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About LinkBacksA recipe calls for 3/5 lb of pasta for a salad. How much pasta should be used for 1/2 of the recipe?
I used 3/5 divided to 2 and I got the outcome of 3/10. Is this correct?
Because the way the person wrote the question is so confusing. While I sort of knew it has to be dividing, I didn't know what to divide with... If I were to divide 1/2 I would have to flip the equation around. BUT if I divide it to number 2 then I would have to flip 2 to 1/2.Originally Posted by TKHunny
Why do you doubt?
I still don't know why the hell did he put that 1/2 there.
Yes, the answer is correct. We can see this intuitively because=
and half of
is simply
.
But I understand that you're unsure with the "mechanical" manipulations of fractions. In the former post (I forget who posted it), we saw that the problem was solved using multiplication, even though by intuition if you want one half of something, you divide. Well, here's the thing. Division is multiplication. Anything that you can write as a division, you can write as a multiplication as well.
Revisiting the problem, we see that. If we multiply something by
, we will get an output of half that thing because we are multiplying by a number less than one. You know that if you multiply by 1, you get the same number. If we multiply by a number larger than 1 (as long as the number we're multiplying is also greater than 1), we get a larger number. But if we multiply it by less than 1, we will obviously get something smaller (for now, we are not considering negative numbers--0 is our endpoint). So if we multiply something by 0.001, we're obviously going to get a much smaller answer, because it's only 0.001 of our original number.
So using this logic, it should be clear why the answer is smaller, despite the multiplication. In rudimentary terms, if you want to divide a numberby a number
, you can simply multiply the number
(and if you multiply it out, you get
which is obviously division). As you can see in the former problem, we're dividing by
and the reciprocal of
) of the original number. And how do we get multiples (by this I mean that the resulting number will be a multiple of the original number, because if you multiply it times 3, you get your original number back) of numbers? We multiply! So if we want a number that gives us our original number back if we multiply it by 3, it only makes sense to multiply it by
I hope this clarifies it...somewhat. It's difficult to explain the fundamentals.
I think I get it. It's somewhat similar to decimal, if you multiply it, it would be smaller while dividing would be bigger.Yes, the answer is correct. We can see this intuitively because
But I understand that you're unsure with the "mechanical" manipulations of fractions. In the former post (I forget who posted it), we saw that the problem was solved using multiplication, even though by intuition if you want one half of something, you divide. Well, here's the thing. Division is multiplication. Anything that you can write as a division, you can write as a multiplication as well.
Revisiting the problem, we see that
So using this logic, it should be clear why the answer is smaller, despite the multiplication. In rudimentary terms, if you want to divide a number
I hope this clarifies it...somewhat. It's difficult to explain the fundamentals.
I agree that sometimes, people do not see it. But sometimes they do, so I think it's safe to include that, along with a more detailed explanation like I did. They might get it immediately, or they may have to carry on to the more detailed explanation.
In more complex problems, I think providing an "intuitive" route to why something works is a good way to try to get someone to think about the problem, and understand why it works. But you're right--sometimes it doesn't work.
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