I think of it as described by poster #3. I tend to think of a fraction in terms of division--the numerator (top number) is divided by the denominator (bottom number.)

You can start by looking at a problem with easier numbers:

1/2 =

1 divided by 2 =

.5

So 7/1216 = 0.00576

3/584 = 0.00514

And then consider whether you'd rather have .00576 or .00514 of a pizza. I'd take the first one (the larger!)

The second of these numbers is smaller. You can find this by multiplying the two bottom numbers by each other and then the top numbers by the other bottom number.

That gets you a fraction where the bottom number is 710144. With that bottom number, the top numbers are 4088 and 3648, respectively, so the second number is smaller.

Which number is smaller

7/1216 or 3/584

To find out which number is smaller you can either convert them to decimal or find the LCM and then the common denominator. I think decimal is simpler so here it is:

7/1216 = 0.00576

3/584 = 0.00514

As you can see above that the decimal of 7/1216 which is 0.**0057**6 is greater than the decimal of 3/584 which is 0**.0051**4.

Therefore,

3/584 < 7/1216

**3/584 is the smaller number.**

Which number is smaller7/1216 or 3/584

The answer is equivilant to a number less than one. Being that there are two answers less than one. I can logically infer that The possible outcome closest to zero is true to the question. .00575658 in decimal form is one of many possible outcomes of the same number(the equation is complete as any representation of the afore metioned number) i.e. 3/584th's of a whole fruit, bottle, or book, etc. Only one whole fruit without .00575658% of itself suggests possibly a portion of the fruits capacity of juice and leaves us with an alternate idea of the whole, juice. Therefore The law of the number zero being inequal to itself, and the number one being a number only equal to zero is helpful. Ref. Gottlobe Frege, Conceptional notation and related articals. Translated by Theil. Oxford Press.

To find which of 7/1216 or 3/584 is smaller.

Several ways are suggested already. Here is one more.

7/1216 and 3/584 the equavalent fractions with unity as common numerator:

1/(1216/7) and 1/(584/3)

=1/(173+5/7) and 1/(194+2/3). So, the second fraction with higher denominator is smaller of the two given fraction.

There can be several way of comparing the two numbers. The one method which appears simplest to me is to change both the fraction in a forms that will have common numerators. Then the fraction with bigger denominator is the smaller number.

Thus:

7/1216 = 7/1216 x 3/3 = 21/3648

3/584 = 3/584 x 7/7 = 21/4088

As 4088 is greater than 3648, the number 3/584 is smaller than 7/1216.

The method given in post #2 is quite similar to the method suggested by me, involves multiplications of bigger numbers, and therefore a little more difficult.

Directly and through a simple calculation, fractions can be brought to the same numerator,by amplifying fraction 3 / 584 with the ratio of both fractions numerator 7 / 3, hence the equivalent fraction 7 / 1362 (denominator approximated). So, no matter the solving method chosen, 3/584 is smaller!