Solving the Expression: (5/4  1/2) x (1/3 + 2/5)
This article will guide you through solving the expression (5/4  1/2) x (1/3 + 2/5). We'll break down the steps using the order of operations (PEMDAS/BODMAS) to arrive at the correct answer.
Understanding the Order of Operations
Before we begin, let's quickly review the order of operations:
 Parentheses/ Brackets
 Exponents/ Orders
 Multiplication and Division (from left to right)
 Addition and Subtraction (from left to right)
Solving the Expression

Simplify the expressions within the parentheses:
 (5/4  1/2): To subtract fractions, they must have a common denominator. The least common denominator of 4 and 2 is 4.
 5/4  2/4 = 3/4
 (1/3 + 2/5): The least common denominator of 3 and 5 is 15.
 5/15 + 6/15 = 11/15
 (5/4  1/2): To subtract fractions, they must have a common denominator. The least common denominator of 4 and 2 is 4.

Multiply the simplified expressions:
 (3/4) x (11/15) = (3 x 11) / (4 x 15) = 33/60

Simplify the fraction: Both 33 and 60 are divisible by 3.
 33/60 = 11/20
Final Answer
Therefore, (5/4  1/2) x (1/3 + 2/5) = 11/20.