When comparing two numbers, we have several fundamental methods. The subtraction method involves finding the difference between two numbers and comparing it to zero. If a minus b is positive, then a is greater than b. The division method compares the ratio of two positive numbers to one. These visual representations on the number line help us understand these comparison methods clearly.
Inequalities follow several fundamental properties. The symmetry property states that if a is greater than b, then b is less than a. The transitivity property shows that if a is greater than b and b is greater than c, then a must be greater than c. We can add the same value to both sides of an inequality without changing its direction. When multiplying by a positive number, the inequality direction remains the same.
The subtraction method is a systematic approach to compare two numbers. We calculate a minus b and examine whether the result is positive, negative, or zero. If a minus b is positive, then a is greater than b. If the difference is negative, then a is less than b. This visual representation shows how the difference between two points on the number line determines their relative size.