**Verification of the given expression:**

To verify the expression (5/4 - 1/2) - 3/2 = 5/4 - (1/2 + 3/2), we will perform the calculations step by step.

Left-hand side:
(5/4 - 1/2) - 3/2 = (10/8 - 4/8) - 12/8 [Multiplying the numerator and denominator of 5/4 by 2]
= 6/8 - 12/8
= -6/8
= -3/4

Right-hand side:
5/4 - (1/2 + 3/2) = 5/4 - 4/2
= 5/4 - 8/4
= -3/4

Since the left-hand side and the right-hand side of the equation are equal (-3/4 = -3/4), the given expression is verified.

**Properties used:**

The property used in this verification is the associative property of addition.

**Associative Property of Addition:**

The associative property of addition states that the grouping of numbers being added does not affect the sum. In other words, when adding three or more numbers, the sum remains the same regardless of how the numbers are grouped.

Mathematically, it can be represented as:
(a + b) + c = a + (b + c)

In the given expression, we can observe the use of the associative property of addition.

- On the left-hand side, we have (5/4 - 1/2) - 3/2. Here, we first subtract 1/2 from 5/4, and then subtract 3/2 from the result.
- On the right-hand side, we have 5/4 - (1/2 + 3/2). Here, we first add 1/2 and 3/2, and then subtract the sum from 5/4.

By using the associative property of addition, we are able to rearrange the numbers being added or subtracted without changing the final result.

**Rational Numbers:**

Rational numbers are numbers that can be expressed as the ratio of two integers, where the denominator is not zero. Rational numbers can be written in the form p/q, where p and q are integers and q is not equal to zero.

Rational numbers include fractions, decimals (both terminating and repeating), and integers (which can be written as fractions with a denominator of 1).

Examples of rational numbers:
- 1/2
- -3/4
- 0.25 (which can be written as 1/4)

Rational numbers can be added, subtracted, multiplied, and divided using the same rules as integers. They form a closed set under addition, subtraction, and multiplication. However, division by zero is undefined in the set of rational numbers.

Understanding rational numbers is essential in various mathematical concepts, including algebra, geometry, and calculus. They have practical applications in everyday life, such as measuring quantities, calculating ratios, and representing probabilities.

In conclusion, the given expression (5/4 - 1/2) - 3/2 = 5/4 - (1/2 + 3/2) is verified, and the property used is the associative property of addition. Rational numbers are numbers