Understanding the Order of Operations

In mathematics, the order of operations is crucial for accurately solving expressions. The order determines which operations to perform first in a mathematical expression. The commonly accepted order can be remembered using the acronym PEMDAS:

1. Parentheses
2. Exponents
3. Multiplication and Division (from left to right)
4. Addition and Subt\fraction (from left to right)

Example:

Consider the expression:

$$3 + 6 \times (5 + 4) \div 3 - 7$$

Step 1: Calculate inside the parentheses:

$$5 + 4 = 9$$

Step 2: Substitute back into the expression:

$$3 + 6 \times 9 \div 3 - 7$$

Step 3: Perform multiplication and division from left to right:

• First, calculate $6 \times 9$: $$6 \times 9 = 54$$
• Substitute back: $$3 + 54 \div 3 - 7$$
• Next, calculate $54 \div 3$: $$54 \div 3 = 18$$

Now substitute again:

$$3 + 18 - 7$$

Step 4: Finally, perform addition and subtraction from left to right:

• Calculate $3 + 18$: $$3 + 18 = 21$$
• Then, $21 - 7$: $$21 - 7 = 14$$

Thus, the final answer is:

$$14$$

Key Questions:

• What does the acronym PEMDAS stand for?
• Why is the order of operations important in solving expressions?
• Can you create an expression and solve it using the order of operations?

Keywords:

• Order of Operations
• PEMDAS
• Parentheses
• Exponents
• Multiplication
• Division
• Addition
• Subtraction