Hi,
I have a a doubt regarding the concept of Estimating values/Benchmarking fractions.
Question:
Estimate to the closest integer: What is 11/40 of 5/16 of 120?
Approach:
11/44 x 5/15 x 120 = 10.
Doubt:
Is there a faster way to avoid/ skip the approach and directly predict (with the help of benchmark values) that
11/40 = 1/4
5/15 = 1/3 .
P.S:
In the above approach i chose 5/15 over 5/20 is because 5/16 is more closer to 5/15...I dont know if that's the right way to think, but if not, tommy please feel free to correct me! :)
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- Videoorchard
- Prospective Students
- Posts: 48
- Joined: Thu Mar 06, 2014 2:58 am
- tommywallach
- Manhattan Prep Staff
- Posts: 1917
- Joined: Thu Mar 31, 2011 11:18 am
Re: Estimating Values.
Hey Video,
Hmm. I think you're misunderstanding the approach.
The idea isn't that one goes:
"Hmm. 11/40? What does that remind me of? I guess it's sorta like 11/44...which is 1/4!
The idea is actually just that one goes, "Hmm. 11/40, that sure is close to 1/4!" And then the explanation is showing you that it is by showing you 11/44.
So there really isn't an extra step there. Make sense?
-t
P.S. Your rounding is perfect!
Hmm. I think you're misunderstanding the approach.
The idea isn't that one goes:
"Hmm. 11/40? What does that remind me of? I guess it's sorta like 11/44...which is 1/4!
The idea is actually just that one goes, "Hmm. 11/40, that sure is close to 1/4!" And then the explanation is showing you that it is by showing you 11/44.
So there really isn't an extra step there. Make sense?
-t
P.S. Your rounding is perfect!
- Videoorchard
- Prospective Students
- Posts: 48
- Joined: Thu Mar 06, 2014 2:58 am
Re: Estimating Values.
Hi Tommy,
Thank you for answering!
Could you please elucidate more on the part " Hmm. 11/40, that sure is close to 1/4! " .....How did you arrive at 1/4 using benchmark?
Whenever a question involves benchmark, what i usually do is: i.e 11/40. So what's half of 40? Okay its 20. 11<20....Therefore 11/40 should be somwhere < 1/2....but i am nonplussed on how to get the exact fraction such as 1/4 as you pointed out above. Could you please elucidate more on it sir?
Thank you for answering!
Could you please elucidate more on the part " Hmm. 11/40, that sure is close to 1/4! " .....How did you arrive at 1/4 using benchmark?
Whenever a question involves benchmark, what i usually do is: i.e 11/40. So what's half of 40? Okay its 20. 11<20....Therefore 11/40 should be somwhere < 1/2....but i am nonplussed on how to get the exact fraction such as 1/4 as you pointed out above. Could you please elucidate more on it sir?
- tommywallach
- Manhattan Prep Staff
- Posts: 1917
- Joined: Thu Mar 31, 2011 11:18 am
Re: Estimating Values.
Hey Vid!
I'm confused how you don't see that 11/40 is similar to 10/40, which is 1/4. That seems fairly straightforward. Am I misinterpreting somehow?
As for the math described here --> "11/40. So what's half of 40? Okay its 20. 11<20....Therefore 11/40 should be somwhere < 1/2" --> I have no idea what you're doing here. Why would you be taking half of 40? If you're going to take half of 40, you have to take half of 11 too (it's a fraction, so you can't half just the denominator), so you'd end up with 5.5 over 20, which is like 5/20, which is 1/4.
-t
I'm confused how you don't see that 11/40 is similar to 10/40, which is 1/4. That seems fairly straightforward. Am I misinterpreting somehow?
As for the math described here --> "11/40. So what's half of 40? Okay its 20. 11<20....Therefore 11/40 should be somwhere < 1/2" --> I have no idea what you're doing here. Why would you be taking half of 40? If you're going to take half of 40, you have to take half of 11 too (it's a fraction, so you can't half just the denominator), so you'd end up with 5.5 over 20, which is like 5/20, which is 1/4.
-t
4 posts Page 1 of 1