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Comment on Evaluate a Fraction
Hey, could you please explain
Hi alicia,
Hi alicia,
At 2:00 in the video, we have a situation where we have a fraction consisting of fractions in the numerator and denominator (which is very awkward).
So, we want to create an equivalent fraction where we don't have fractions in the numerator and denominator.
To create equivalent fractions, we multiply top and bottom by the same value. For example, if we take 2/3 and multiply top and bottom by 5, we get an equivalent fraction of 10/15 (in other words, 2/3 = 10/15)
We want to do the same thing with (1/4)/(1/8).
So, we want to multiply top and bottom by some nice value so that we no longer have fractions in the numerator and denominator.
Well, if we multiply top and bottom by 8 (the least common multiple of 4 and 8), then we get the equivalent fraction of 2/1. In other words, (1/4)/(1/8) = 2/1
As you can see, 2/1 is much simpler than (1/4)/(1/8).
The same steps and logic apply to the other fraction.
Does that help?
Hey, i tried to round off the
Rounding/estimating works
Rounding/estimating works only when the answer choices are relatively spread apart (for more, see https://www.gmatprepnow.com/module/general-gmat-strategies/video/1111).
In this question, the answer choices are too close together to use that approach.
If you want to use estimation, you need to be a little more precise and round to the nearest hundredth (which could be quite tine consuming).
Your best bet here is to convert to fractions.
This is such a brilliant
Glad you like it!
Glad you like it!
do we need to memorise this
The best (i.e., fastest) way
The best (i.e., fastest) way to solve this question is to convert the decimals to fractions. To do so, you must be familiar with the table that appears at 2:05 in the following video: https://www.gmatprepnow.com/module/gmat-arithmetic/video/1066
Another approach we might CONSIDER is using some estimation. However, we should probably reject that approach since the answer choices are too closely packed together.
Cheers,
Brent
Hi Brent!
I chose to round off the decimals and arrive at 3.28. I understand why this approach was wrong, but how do we determine which questions require you to round-off and which require you to convert to fractions?
It all depends on the answer
It all depends on the answer choices and how spread out they are (see this video for more on this: https://www.gmatprepnow.com/module/general-gmat-strategies/video/1111)
Rounding off is fine when the answer choices are reasonably spread apart.
However, in this question, the answer choices are pretty close together (e.g., 3.75, 4, 4.25), which means we need more accuracy in our calculations. So, in this case, rounding off will get us in trouble.
Does that help?
Cheers,
Brent
Hi Brent!
This fraction could be evaluated even without the conversion chart.
So, the nominator can be transformed in 375(10)-3 * 6666(10)-4 * 11111(10)-4, and the denominator can be transformed in 1666(10)-4 * 5555(10)-4 * 75(10)-2. Then we can simplify the fraction, which gives us 6666.6 divided by 1666, which is something about 4.
That works too - nice work!
That works too - nice work!
Keep in mind that you won't have a calculator on test day :-)
Cheers,
Brent
My only question is that
when should i consider to convert decimals to fractions to solve that kind of question?
In general, the GMAT tends to
In general, the GMAT tends to reward students who use fractions over decimals.
That said, if we first examine the answer choices, we can often (but not always!) gain some insight into whether it's best to use fractions or decimals. For example, if the answers are all fractions, then there's a good chance your solution may be faster if you use fractions.
Cheers,
Brent
Hi Brent,
The way I do it is that I converted everything to a whole number first.
(375)*)(6666)*(11111)/(1666)(5555)(75)= 7/15
My question is, on the numerator, I moved 11 digits, and on the bottom I moved only 10 digits. So after I got my answer, how many digits am I supposed to move to the left? Could you please clarify?
Thank you
Hi David,
Hi David,
Basically, you multiplied the numerator by 10^11, and you multiplied the denominator by 10^10. So, to create an equivalent fraction, you must multiply your result (7/15) by 10.
However, in your case, that will still yield an incorrect answer, since your original calculation of 7/15 is incorrect.
Give it another try.
Cheers,
Brent
I used the method of ABC/DEF
Great question!
Great question!
I should note that I don't mean to suggest that my approach is always the best/fastest. It's just an approach. Each learner will have different preferences regarding the best approach for them.
Your solution is fantastic! The only hard part is determining which pairs of values work best together.
Cheers,
Brent
Hi Brent,
Can you please explain the rationale why Option I is correct? Karishma has tried to explain it but if you could explain it simpler, that would be much appreciated.No issues with why II and III are not correct
https://gmatclub.com/forum/if-m-p-s-and-v-are-positive-and-m-p-s-v-which-of-the-following-160298.html#p1269836
Thanks!
Looks like I was the 20th
Looks like I was the 20th person to answer that question. So I'm on page 2 here: https://gmatclub.com/forum/if-m-p-s-and-v-are-positive-and-m-p-s-v-which...
Awesome! Thanks Brent.
I also have a general question for parallel lines. We say that parallel lines have the same slope, but I came across one question where although the lines had the same slope, it said we can't assume that the lines are parallel and will never cross each other. Why is that? I think it had something to do with the different y intercepts. However, as per Bunuel mentions, there is nothing about the y-intercept restricting the lines to be parallel though.
https://gmatclub.com/forum/math-coordinate-geometry-87652.html
Thank you!
Link: https://gmatclub.com
Link: https://gmatclub.com/forum/math-coordinate-geometry-87652.html
I checked the link, but I'm not sure what part you're referring to.
If two lines are parallel, they'll never share a point (i.e., cross each other)
I guess we could say that if two equations are equivalent, they can't be parallel.
For example, the equation x + 2y = 3 and the equation 2x + 4y = 6 both represent the exact same line.
So, even though the two lines have the same slope, we can't say they're parallel.
I'm not sure if this is what you're referring to.
Hi Brent,
Yes, that's pretty much what I meant. I guess if we are given one linear equation (y=2x+2) for instance, then if the question asks whether two lines are parallel or not and gives us only the slope (being equal to 2) of the second equation without the linear equation, then we can't assume these two lines are parallel even though their slopes are equal, right? Because we are not given any restriction of these two lines being one line or crossing one another at some other point?
That's correct.
That's correct.
From the Official Guide: If two lines that are in the same plane do not intersect, the two lines are parallel.
The key here is that the lines do not intersect.
So, if two equations represent the same line, we can't say we have two parallel lines.