# Fraction beginner (or refresher)

• Jun 11th 2008, 07:11 PM
mdudley
Fraction beginner (or refresher)
I have this problem: 3/4x - 5 = 2/3x

I do not know what to do after I do this:

3/4x - 5 + 5 = 2/3x + 5

3/4x = 5 2/3x

Do I take the 5 and mulitply it with the 2 and the 3 to get

10/15x to look like

3/4x=10/15x

Then divide 3/4x * 4/3 = 4/3 * 10/15x

or find the common demonitators to simplify?
• Jun 11th 2008, 07:53 PM
Aryth
Quote:

Originally Posted by mdudley
I have this problem: 3/4x - 5 = 2/3x

I do not know what to do after I do this:

3/4x - 5 + 5 = 2/3x + 5

3/4x = 5 2/3x

Do I take the 5 and mulitply it with the 2 and the 3 to get

10/15x to look like

3/4x=10/15x

Then divide 3/4x * 4/3 = 4/3 * 10/15x

or find the common demonitators to simplify?

You've made a few slight errors here. Let's do this step-by-step:

$\displaystyle \frac{3}{4}x - 5 = \frac{2}{3}x$

First, you add the 5 to both sides:

$\displaystyle \frac{3}{4}x = \frac{2}{3}x + 5$

Then we subtract $\displaystyle \frac{2}{3}$ from both sides:

$\displaystyle \frac{3}{4}x - \frac{2}{3}x = 5$

Now we find the common denominator between the two fractions, it happens to be 12:

$\displaystyle \frac{9}{12}x - \frac{8}{12}x = 5$

Now, we subtract the two fractions:

$\displaystyle \frac{1}{12}x = 5$

Now we multiply both sides by 12:

$\displaystyle \frac{1}{12}x*12 = 5(12)$

$\displaystyle x = 60$

There you go.

To verify all we do is plug in for x:

$\displaystyle \frac{3}{4}(60) - 5 = \frac{2}{3}(60)$

$\displaystyle \frac{180}{4} - 5 = \frac{120}{3}$

$\displaystyle 45 - 5 = 40$

This is a true statement. Thus x does in fact equal 60.
• Jun 11th 2008, 08:19 PM
mdudley
Now I see, the 2/3x and the 3/4 x are alike so you can subtract them, thank you so much I haven't done math in over 10 years and I might over complicate something easy.
• Jun 11th 2008, 08:40 PM
Aryth
No problem. Just some tips:

If a term has an $\displaystyle x$ in it it can't be added to something that does not have an $\displaystyle x$ in it. For example:

$\displaystyle \frac{1}{2}x + 3 \text{ Does not equal } \ 3\frac{1}{2}x$

On the other hand, you CAN add and subtract two terms with x's because they are what's called "like terms". They are alike, therefore operations between the two can be performed without changing the solution to the equation, for example:

$\displaystyle \frac{1}{2}x + \frac{1}{2}x = 1x$

This is true because they are like terms.

Hopefully this helps. Once you understand the ideas, it all just flows naturally.