You don't have to. Some people find that it makes subsequent calculations easier - but not all do.
There is absolutely no REQUIREMENT to do so. It is simply that many people prefer to work with whole numbers.
Multiply every term in the equation by a common denominator of all the fractions. The least common denominator (if different) will result in smaller numbers that you then have to work with but it is not essential that you use it.
it often simplifies arithmetic
It makes it allot less confusing. But, that is just my opinion.
because you just do!
That process will do it every time.
It is not clear why a dividend which is a fraction should result in a mixed number of any kind. In any case, being hopeful will not help you to get an answer.
Multiply the whole equation by the lowest common denominator. ie. multiply each number by the lowest factor that goes into all of the denominators. Example: if you have y/2 = 3x/4 + 16/6 -> the lowest common denominator is 12, because 12 is the lowest number that will clear all the fractions, so: 12 (y/2 = 3x/4 + 16/6) 6y = 9x + 32 -> of course, if you want to graph this linear equation, you need to solve for y, so you would have to divide the whole equation by 6. (6y = 9x + 32)/6 y = 9x/6 + 32/6 -> simplify the fractions y = 3x/2 + 16/3 -> this is your equation for y.
I am not entirely sure what you mean with "clear". But if you want to get rid of fractions in an equation, you can multiply both sides of the equation by the least common multiple of the fractions. For example, take the equation: (1/2)x + 3 = (1/5)x If you multiply both sides by 10, you get: 5x + 30 = 2x
I'm not altogether clear about what you mean. However, the term 'linear programming' means a category of optimisation problems in which both the objective function and the constraints are linear. Please see the link.
The question depends on whether you mean the base is a fraction or the power. It is not clear from the question and the answer will depend on which it is.
It is not clear why you would wish to add them! Changing them to fractions is generally the better option because it averts rounding errors.