i have three fractions (9/10, 2/3, 2/4), i know that the order from largest to smallest is 9/10, 2/3, 2/4, but how do i actually go about figuring out WHY its in that order without just looking at it or using graphs?

You need to convert the numbers into the same format.

Step-by-step explanation:

If you want to keep them in fraction form, you need to find the least common multiple. This means the smallest number that can be divided by all of the denominators. For this example, the number would be 60, because 60/10 is 6, 60/3 is 2, and 60/4 is 15. Now that we know this, you need to make every denominator 60. You do this by multiplying the numerator by whatever you needed to multiply the denominator by to get 60. For example, you need to multiply 10 by 6 to get sixty, so you would multiply 9 by 6 as well. You would repeat this pattern with all of the numbers, getting 54/60 (9/10), 40/60 (2/3), and 30/60 (2/4). This makes it very easy to tell which is the larger number.

If you don't want to do all of that, you can use decimal form. To find what each number would be in decimal form, divide the numerator by the denominator. For example, 9 divided by ten is. 9, 2 divided by 3 is. 66 ..., and 2/4 is. 5.

Step-by-step explanation:

To compare fractions, they need to have the same denominator. So you need to find the least common multiple (LCM) of 10, 3, and 4.

To find the LCM, first write the prime factorizations.

3 = 3

4 = 2²

10 = 2*5

The LCM is the product of each factor raised to its highest exponent.

LCM = 2²*3*5

LCM = 60

Now we rewrite each fraction with this new denominator.

9/10 = 54/60

2/3 = 40/60

2/4 = 30/60