What is the quickest way to solve #8? I tried to find common denominators and then end up with large numbers.
I don’t think you need any actual calculations to solve this. You can just compare relative values of each fraction.
For example, (-1/6) + (1/7) can be solved but just based on how fractions work, we know that this will be a negative number. (1/7) is not large enough to offset the (1/6). The same can be said for (-1/8) and (1/9).
From here I can see this playing out differently based on how you order things in your mind. I see this as (1/5) minus some value, minus another value. Or sticking with our logic above, (1/5) plus a negative, plus another negative. Regardless of how you choose to order it, this logic shows that value B will be less than value A, even though we don’t know the actual value.
Further, I plugged the fractions into a calculator I found online to find out the lowest common denominator. For reference, it is 2520 (I didn’t check this so we’re just trusting I used the calculator right but it shouldn’t matter). You already saw that this process got some unwieldy results so we ought to find some trick or concept we can apply. If you want to go through the math, I am sure you will find that the answer is A but like you alluded to, it will take far too long.
I’m new to the forums so I might miss any messages but let me know if this makes sense or I can try to explain a different way
The logic is if you divide some into half 1/2 it will greater than say if you divide it into say 4 quarters or 1/4 or 1/2 > 1/4 or 1/2 >1/3 and so on.
So, for positive fraction if numerator is the same then : lower the denominator --> bigger the fraction.
In step 3: without doing any calculation you can see that if numerator are the same then the Qty which will have lower denominator will be bigger, so you can roughly estimate that whatever quantity you get at Qty A will be bigger than whatever you get at Qty B because Qty A has lower number in the denominator.
Oh cool. I didn’t think about doing that! Thanks!
Thank you!
You can use calculator 
If you encountered these kind of question during the exam, it will be time consuming to find common denominator.