Brand-new FREE 28-page GMAT Fractions Gymnastics Guide!

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Junior | Next Rank: 30 Posts
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Joined: 24 Nov 2014
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Hi GMATters,

Here's a link to my brand-new GMAT fractions guide.

It starts with a review and finishes with advanced, GMAT-specific fractions skills and worked examples.

Check it out here: ... gymnastics


Here are some samples (there are images in the full file):


Cancel, cancel, cancel!

You want the bastard numbers to get smaller, not larger. Remember, arithmetic is not your friend. The less arithmetic you have to do, the better.
Smaller numbers means less arithmetic!

If you rearrange the numbers in a fraction-and you can do this because they're all multiplied together!-then you'll see that you can almost always arrange the numbers in a way that at least one little tiny term cancels. Often it's more than one!

Remember, don't make things any harder than they need to be. Laziness is a virtue, at least on the GMAT.

Dividing Fractions by Fractions

The best way to approach this is to remember the phrase "flip and multiply."

This requires that you be clear on what you're flipping, though. I usually like to bracket off the part that I'm dividing by so that it's clear what gets flipped.
Remember, practice safe X: bracket early, bracket often. (Sorry.)

Once you've flipped, just cancel and you'll have your answer in hand.

In other words, it's the same as 15 plus 1/3. In fact, you could also say it's the same as 15.33...

So a mixed number is actually just a different way to represent a decimal number.

In fact, the quotient, 15, remains exactly the same. Check out this diagram:

So, reversing the steps, all we need to do to turn a mixed number into an improper fraction is to multiply the quotient by the denominator, then add that product to the remainder, and put the whole thing over the divisor.

Another thing that is useful to memorize is what you see with the 1/3:


WTF? Indeed. Just look back at the chicken-scratch above, and it'll make more sense.

(Or just memorize that fact and move on. Your choice. Either way, it will come back in many shapes and forms.)
Check it out! ... gymnastics
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