Why do we cancel out the denominator of fractions with variables in a equation with their LCDs?

Question

$$x + \frac{5} {2} = \frac{1} {6}$$

$$6 ( x + \frac{5} {2} ) = 6 ( \frac{1}{ 6})$$

$$3 ( x + 5 ) = 1$$

$$3x + 15 = 1$$

$$3x = -14$$

Why is it that we do that?

Answer 1

Well, for starters, your solution in incorrect. It should proceed:

$6(x+5/2)=6(1/6)$

$6x+30/2=1$

$6x+15=1$

$6x=-14$

That aside, this is not a required method, but rather one technique. We could, instead, deal with the fractions directly:

$x+5/2=1/6$

$x=1/6-5/2$

$x=1/6-15/6$

$x=-14/6$

The reason (probably) that you were told to get rid of the fraction first is because it makes the problem slightly easier as you are only dealing with integers instead of fractions, which many students find cumbersome and intimidating. So, instead of carrying around a bunch of fractions, you can instead do a simple multiplication early on to make the problem less scary (with fewer opportunities for mistakes).