You have the following problem: 1/2 = x/6

This is a proportion equation, in which you are comparing 2 ratios ( 1/2 and x/6 ). Since the ratios you are comparing here are fractions, your goal is to make them equivalent by solving for the unknown variable (x).

1.) You know that the means are 2 and x, and the extremes are 1 and 6. We use these means and extremes to solve for the proportion. Properties of algebra tell us that the product of the means (2*x) is equal to the product of the extremes (1*6).

2.) From the above info, you have found that

2 * x = 1 * 6 ==> 2x = 6

3.) 2x = 6 : Since our goal is to solve for the proportion by solving for x, we want to isolate x to one side of the equation (that is, to have the equation in the form of " x = "). This is why we divide both sides of the equation by 2....dividing
the left side of the equation (2x) by 2 we get:

2x / 2 = 1x = x

...dividing the right side of the equation (6) by 2 we get:

6 / 2 = 3

So, 2x / 2 = 6 / 2 ==> 1x = 3 ==> x = 3

4.) No, 2x divided by 2 is not 1 ==> (2*x) / 2 = (2/2)*x = 1x ....

....you don't know the value of x yet, which is why you are trying to solve for it. You are dividing both sides of the equation by 2 to get rid of the 2 on the left hand side of the equation so as to solve for x.

5.) Yes, 6 divided by 3 is equal to 2.

Let's summarize what we did:

1/2 = x/6

2*x = 1*6 ==> 2x = 6

2x / 2 = 6 / 2 ==> 1x = 3 ==> x = 3

Thus, the answer, to solve for the proportion by making the fractions equivalent, is x = 3.

Check to see that the answer is correct:

1/2 = x/6 plug in 3 for x in the equation

1/2 = 3/6

1/2 = 1/2 CORRECT!

## Comments

"story prolems" were the bane of my extistance

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