Question 700161
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Either process results in the same answer -- given CORRECT arithmetic.  In your first method you also need to convert your mixed number to an improper fraction.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{2\frac{1}{2}}{24}\ =\ \frac{x}{30}]


Multiply by the LHS denominator.  (Note:  6 goes into 24 four times and into 30 five times)


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 2\frac{1}{2}\ =\ \frac{24x}{30}\ =\ \frac{4x}{5}]


Now convert to an improper fraction. 2 is four halves plus one-half is *[tex \LARGE \frac{5}{2}]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{4}{5}x\ =\ \frac{5}{2}]


Multiply by the reciprocal of the coefficient on *[tex \LARGE x]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ =\ \frac{5}{2}\,\cdot\,\frac{5}{4}\ =\ \frac{25}{8}]


Then you can integer divide 25 by 8 to convert back to a mixed number if that happens to tickle your fancy.


If you do it by changing everything to decimals, you end up with *[tex \LARGE x\ =\ 3.125]  which is the same thing as 3 and 1/8 or 25/8.


Now for the way I would have done it in the first place.


Step 1:  Multiply the LHS by 1 in the form *[tex \LARGE \frac{2}{2}]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{2}{2}\,\cdot\,\frac{2\frac{1}{2}}{24}\ =\ \frac{x}{30}]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{5}{48}\ =\ \frac{x}{30}]


Multiply both sides by 48


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{48x}{30}\ =\ 5]


Reduce the fraction in the RHS


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{8}{5}x\ =\ 5]


Multiply by the reciprocal of the coefficient in the LHS


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ =\ \frac{25}{8}]


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
<font face="Math1" size="+2">Egw to Beta kai to Sigma</font>
My calculator said it, I believe it, that settles it
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