the grammar analogy holds.

 

The dog eat the ball.

 

okay, that's barok. but here's a challenge:

 

The ball ate the dog yesterday.

 

can you point out the grammatical error?