Final answer:
The simplified value of the expression 4.2 + 0.6 / 3 - 5(0.9 - 0.5) is 2.4 after performing operations within the parentheses, multiplication, division, and then addition and subtraction in order.
Step-by-step explanation:
The question involves simplifying a mixed numerical and algebraic expression using the order of operations, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction). We must first address any calculations within parentheses, then perform any multiplications or divisions from left to right before moving on to addition and subtraction.
To simplify the expression 4.2 + 0.6 / 3 - 5(0.9 - 0.5), we read the expression from left to right, taking care of the operations as they come according to PEMDAS:
- Calculate inside the parentheses: (0.9 - 0.5) = 0.4.
- Multiply by 5: 5 × 0.4 = 2.0.
- Divide 0.6 by 3: 0.6 / 3 = 0.2.
- Add and subtract from left to right: 4.2 + 0.2 - 2.0 = 4.4 - 2.0 = 2.4.
The simplified value of the expression is 2.4.