Math Problem Statement

Evaluate 40 - 32 ÷ 8 + 5 × 2 using the order of operations.

Solution

The expression from the images is:

4032÷8+5240 - 32 \div 8 + 5 \cdot 2

To solve this, we must follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).

Let's solve step by step:

  1. Division: 32÷8=432 \div 8 = 4 Now the expression becomes: 404+5240 - 4 + 5 \cdot 2

  2. Multiplication: 52=105 \cdot 2 = 10 Now the expression becomes: 404+1040 - 4 + 10

  3. Subtraction and Addition (from left to right): 404=3640 - 4 = 36 Then: 36+10=4636 + 10 = 46

Thus, the value of the expression is 46\boxed{46}.

Do you want further details or have any questions?

Here are 5 related questions you could consider:

  1. What is the importance of the order of operations in complex expressions?
  2. How would adding parentheses change the result of this expression?
  3. How do the order of operations rules differ across different countries or mathematical systems?
  4. Can you provide an example of when the order of operations would lead to a different result if applied incorrectly?
  5. What happens if there are exponents in the expression?

Tip: When faced with expressions, always evaluate multiplication and division before addition and subtraction, even when no parentheses are present.

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Math Problem Analysis

Mathematical Concepts

Order of Operations
PEMDAS
Arithmetic

Formulas

Division
Multiplication
Addition
Subtraction

Theorems

Order of Operations

Suitable Grade Level

Grades 6-8