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Why are two fractions able to settle their differences peacefully
You cannot solve proper fractions. You may be able to solve problems involving fractions but that is NOT the same thing. Furthermore, the solution methods depend on the problem.
The majority of fractions will not be able to become whole numbers. Certain improper fractions, where the numerator is a multiple of the denominator, can become whole numbers. No proper fractions can.
it helps you find the distance between fractions because the new name should be an equivalent fraction. Therefore it should be able to be divided\multiplied by 2 to make the original number.
It may be simplest to convert them all to a common form: rational fractions, decimal fractions or percentages and then compare them. When you are more expert, you may be able to convert them pairwise into a common basis and compare.