Missing denominator

[Rengoku0510]

Hi, I would like to get some help on question 8.

The correct answer is 45xy^3 but does it equal to 2xy/5y^2?

My calculation for this is 18x^2y^2/45xy^3 = 2x/5y and it does not match to the answer.

Also I'm confused when you simplify 18x^2y^2/45xy^3, it equals to 2xy/5y^2. I thought numerator y should be taken away and only leaves denominator y.

 

[Harry_the_cat]

Note that the right hand side can be simplified to \(\displaystyle \frac{2x}{5y}\).

 

[JeffM]

You do not say how you attacked any of these problems, but presumably you assigned a letter to represent the unknown variable. I am choosing z for problem 8. Naming your unknowns or variables should be one of the first things to do in any problem in algebra.

I am not crazy about how this problem is presented because it is solvable ONLY IF neither x nor y is zero, but the problem does not disclose that.

Finally, you say that you provide your calculation, but actually you show a result without showing in detail how you got there. But you are correct. I presume you did something like

[math]\dfrac{18x^2y^2}{z} = \dfrac{2xy}{5y^2} \implies \dfrac{z * 5y^2}{2xy} * \dfrac{18x^2y^2}{z} = \dfrac{z * 5y^2}{2xy} * \dfrac{2xy}{5y^2} \implies[/math]
[math]z = \dfrac{5y^2 * 18x^2y^2}{2xy} = 5y * 9xy^2 = 45x(y * y^2) = 45xy^3.[/math]
So that answer is correct.

Now it seems that you got confused when you tried to validate that answer against the ORIGINAL problem.

[math]\dfrac{18x^2y^2}{45xy^3} = \dfrac{2x}{5y}.[/math]
Very sensible. But because the problem requires that y not be zero

[math]\dfrac{2x}{5y} = \dfrac{2x}{5y} * 1 = \dfrac{2x}{5y} * \dfrac{y}{y} = \dfrac{2xy}{5y^2}.[/math]

 

[Dr.Peterson]

My calculation for this is 18x^2y^2/45xy^3 = 2x/5y and it does not match to the answer.

Also I'm confused when you simplify 18x^2y^2/45xy^3, it equals to 2xy/5y^2. I thought numerator y should be taken away and only leaves denominator y.

The claim is that the two sides are equal, not that the right side is the result of simplifying the left side, which is what you did. The equal sign doesn't mean, as many students initially think, "the answer is ...", but simply "has the same value as".

One way to show that they are equal is to simplify each side, and see that the results are equal.