Calculating the Expression Value

This solution explains how to find the value of the given mathematical expression using the standard order of operations.

Understanding the Order of Operations

To solve this problem correctly, we need to follow the order of operations, often remembered by the acronym BODMAS or PEMDAS:

• Brackets (or Parentheses)
• Orders (or Exponents/Indices)
• Division and Multiplication (performed from left to right)
• Addition and Subtraction (performed from left to right)

The expression we need to evaluate is:

15.2 + 5.8 ÷ 2.9 × 2 - 3.5 × 2 ÷ 0.5

Step-by-Step Calculation

We will break down the calculation step by step, applying the BODMAS/PEMDAS rules.

Step 1: Perform Divisions and Multiplications (Left to Right)

First, identify all the division and multiplication operations and perform them in the order they appear from left to right.

• The first operation to consider is the division: 5.8 ÷ 2.9. Using LaTeX for the calculation: $$ \frac{5.8}{2.9} = 2 $$ The expression now becomes: 15.2 + 2 × 2 - 3.5 × 2 ÷ 0.5
• Next, perform the multiplication: 2 × 2. Using LaTeX: $$ 2 \times 2 = 4 $$ The expression becomes: 15.2 + 4 - 3.5 × 2 ÷ 0.5
• Continue with the next multiplication: 3.5 × 2. Using LaTeX: $$ 3.5 \times 2 = 7 $$ The expression becomes: 15.2 + 4 - 7 ÷ 0.5
• Finally, perform the remaining division: 7 ÷ 0.5. Using LaTeX: $$ \frac{7}{0.5} = 14 $$ The expression simplifies to: 15.2 + 4 - 14

Step 2: Perform Additions and Subtractions (Left to Right)

Now, perform the addition and subtraction operations from left to right.

• First, perform the addition: 15.2 + 4. Using LaTeX: $$ 15.2 + 4 = 19.2 $$ The expression becomes: 19.2 - 14
• Finally, perform the subtraction: 19.2 - 14. Using LaTeX: $$ 19.2 - 14 = 5.2 $$

Final Result

The final value of the expression 15.2 + 5.8 ÷ 2.9 × 2 - 3.5 × 2 ÷ 0.5 is 5.2.