Strategies, Sample Questions, and Random Ramblings.
July 18, 2015
On the GMAT fractions are going to make your life easier. Just about every problem will involve fractions on some level. The more comfortable you are with them, the better you will do on this exam. Period. Even though you are not going to see a bunch of problems specifically testing fractions alone, you are going to have plenty of opportunities to use them to make questions easier.
Focus on simplification (this is going to remain a theme in this book) - if you see the fraction , simplify it to . Use the factoring concepts talked about in the number properties section to make this process easier. The process would look like this as you cancel:
This process also works with variables:
However, it is common for people to make this mistake:
The key here is that this fraction can be broken down as follows:
Because the x cannot be cancelled in both fractions, it cannot be cancelled at all. The only way values can be cancelled is if they are being multiplied by all terms in both the numerator and the denominator. This is why factoring is so important with fractions.
Keeping with the simplification theme, there are two different ways for you to write out fractions that are greater than zero. Either as a mixed fraction, 3 2/5, or an improper fraction, 17/5. Both of these values are the exact same, but you will be better served to keep your fractions as improper when doing GMAT problems. The one exception to this rule is when thinking about remainders. We will discuss this in a couple of chapters...
Ironically enough, before we talk about adding and subtracting fractions we must talk about multiplying and dividing fractions. Actually it is quite simple - for multiplication you just multiply numerator by numerator and denominator by denominator.
To divide fractions, simply multiply the numerator by the reciprocal of the denominator.
We will need these skills to prepare fractions for addition and subtraction.
Adding and subtracting fractions comes down to a concept that we already learned with the lowest common multiple. The distinction is that in order to add or subtract fractions, we need the denominators to be equal. The best way to do this is to find the lowest common multiple of the denominators, or the lowest common denominator.
Lowest Common Denominator (LCD) - The lowest common multiple of two (or more) different denominators.
Once you find the LCD, multiply each fraction by a fraction equal to 1 ( ) that will give you the LCD for both. The result is a fraction that has the same value, but with a different denominator. Then, simply add or subtract the numerators.
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