An interesting article on fractions appeared this week in the Wall Street Journal. You must be thinking: fractions? interesting? Well, it’s interesting at least for those of us who teach the GMAT.
According to the article, “national tests show nearly half of eighth-graders aren’t able to put three fractions in order by size.” Can you? Here’s a Problem Solving question from the 2nd Edition of the GMAT Quantitative Official Guide.
Which of the following is greater than 2/3?
Methods to Compare Fractions
By definition, only one answer can be correct, and therefore only one answer can be greater than 2/3. So we are essentially looking for the biggest of these five fractions. There are two common methods by which to compare fractions: find a common denominator and then compare the numerators OR convert the fractions into decimals. Two more subtle approaches are comparing the fractions to a point of reference (such as 1/2) and finding a common numerator in order to compare the denominators.
Solution to Problem
For this problem, finding a common denominator seems messy. We can quickly eliminate (D) by noting that 13/27 < 13/26 = 1/2 < 2/3. For the remaining answers, it’s best to convert them into decimals. In order to save time, we don’t need to convert them all into decimals. We just need to find one that is greater than 0.6666 (the decimal equivalent of 2/3). So we should start with whichever answer seems the biggest.
GMAT Genius recommends that you memorize the fraction-to-decimal conversions for halves, thirds, fourths, fifths, sixths, eights, ninths, tenths, and elevenths. If you know these conversions, we can quickly identify (B) as the correct answer. 1/11 = 0.090909. To find any other eleventh, just multiply the numerator by 9. So 8/11 = 0.727272, which is clearly more than 2/3. For the record, (A) 33/55 = 0.66, (C) 3/6 = 0.6, and (E) 5/8 = 0.625. But again, once we have identified (B) as the correct answer, we should not spend our time with these additional conversions. Let’s save those precious few seconds for other problems.
Benefits of Fractions
Although this is admittedly an easy question by GMAT standards, fractions are essential to the GMAT math section. Fractions tend to make calculations easier than decimals, because numbers often conveniently cancel out when using fractions. Fraction calculations can appear directly and indirectly on all types of GMAT math problems, not just on basic arithmetic problems. As Dr. Bob Siegler of Carnegie Mellon University states in the Wall Street Journal article, “If you don’t understand fractions, it’s literally impossible for you to understand algebra, geometry …”. So be sure to study your fractions!