When comparing two numbers, we have several fundamental methods. The difference method involves subtracting one number from another and comparing the result with zero. If a minus b is negative, then a is less than b. The quotient method compares the ratio of two positive numbers with one.
The difference method follows four clear steps. First, we calculate a minus b. Then we simplify the expression. Next, we compare the result with zero. Finally, we draw our conclusion. If a minus b is positive, then a is greater than b. If a minus b is negative, then a is less than b.
The quotient method is particularly useful for comparing positive numbers. We divide a by b and compare the result with one. If the quotient is greater than one, then a is greater than b. If the quotient is less than one, then a is less than b. This method is especially effective when dealing with fractions or ratios.
Inequalities follow several fundamental properties. The symmetry property states that if a is less than b, then b is greater than a. The transitivity property means if a is less than b and b is less than c, then a is less 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.