Why is it that when you divide fractions & change it to multipilcation you have to use the invert to solve it?
151310
Division is opposite of multiplication.  Inverting a fraction creates the opposite function.
865685
You did mean 1/s not (1-s), right?\n\nYou can't invert when two fractiona are added.  You must combine 1/f - 1/s, THEN invert.\n\n1/f - 1/s = s/fs - f/fs = (s-f)/fs\n\nNow invert: s' = fs/(s-f)
620710
A prime number cannot be divided to simpler terms, you cannot multiply two numbers to get to it, a fraction with that number in the numerator or denominator cannot be simplified... its relatively illogical and impossible to use an equation to find a number that can't be divided, multiplied, or simplified. \n\nIn simpler terms, in order to find a solution to ANY answer the solution has to have clues, probabilities, a paper trail, something....
188200
I had trouble with the same thing. The best way, and it's worked till now in college, is to take the most complicated element used (i.e. CH3OOH + C2H3O9 ---> etc), figure out O's first since O is used the most. Then work backward using the 2nd most used element. You might get a non-reduced form of balancing, but you can check whats divisible (i.e.  4CH + 2 CH2H3O2 <---> 4 OH + 2 CH3; all divisible by 2 so it'd be 2, 1, 2, 1 respectively). See if this works, it's worked when I've helped other people in the past as well.
460346
You can try multiplication since it is the inverse property of division.
1061582
Since it's multiplication you can multiply the fractions in any order.  Use that to your advantage.  Multiply the 4/15 * 3/4 first, the 4s are diagonal so you can cancel them out.  3 and 15 are both divisible by 3, so go ahead and cancel a 3 factor out in each there.  Now we're left with 1/5 * 1/1, which gives us 1/5.  Multiply the 1/5 by 7/12 to get 7/60.  \n\nHope this is helpful.
889540
I have taken the liberty of listing one or two good references as links below.  But I can give you a very brief explanation here:\n\nWe say two quanities are "in proportion" if they behave in such a way that the size of one directly affects the size of the other.  The relationship between the two quantities (let's call them 'x' and 'y') does not need to be "equal;" it could just as easily be "twice as much as" or any other ratio that you like.\n\nHow does this show up in equations?\n\nIf x and y are related by "x is twice y", we might write: x/y = 2/1.\nNotice how fractions appear on both sides of the = sign.  Most students learn to expect fractions in any "proportion problem."  Many textbooks, however, would write this equation x = 2y.\n\nContinuing with our example of x:y = 2:1 (read "x is to y as 2 is to 1"), it's fair to say that we can find one value if we know the other.  Suppose y=3.  What is the value of x?  Here's how you solve that using an equation:\n\nx/(3) = 2/1  where I've substituted '3' in place of 'y'\n\nNow, we "cross multiply" -- a handy way of simplifying a "fraction equals a fraction" equation -- and we get:\n\n1x = 3 * 2\nSo, x=6\n\nDoes that make sense?  Sure, because we expected 'x' to be twice the value of 'y' all along.  Six is twice three!\n\nSo far, I have been discussing a "direct proportion" where one quantity growing larger causes the other to grow larger.  Using the above example, if we said the value of y were 10, then x would be 20.  And so on.\n\nBut there are times when the opposite happens -- one variable shrinks in value whenever the other grows.  This is called "inversely proportional", and a typical problem goes like this:\n\nX and Y are inversely proportional.  X equals 15 when Y equals 5.  Find X when Y equals 25.\n\nFirst, we set up the inverse proportionality:\n\nX = c/Y\n\nThe only 'problem' is that we do not yet know the value of the "constant of proportionality" c.  Let's find it!\n\n15 = c/5\n\nMultiply by 5:\n\n75 = c\n\nRe-write the equation, replacing 'c' with 75:\n\nX = 75/Y\n\nThe problem I posed asks for the value of X when Y=25.\n\nSubstitute:  X = 75/(25) = 3\n\nAs predicted, X got smaller when Y grew!\n\nI hope this helps introduce you to the world of Proportions!
1025264
pls specify ur question, didnt quite understand it\n\nIf there is "OR" u have to add and if it is "And" u have to multiply.
210386
I think the point may be to use synthetic division.  Look that up in your text.
163557
well to make it easy... 2/4+1/4= 3/4 because when you have the same denominator, or the one below the line, you can just add the numerators, or the ones on top. remember that the numerator is over the denominator
195987
although there can be some patterns seen in the numbers it is not a repeating decimal and can be taken out to a lot more decimal places then humans can calculate.  Also if you put it into fraction (22/7) that is the most accurate way to actually utilize the number.
1187434
I think that's dalton's law.  Whoever came up with it, the pressure is additive.  So convert so everything is in the same units, multiply by the percent, add, and then compare to the answers.  I bet it's more fun than you predict.  Whooo!  Conversion factors!  I don't want to take that kind of enjoyment away, so get cracking!
920569
It looks like you are trying to solve a literal equation, which is an equation with more than one variable, and you have to solve for a specified variable.  You can use the SAME rules to solve this kind of equation as you do with regular equations (those with numbers).  For example, if you had 8=2(b)(9), you would divide by 2 and then again by 9 (which is like dividing by 18).  \n\nIf your problem is a=(1/2)bc^2, then you would divide by 1/2 and then again by c^2.  Remember that to divide by a fraction, you multiply by the reciprocal.
944997
you divide or multiply by a negative numberand the sign of inequality flips
593727
I can remember upto 4 to 5 ways of doing it and not more than that.  btw you are talking about halving a square (diagram)! Right ?
92491
OK, first off no one seemed to be able to answer the dividing by 0 and 1 issue correctly, so here goes...\n\nDivision by n is defined as multiplication by the multiplicative inverese of n.  The multiplicative inverse of n is defined as the number 1/n such that n*(1/n)=1.  Zero has no multiplicative inverse because 0 times anything is 0.  Therefore division by zero implies multiplication by a number that does not exist.  One does have a multiplicative inverse (1x1 = 1), so division by 1 is perfectly valid, although you are correct that the result is the number which was divided by 1.  It is exactly the same as multiplying by 1.\n\nNow on the area of a circle issue...\n\nYou seem to be trying to relate area to circumferance.  It's not hard.\nLet A = the area of the cirlce, c = the circumferance, and r = the radius.\nYou already know that A=(pi)r^2 and c=2(pi)r.\nSolve the second equation for r and get r=c/(2pi).\nNow substitute that into the first equation to get A=(pi)(c/(2pi))^2.\nThen simplify and you get A=(c^2)/(4pi).\n\nLike it or not, you can't get rid of the pi.  Pi is defined as the ratio of the diameter of a circle to its circumference, so it's going to be there no matter what.  When you say it's useless unless you know all the digits, this simply isn't true.  Depending on what you're doing, you can either get the pi's to cancel out, or you will be finding a decimal approximation of the area or circumference.  If the radius is a whole number, the area simply won't be (there may be a few values for which it will be, but most of the time it isn't), and any formula you come up with that says otherwise is incorrect.\n\nAs for the sphere question, I don't understand what you're asking.  Are you trying to equate area to volume?  They're not the same thing.  You can't find the area by sticking together infinitely thin slices as the slices have no height so you will never have a third dimension.  You might be able to do it using limits, but that's not going to be the kind of nice simple numbers you're looking for.  If you can explain what you meant, I might be able to do a bit better.
342027
hahahah that doesn't make sense in order for two sides of an equation to be equal the numerical value of each side must be the same.  Whats with all the equals signs!