You are not alone at all. Many of my students find that percent and fraction word problems can be very time-consuming and difficult!
I recommend that you start back at square one. Get the Manhattan Foundations of Math book (the new 5th edition guide), and work through all of the % and fraction material. There are drills for mechanics (just manipulating percents and fractions) and setting up word problems. The goal should be to get very automatic with the underlying skills, so you can focus all your brainpower on understanding the problem and working for accuracy. I also highly recommend that you try to set up a solution expression in advance. For instance, let's say you are working on the following problem:
Andres is eating a snack mix that consists of almonds, pistachios, and chocolate chips. The quantity of chocolate chips, by weight, is 1/3 the quantity of pistachios. The quantity of almonds is four times the combined quantities of chocolate chips and pistachios. What fraction of the mix, by weight, consists of chocolate chips?
Even if we're not sure exactly where to start on this problem, if we understand the final question, we can set up a solution expression:
weight of chocolate chips/total weight =
If we assign variables to represent each quantity (a,p,c), this becomes
c/(a+p+c) =
The importance of this is that it gives us a focus for our work, and it often helps to prevent errors later in the process, when we may have lost sight of what we're actually trying to do. Now, let's solve. We'll start by translating the statements into equations:
The quantity of chocolate chips, by weight, is 1/3 the quantity of pistachios.
c=(1/3)p
The quantity of almonds is four times the combined quantities of chocolate chips and pistachios.
a=4(c+p)
Now let’s try to combine this information. Note that c appears in both equations, and we want it in our numerator. We might be tempted to solve for c right away, but we should do the opposite. Since we want to have c at the end, we should get the other variables out of the way by solving for them
in terms of c, like this:
c=(1/3)p
3c=p
a=4(c+p)
a=4(c+(3c))
a=4(4c)
a=16c
We now have all of our variables in terms of the desired quantity, c. Now we just have to drop these values into our solution expression.
c/(a+p+c) =
c/(16c+3c+c) =
c/20c=
1/20
I hope this helps. Definitely check out our Foundations book, and best of luck with your fraction odyssey!
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Dmitry Farber | Manhattan GMAT Instructor | New York
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