To determine the difference between rational numbers, you can subtract one rational number from another. Here's how you can do it:
1. Start with two rational numbers, let's say a/b and c/d, where a, b, c, and d are integers and b and d are not equal to zero.
2. Find a common denominator for the fractions, which is the least common multiple (LCM) of b and d. This is necessary to ensure that the fractions have the same denominator.
3. Rewrite the rational numbers with the common denominator. Multiply both the numerator and denominator of a/b by d and both the numerator and denominator of c/d by b. This step is needed to make sure that the fractions have the same denominator.
4. Now that the fractions have the same denominator, subtract the numerators. The difference between the rational numbers a/b and c/d is (ad - bc) / (bd).
The resulting fraction, (ad - bc) / (bd), represents the difference between the two rational numbers. Simplify this fraction if needed.
Understanding this process allows you to find the difference between any two rational numbers.