Cheryl N. answered • 12/05/12

Certified; experienced with learning-different and advanced students!

5/8 x - 7/12 = 0

Short answer:

5/8 x - 7/12 = 0

Add 7/12 to both sides.

5/8 x = 7/12

Divide 5/8 from both sides.

x = (7/12) / (5/8)

Remember, you divide fractions by flipping the second and multiplying.

x = (7/12) * (8/5) = 56/60

Reduce by dividing the numerator and denominator by 4.

x = 14/15

The important trick with these kinds of questions is to reverse the order of operations!

Longer explanation:

A lot of students struggle to know what order to do the steps in, with these kinds of questions. But there is a rule! When you're solving a problem like this, trying to get the x out of a bunch of other numbers, the rule to remember is "reverse order of operations".

To review, the order of operations is PEMDAS: Parentheses, Exponent, Multiplication/Division, Addition/Subtraction.

So, reversing that, the first thing you do is any addition or subtraction. That would be the 7/12 fraction. Add 7/12 to BOTH sides of the equation. Now you have 5/8 x = 7/12.

There's no more addition or subtraction to do, so the next thing in reverse order of operations is multiplication and division. That would be the 5/8 attached to the x. There's two ways to do this. The more direct way is to just divide both sides of the equation by the fraction 5/8. Now you have x = (7/12) / (5/8). Remember, to divide one fraction by another, you just flip the SECOND fraction (order is important!) and multiply: x = (7/12) * (8/5). Multiplying fractions is easy! You multiply the numerators, and the result is the new numerator, and you multiply the denominators, and the result is the new denominator: x = (7 * 8) / (12 * 5) = 56/60. You also want to reduce your fraction. Divide both the top and the bottom by 4 (You get that number mainly by trail and error, don't be afraid to take a few wrong tries when reducing fractions!), so now you have x = 14/15!

x = 14/15

You're done! However, if you were having trouble with dividing the fractions, here's an alternate method:

I mentioned there were two ways to do this above, underlined for your skimming convenience! At that point, we had 5/8 x = 7/12.

Another way to think of "5/8 x" is "5x/8"! Any time you have a fraction times something, that something can be multiplied by the numerator of the fraction. So, now we have 5x/8 = 7/12.

With the reverse order of operation, we're still on multiplication and division. It doesn't actually matter what order you do these in! I'm going to take care of the division first, by getting rid of that 8 in the denominator. Multiply both sides of the equation by 8: 5x = (7/12) * 8 = (7*8)/12 = 56/12 = 14/3. So, 5x = 14/3.

Now all that's left is that 5! Divide both sides by 5: x = (14/3) / 5. The same way that something multiplied by a fraction can just be multiplied by the numerator, a fraction divided by something can just multiply that something into the denominator: x = 14/(3*5) = 14/15.

x = 14/15

Personally, I prefer the second method, since I find it a little bit cleaner! However, the steps in the first method are more direct and easier to remember. It's good to be familar with both method, as sometimes one will just be easier than the other, but they will both get you the right answer every time!

Hope that helped!