I assume you mean, with different denominators. If you want to add the fractions, subtract them, or compare them (determine which one is greater), you have to convert them to similar fractions (fractions with the same denominator) first. Converting to similar fractions is not necessary, and usually doesn't even help, if you want to multiply or divide fractions.
No.
Finding the LCM will help you add and subtract fractions. Finding the GCF will help you reduce fractions.
The largest factor of any number is the number itself.
LCD (lowest common denominator) refers to fractions and your question did not include any fractions. However, assuming that you're looking to reduce 75/275, the answer is 3/11.
As fractions are numbers you would use the same methods as any other comparison or ordering of numbers. Largest to smallest or smallest to largest are the most likely ways
Rational numbers are (basically) fractions. You can compare any two fractions by converting them to fractions with a common denominator, and then comparing their numerators.You can also convert them to their decimal equivalent (just divide numerator by denominator); that also makes them fairly easy to compare.
I assume you mean, with different denominators. If you want to add the fractions, subtract them, or compare them (determine which one is greater), you have to convert them to similar fractions (fractions with the same denominator) first. Converting to similar fractions is not necessary, and usually doesn't even help, if you want to multiply or divide fractions.
Assuming the fractions are "normalized" (the fractional part is less than 1): First compare the integer part. If the integer part is the same, you need to compare the fractions. If the denominator of the fractions is different, you have to convert to a common denominator. The simplest way to find a common denominator is to multiply both denominators (i.e., you don't need the LEAST common denominator - any common denominator will do).
If the fractions have different denominators, you need to: 1) Convert to equivalent fractions with a common denominator, 2) Compare the numerators. If the fractions already have the same denominator, there is no need for the first step - which happens to be the most difficult step. Note that as a shortcut, you don't need the LEAST common denominator, any denominator can do. Thus, you can just use the product of the two denominators as the common denominator. As a result, to compare the fractions, you simply multiply the numerator of each fraction by the denominator of the other one, and then compare. However, this is still more work than simply comparing two numbers.
Rational numbers are infinitely dense so there is no "next" fraction. There are infnitely many fractions between any two numbers. And there are infinitely more between any two of them, and so on.
To compare any two fractions they first need to be converted to numbers on a similar basis: Convert both to decimals: the smaller decimal is the smaller fraction. Find equivalent fractions with the same denominator: the fraction with the smaller numerator is the smaller number. Find equivalent fractions with the same numerator: the fraction with the larger denominator is the smaller number. I recommend that the last of these is used for integral reciprocals (comparing 1/2, 1/4, 1/7 etc) or by more proficient users.
You need to be able to compare two fractions at a time, to see which one is greater. One way to do this is to convert two fractions at a time to a common denominator. It need not be the least common denominator - any common denominator will do, therefore you can just multiply the two denominators. Another way to compare fractions is to convert them to decimal. This can quickly be done with a calculator.
fractions that can not be simplified any more
You should not have any remainders in fractions!
The concept of consecutive has no meaning for fractions. This is because there are infinitely many fractions between any two fractions. And between any two of them, there are infinitely many, and so on. As a result, there cannot be any "next" fraction.
If two fractions have the same [positive] denominator, then the smaller numerator implies the smaller fraction. Furthermore, the ratio of the numerators is the ratio of the fractions. So, for example, if you have 3/17 and 5/17 then, since 3 < 5, it follows that 3/17 < 5/17 and the two fractions are in the ratio 3:5. That is, the first fraction is 3/5 of the second. All of the above remains true if you replace 17 by any other positive number (including an irrational number).