When we come across the integers, we can look a series of positive, negative numbers along with zero. We must remember that the negative numbers are always smaller than zero. The positive numbers are always greater than zero. More over we must remember that the negative numbers are always smaller than the positive numbers. Besides this if we need to compare two negative numbers, we first compare the absolute value of the two numbers. Then the greater absolute number if in negative form is smaller than the number with smaller absolute value.
Now we come at the Rational Numbers. We know that the rational numbers include the series of integers and the Fractions with their negative values. Now let us compare two fraction numbers.
If we come across the two fraction numbers, then we must first check if the two fraction numbers have same denominators or not. In case the two fractions have same denominators, the smaller numerator represents the smaller number. On other hand, if we come across the fraction numbers where the numerators are same but the denominators are different. In such a case, the reverse rule works. If the denominator of one number is smaller, it represents the larger number.
Now let us look at the numbers where neither the numerators, nor the denominators are equal, so in such cases, we simply try to make the denominators of the two fractions same by taking the L.C.M. Once the L.C.M. is taken, we make two fractional numbers equivalent such that the two denominators become same. So now it looks like an ordinary fraction number, which can be easily compared and can be arranged in the ascending or descending order on the same basis.
This is how we compare and order integers and Positive Rational Numbers.