"Vincent Johns" <firstname.lastname@example.org> wrote in message news:7GZ8e.8666$An2.email@example.com... > Sally wrote: >> "ticbol" <firstname.lastname@example.org> wrote in message >> news:email@example.com... >> >>>x/4 +y/3 = 1 >>>Multiply both sides by 3*4 >>>(x/4)(3*4) +(y/3)(3*4) = 1(3*4) >>>(3*4*x)/4 +(3*4*y)/3 = 12 >>>3x +4y = 12 >>>That is how. >>>(I hope you know how to cancel quantities that are common to both >>>numerator and denominator in the same fraction.) >>> > [...] >>> >>>>Are you saying that to clear those two specific >>>> fractions above, (x/4 & y/3), I should multiply >>>> them both by 12? Product of 3 & 4? >>> >>>Yes. >>>We have to multiply x/4 by 4 so that the fraction will "clear" or be >>>"removed" or be changed to a whole number. >>>Likewise, we have to multiply y/3 by 3 to to clear this fraction. >>>Why 3*4? >>>Because those are the denominators. >>>We multiply x/3 not by 3 only. We multiply it by the product 3*4 which >>>is 12, of course. (Later on in your studies you will find why it is >>>better to leave it as 3*4 than 12.) > [...] >>> >>>Regards, >>>ticbol >> >> Okay, I now understand how to work these problems with your method of >> multiplying both sides by the product of the denominators. Thank you once >> again ticbol for your assistance. And I will take you up on the keep >> asking questions when I run into future problems. Much appreciated ;) > > When you learned to add fractions containing only integer constants, such > as > > 3/4 + 1/6 > > you were probably told that you needed to convert these to equivalent > fractions that shared a denominator (or divisor, or number below the > fraction bar), which is correct. > > You were probably also told that the only correct denominator to use was > the lowest common multiple (LCM) of the two denominators; in the case of 4 > and 6, this would be 12 = 4 * 3 = 6 * 2 . This is not really correct; any > common multiple will do, it's just that the LCM keeps the arithmetic > simpler, since you deal with smaller numbers. But you could simplify > > 3/4 + 1/6 > > by rewriting it as > > (3/4)*(6/6) + (1/6)*(4/4) [multiply top & bottom of each fraction > by the denominator of the other fraction] > = (3*6)/(4*6) + (1*4)/(6*4) > = (18)/(4*6) + (4)/(4*6) [simplify top of each fraction] > = (22)/(4*6) [add tops (numerators or dividends)] > = (11*2)/(4*3*2) [factor 2 out of top & bottom] > = (11)/(4*3) [divide top & bottom by common factor 2] > = 11/12 > > You get the correct answer this way; it just involves the extra step of > reducing the fraction by dividing top & bottom by 2, which you would not > have needed to do if you'd used the LCM of 12 instead of 4*6 = 24. > > Many times you'll have denominators like (x + 13) which have no factors, > so looking for an LCM that is less than the product of the denominators > would just be a waste of time; it's often simpler to follow ticbol's > advice and just multiply the denominators. Expressing denominators as a > product of factors, such as (3 * 4) instead of (12), makes it easier to > cancel common factors on top & bottom of a fraction, but this is perhaps a > matter of personal preference. > > Your final answer, however, should normally be expressed in lowest terms, > with no factor common to both top and bottom; (2/3) is preferable to > (4/6). Mathematically, there's no difference, but fractions in lowest > terms are usually easier to understand and work with, so expressnig them > in lowest terms is customary. (For any purists reading this, notice that > I said "usually"; I know there are exceptions -- you write for your > intended audience.) > > -- Vincent Johns <firstname.lastname@example.org> > Please feel free to quote anything I say here.
Hi Vincent, thank you for taking the time to explain this to me. With enough help/pratice I have figured out how to work the solutions to the problems I was working on. I truly appreciate your assistance.