# Put these fractions in order of size, largest to smallest: 1/3, 1/8, 1/2, 1/4.

**Kinogu16**- 10 Answers

Hello Kinogu16

Well since they all are fractions with a one on top (the numerator) this is a particularly simple case. The order of the reciprocal fractions will always be the opposite, and any fraction with a one in the denominator is equal to the numerator. So essentially, all you have to do is erase all the ones, "1", and the fractional signs, or slashes, "/",and place the numbers in order; then simply reverse the order and the fractions from which each value originated is in the reverse order of size (smallest to largest).

In the example you've given, 1/3, 1/8, 1/2 and 1/4, you would just sort 3, 8, 2, and 4 from smallest to largest: 2, 3, 4, and 8. Now that tells you that the correct order for the original fractions from largest to smallest is 1/2, 1/3, 1/4, and 1/8. Easy-peasy - right?!

It works in the general case too - regardless of what the numbers are. You simply must know how to place the reciprocal fractions in order, relative to the numbers. So if you were given the same group of fractions as given above, with the addition of something like 2/15, the inverse (i.e., reciprocal) of this fraction is 15/2, and you can (hopefully) see that this is equivalent to 7.5 and therefore fits between 4 and 2 (representing 1/4 and 1/2 respectively). So that is were the fraction belongs in the chronological ordering, and it ends up being exactly in the middle of the group. The final order predicted by this method would be 1/2, 1/3, 2/15, 1/4, 1/8.

It's merely an alternative simpler method that lends itself good to being preformed in one's head if you choose to be ambitious and look for these type of neato ways to go about your tactics for tackling such problems. Dividing it out into decimal form or finding the least common multiple or whatever is great if you want to avoid mistakes or show proof, but it's kind of retarded to do it if your working it in your mind - especially when the answer is so simple it's staring you right in the face! I personally prefer to come up with my own methods to analyze a problem anyway and that works great for me, and there's a certain satisfaction that comes with doing it this way - not to mention it is profoundly faster to look at and just start rattling off the answer as you go - it will be sure to make your professors check you closely to make sure your not cheating and your friends will be both amazed and jealous if you like to mess with them, or even if you just like to make math easier, quicker an more "fun".I can't believe I just said that, but it's true!

If you can't do it as they are presented, change denominators, so that all of them are equal.

Start with you highest denominator--maybe the others can be raised to it. Here, 8 is your highest denominator, and the 2 and the 4 divide evenly into 8, (so they can be raised to an eight by multiplying), but the 3 won't divide into an 8 evenly.

Continue to raise your highest number--the next multiple of 8 is 16; 2 x 8 = 16. While the 2 and the 4 will divide evenly into 16, the 3 won't.

Next, 8 x 3 =24, and this one is going to work--a 2, 3, and 4 will divided evenly into it. Raise each denominator to a 24, by multiplying the denominator (and the numerator) by the amount of times that the denominator divides into the 24.

It looks like this:

24 divided by 8= 3. So, 3 x 1/8 = 3/24.

24 divided by 2=12. So, 12 x 1/2 =12/24.

24 divided by 3 = 8. So, 8 x 1/3 = 8/24

24 divided by 4 = 6. So, 6 x 1/4 = 6//24

From smallest to largest: your fractions are now 3/24; 6/24; 8/24; 12/24. The largest one is 12/24, which is 1/2. So, the order of largest to smallest is 12/24; 8/24; 6/24; 3/24.

To order fractions, it is easy to change them all from fractions to decimals and then compare them if you cannot visualize their size.

Change fractions to decimals by dividing the denominator (bottom number) into the numerator (top number) by adding a decimal point behind the number and at least 2 zeroes.

1/3 = .33; 1/8 = .125; 1/2 = .50; 1/4 = .25

1/3, 1/8, 1/2, 1/4.

1/3 * 360 = 120Â°

, 1/8* 360 = 45Â°

, 1/2 *360 = 180Â°

, 1/4 *360 = 90Â°

in order of size, largest to smallest it becomes;

1/2,1/3,1/4,1/8