long problem with fractions, getting different answers

[iceTea]

Hi I have a long problem that I can't figure out. I've looked at the solution steps to Microsoft Math and it doesn't make sense to me and so I tried to look at solution steps on QuickMath and it gives me a different solution!!

Here is the problem:
[MATH] 1\frac{2}{3}\div5.5 + 1\frac{7}{12} \div (2.25 - x) = 1\frac{1}{6} [/MATH]
So I first tried converting everything to improper fractions:
[MATH] \frac{5}{3}\times\frac{2}{11} + \frac{9}{12} \div (\frac{9}{4} - x) =\frac{7}{6} [/MATH]Next:
[MATH] \frac{10}{33}+\frac{9}{12}\div (\frac{9}{4} -x) = \frac{7}{6} [/MATH]Then I tried to subtract 10/33 from both sides and got:
[MATH] \frac{9}{12} \div (\frac{9}{4} -x) = \frac{19}{22} [/MATH]It's here that I'm not really sure what to do. Should I multiply both sides by 12/9? What am I supposed to do with the parenthetical part? The first solution step in Microsoft Math is to multiply both sides by 6 but this makes no sense to me and it looks like it is skipping steps.

 

[Dr.Peterson]

1 7/12 is 19/12, not 9/12.

I would multiply both sides by 9/4 - x, to get it out of the denominator.

There are many ways to start. I especially wouldn't worry about what a computer does. There are a number of things I'd do differently, just because I have more experience and can see what's coming. You should just do whatever makes sense to you (up to a point); what you've done so far makes sense to me.

 

[lookagain]

So I first tried converting everything to improper fractions:
[MATH] \frac{5}{3}\times\frac{2}{11} + \frac{9}{12} \div (\frac{9}{4} - x) =\frac{7}{6} [/MATH]

Also, please do not use the \(\displaystyle \ " \times " \ \) symbol in your algebraic expressions or
equations, especially as it resembles the x variable.

 

[iceTea]

Thanks for the points Dr.Peterson and the formatting tip, lookagain.

So, to make sure I follow your suggestion, Dr.Peterson, the rest of my steps would be:
[MATH] \frac{19}{12} = \frac{19}{22}(\frac{9}{4}-x) [/MATH]Next, multiply 22/19 by both sides:
[MATH]\frac{11}{6} = \frac{9}{4}-x[/MATH]Next, subtract 9/4 from both sides:
[MATH]\frac{5}{12} = x[/MATH]

 

[Dr.Peterson]

So now we can check it out (I just use my calculator for that):
[MATH]1\frac{2}{3}\div5.5 + 1\frac{7}{12} \div (2.25 - \frac{5}{12}) = 1.666...\div5.5 + 1.583... \div (2.25 - 0.416...) = 1.166...= 1\frac{1}{6}[/MATH]
So you got it.

 

[Steven G]

Hi I have a long problem that I can't figure out. I've looked at the solution steps to Microsoft Math and it doesn't make sense to me and so I tried to look at solution steps on QuickMath and it gives me a different solution!!

Here is the problem:
[MATH] 1\frac{2}{3}\div5.5 + 1\frac{7}{12} \div (2.25 - x) = 1\frac{1}{6} [/MATH]
So I first tried converting everything to improper fractions:
[MATH] \frac{5}{3}\times\frac{2}{11} + \frac{9}{12} \div (\frac{9}{4} - x) =\frac{7}{6} [/MATH]Next:
[MATH] \frac{10}{33}+\frac{9}{12}\div (\frac{9}{4} -x) = \frac{7}{6} [/MATH]Then I tried to subtract 10/33 from both sides and got:
[MATH] \frac{9}{12} \div (\frac{9}{4} -x) = \frac{19}{22} [/MATH]It's here that I'm not really sure what to do. Should I multiply both sides by 12/9? What am I supposed to do with the parenthetical part? The first solution step in Microsoft Math is to multiply both sides by 6 but this makes no sense to me and it looks like it is skipping steps.

You could get a common denominator for 9/4 - x = (9-4x)/4 and then multiply 9/12 by the reciprocal of (9-4x)/4.