Fractions - Chapter 2 question 15

[Guest]

Question asks to Estimate 11/30 of 6/20 of 120.

Approach I took (using benchmark values):
11/30 is approx 10/30 = 1/3
6/20 is approx 5/20 = 1/4

1/4 of 120 = 30
1/3 of 30 = 10

However the answer in the book states:
11/30 is slightly more than 1/3
6/20 is slightly less than 1/3
Therefore, 11/30 of 6/20 of 120 should be approx 1/3 of 1/3 of 120, or slightly more than 13 (exact answer is 13.2).

So where I went wrong was with 6/20. I took the approach of saying that it was slightly more than 1/4 (5/20) instead of saying that it was slightly less than 1/3 (7/21).
Whats the best way to determine how to approximate for 6/20 ?

thanks.

[StaceyKoprince]

Whenever you're going to approximate, you have to make sure that you balance out the error you introduce in your approximations. You rounded down both times, which compounds the error in the approximations. Round one up and one down to balance out the error (it doesn't matter which - just look at the numbers and see what makes the most sense). In this case, it's fairly obvious to round 11/30 down to 10/30 = 1/3, so you should be looking to round 6/20 up to the closest "easy" fraction (which, in this case, also happens to be 1/3 - you can see that if you simplify 6/20 to 3/10, which is very close to 1/3).

[Guest]

makes sense. Thanks !

[brian]

Glad that Stacey was able to help you out.
-Brian