Question

Need.Math.Help.Very.Badly.In.Comments.

Answer 1

\[\frac{x}{9}-\frac{4}{3}=x-\frac{5}{6}\] I don't know how to do this, please help me!

Answer 2

@ajprincess @ash2326

Answer 3

What is the least common multiple of 3, 6, and 9? Multiply the whole equation by that number and you should be in good shape

Answer 4

\[\frac{x}{9}-\frac{4}{3}=x-\frac{5}{6}\]Multiply through by 18
\[18*\frac{x}{9}-18*\frac{4}{3}=18*x-18*\frac{5}{6}\]\[2x-24=18x-15\]Collect like terms\[2x-2x-24+15=18x-2x-15+15\]\[-9=16x\]\[x=-\frac{9}{16}\]

Answer 5

Okay, I'm REALLY confused now.

Answer 6

there less information to take in now >_>

Answer 7

No, just both of you talking at once is really confusing me. One at a time.

Answer 8

And dan, you're the one that really helped me (also for not just giving me the whole problem). so have fun with a medal.

Answer 9

I chose 18 because it is the least common multiple of 3, 6, 9. To find the LCM, you can either make a list of multiples:

3: 3 6 9 12 15 18 21 24
6: 6 12 18 24
9: 9 18 27 36

18 is the first number that appears in each list

Or factor each number:
3: 3
6: 2*3
9: 3*3 = 3^2

Multiply together the highest power encountered of each factor: 2*3^2 = 2*9=18

Answer 10

lisn to whpalmer he is a good teacher

Answer 11

what Dan and I are doing is essentially the same thing. he goes around the tree to the left, I go around the tree to the right ;-)

Answer 12

yes this is your lesson one
there are many ways to solve one math question

Answer 13

just dont get too restricted to one way, understanding all ways will help you get a grasp on math faster

Answer 14

Not when your dyslexic and you can't do variables very well. >.< Thanks to both of you guys at least.

Answer 15

oh that sucks!!

Answer 16

the underlying concept we both make use of is that you can multiply a fraction by the same number top and bottom and you don't change its value.

for example:

\[\frac{1}{2} = \frac{1}{2}*\frac{3}{3} = \frac{3}{6}\]If you divide 1 by 2 on your calculator, you get 0.5. If you divide 3 by 6 on your calculator, you also get 0.5.

So, what Dan was doing is multiplying each fraction by another fraction which has the value 1, but converts the denominator to a common denominator so you can add them all together. Here, I'll typeset it:

\[\frac{x}{9}-\frac{4}{3}=x-\frac{5}{6}\]If we need to add and subtract those fractions, we need to use a common denominator. As I showed above, 18 is the least common multiple of the denominators in this problem, so we'll make each fraction into one with 18 as the denominator. 9*2 = 18, so the x/9 gets multiplied by 2/2. 3*6=18, so the 4/3 gets multiplied by 6/6. 6*3=18, so the 5/6 gets multiplied by 3/3. Finally, we multiply the solitary\(x\) by 18/18 to give it a common denominator with the rest.

Answer 17

\[\frac{x}{9}*\frac{2}{2}-\frac{4}{3}*\frac{6}{6}=x*\frac{18}{18}-\frac{5}{6}*\frac{3}{3}\]\[\frac{2x}{18}-\frac{24}{18}=\frac{18x}{18}-\frac{15}{18}\]Now we can add and subtract the fractions and rearrange to get all of the \(x\)'s on one side, and the numbers on the other. Because there's a bigger coefficient of \(x\) on the right, I'll move the other \(x\) of there, and the numbers to the left.\[\frac{2x}{18}-\frac{2x}{18}-\frac{24}{18}+\frac{15}{18}=\frac{18x}{18}-\frac{15}{18}-\frac{2x}{18}+\frac{15}{18}\]\[\frac{-9}{18}=\frac{16x}{18}\]We can cancel the 18's and we have \[-9=16x\]\[x=-\frac{9}{16}\]

Answer 18

Now, what I did was essentially put everything over a common denominator of 18 and cancel the 18's all in one step. I did that by multiplying each term of the equation by 18 — perfectly legal to do, just need to multiply everything by the same value and the equation holds. \[2+2=4\]Multiply everything by 3\[3*2+3*2=3*4\]\[6+6=12\]Right? When I multiplied through by 18, I made a common denominator and canceled it out, leaving me just the numerators and skipping a bunch of tedious work.

Answer 19

This is a very handy technique when working with problems involving decimal amounts, too. If you had some equation \[0.23x+0.47y = 3.96\]you could work with it like that, or you could multiply through by 100:\[100*0.23x+100*0.47y = 100*3.96\]\[23x+47y=396\]I don't know about you, but I'd prefer to work with the latter equation! It is exactly equivalent, and you'll get the same answer.

Answer 20

You could think of that equation as \[\frac{23}{100}x+\frac{47}{100}y = 3+\frac{96}{100}\]and then the multiplication becomes
\[\cancel{100}*\frac{23}{\cancel{100}}x+\cancel{100}*\frac{47}{\cancel{100}}y=100*3+\cancel{100}*\frac{96}{\cancel{100}}\]\[23x + 47y = 300+96\]\[23x+47y=396\]

Answer 21

Does that make sense?