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### Solving Mixed Operations Problems

Solving order of operations math problems involves following a specific set of rules to determine the correct sequence of operations when multiple operations are present in an expression or equation. The common acronym used to remember the order of operations is PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). Here are the steps for solving order of operations problems, along with two examples:

**Example 1: Solve the expression 5 + 3 × (7 – 2)**

Step 1: Parentheses

Evaluate the expression within the parentheses first:

7 – 2 = 5

Now, the expression becomes: 5 + 3 × 5

Step 2: Multiplication

Perform multiplication from left to right:

3 × 5 = 15

Now, the expression becomes: 5 + 15

Step 3: Addition

Perform addition from left to right:

5 + 15 = 20

So, the solution to the expression 5 + 3 × (7 – 2) is 20.

**Example 2: Solve the expression 8 ÷ 2 + (4 – 1)²**

Step 1: Parentheses

Evaluate the expression within the parentheses first:

4 – 1 = 3

Now, the expression becomes: 8 ÷ 2 + 3²

Step 2: Exponents

Calculate the exponent:

3² = 3 × 3 = 9

Now, the expression becomes: 8 ÷ 2 + 9

Step 3: Division and Addition

Perform division and addition from left to right:

8 ÷ 2 = 4

4 + 9 = 13

So, the solution to the expression 8 ÷ 2 + (4 – 1)² is 13.

In both examples, the order of operations was applied correctly, starting with parentheses (or brackets), then exponents, followed by multiplication and division (from left to right), and finally addition and subtraction (from left to right). Adhering to these rules ensures that the expression is evaluated in the correct order, leading to the accurate solution.