Math Problem Statement

Solve the expressions: 1. 9 ÷ 3 × 2 - 12 ÷ 9 = ? 2. 19 - 5 + 12 = 19 - 16 = ?

Solution

It seems that you've provided an image with mathematical problems. Let me extract the expressions and their explanations:

Problem 25:

  • The expression given is 9÷3×212÷99 \div 3 \times 2 - 12 \div 9.
  • The result obtained is 106106, but this appears incorrect.

Problem 26:

  • The expression is 195+12=191619 - 5 + 12 = 19 - 16.
  • The result obtained is 11, and this is correct.

Let's correct the reasoning for Problem 25:

  1. First, apply the order of operations (PEMDAS/BODMAS: Parentheses/Brackets, Exponents/Orders, Multiplication and Division (left to right), Addition and Subtraction (left to right)).

    The correct steps are:

    • 9÷3=39 \div 3 = 3
    • 3×2=63 \times 2 = 6
    • 12÷91.3312 \div 9 \approx 1.33

    Now the expression becomes: 61.33=4.676 - 1.33 = 4.67

Thus, the correct result should be approximately 4.67, not 106.

Would you like more details on the solution?

Here are 5 related questions to deepen your understanding:

  1. What is the correct order of operations in mathematics (PEMDAS/BODMAS)?
  2. How do you handle division with decimals?
  3. Why is it important to follow the order of operations strictly?
  4. What is the significance of rounding in calculations involving decimals?
  5. How can you check your work when evaluating mathematical expressions?

Tip: Always double-check operations step-by-step, especially when multiple division and multiplication actions are involved.

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Math Problem Analysis

Mathematical Concepts

Order of Operations
Division
Multiplication
Subtraction
Simplification

Formulas

PEMDAS (Parentheses, Exponents, Multiplication/Division, Addition/Subtraction)

Theorems

Basic Arithmetic Rules

Suitable Grade Level

Grades 6-8