Hi all,
In using the MGMAT Fractions Guide, I've come up against a question on utilizing benchmark fractions (1/2, 1/3, 2/3, 3/4) to approximate values for less obvious fractions.

When a fraction appears to be close to two benchmarks (ie. 5/18 is close to both 1/4 and 1/3), how does one choose? In the 5/18 example, I estimated it as 6/18, or 1/3, but the Guide estimated it as 1/4. Later, with 6/20, the Guide used the benchmark value of 1/3, where I would have gone with 1/4 (for 5/20).

Is there any good rule for these close calls?

Thanks!

Generally, if you're going to do this, you will have to estimate at least twice within the problem. In this case, choose with the idea that you want to minimize the error that you introduce via estimating - so if you choose the higher option on one fraction, choose the lower option on the other fraction.

For the examples you list, generally try to adjust the larger number because that will introduce less error. In both of these examples, that means adjusting the denominator.

We could make 5/18 either 5/15 = 1/3 or 5/20 = 1/4. I don't have to go as far to change it to 18 to 20, so I should choose that route.

For 6/20, I could do 6/18 or 6/24. 6/18 is closer, so go that route. (Note: although changing 20 to 18 is a difference of two digits, and changing 6 to 5 is a difference of only one digit, the proportional difference of changing the smaller number is much higher. A 1-digit difference from 6 is 1/6 or about a 17% difference, while the 2-digit difference from 20 is 2/20 or only a 10% difference.)

stacey is right on, but there's a very important point buried deep within her post that deserves to be brought forth in all its regal splendor:



that's the most important part here.

if you multiply fraction X times fraction Y, then, to mitigate the error ensuing from estimation, you should, if possible, adjust one of the fractions UP and the other one DOWN.

the rest of stacey's post speaks for itself.