Problems Understanding Division of Fractions

[bballwaterboy]

This is frustrating me.

The formula for division of fractions in my Pre-Calculus book is a/b = a x 1/b.

However, when you apply this to an actual problem, it doesn't make sense. For example:

3/4 divided by (sorry, I don't see a divisor sign in the list of symbols we can choose from) 6/11

This becomes 3/4 x 11/6. So you just flip the 6/11 and use its reciprocal to multiply by. I remember this from high school. However, when thinking about the formula (above), shouldn't it be:

3/4 x 1/11/6 (1 in the numerator and 11/6 in the denominator)? THAT would fit the formula and not merely the reciprocal. "b" is a fraction (6/11). The formula says to place b under a 1 and that's what I did. So I'm confused now. Anyone understand what I'm missing? Thanks.

 

[ellipsis]

(1 in the numerator and 11/6 in the denominator)? THAT would fit the formula and not merely the reciprocal.

Reciprocal of a = 1/a.

As an example:
$$ \frac{1}{(\frac{7}{2})} = \frac{2}{7} $$

Try it in your calculator. The reciprocal of $x$ is defined as $\frac{1}{x}$. Let me reiterate: The action of flipping a fraction over is expressed mathematically as dividing 1 by that fraction.

As you continue on you'll realize more 'computational heuristics' like this are formally expressed a different way in algebra.

 

[DiracPool]

So you just flip the 6/11 and use its reciprocal to multiply by. .

Flipping the 6/11 and "using it's reciprocal" are the same operation. So you are doing the same reciprocal operation twice. It's going to get you back to the same place. If you "flip the 6/11 and use it's reciprocal to multiply by...", you aren't doing anything at all but multiplying by the original 6/11. Maybe that's where you're going wrong.

In the formula a/b = a x 1/b, the "1/b" term operates to take the reciprocal of b, once, that's it. So if b = 6/11, then 1/b = 11/6. Therefore, (3/4) / (6/11) = (3/4) x (11/6).