Problem 68 - Algebra 2

Question

Evaluate each expression. (lesson \(1-1 )\) $$ 5+9 \div 3(3)-8 $$

Step-by-Step Solution

Answer

The expression evaluates to 6.

Step 1: Parentheses First

According to the Order of Operations (PEMDAS/BODMAS), we first evaluate any operations inside parentheses. In this expression, there is no arithmetic operation inside parentheses, just a number. Hence, we move to the next step.

Step 2: Division

Next, we perform division, which appears before multiplication and addition. The expression is: \[ 9 \div 3 \]This simplifies to: \[ 3 \]

Step 3: Multiplication

Now, multiply the result from the division with 3 (the number inside parentheses): \[ 3 \times 3 = 9 \]

Step 4: Addition

Now we add 5 to the result obtained from multiplication: \[ 5 + 9 = 14 \]

Step 5: Subtraction

Finally, subtract 8 from the result of the addition: \[ 14 - 8 = 6 \]

Key Concepts

PEMDAS

When solving mathematical expressions, it's crucial to follow a specific order to ensure accuracy. This is where PEMDAS comes in handy. PEMDAS stands for Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). This acronym serves as a guide to help us prioritize the operations correctly.

• Parentheses: Always start by solving any operations inside parentheses.
• Exponents: Next, take care of powers and roots, if any.
• Multiplication and Division: Perform these operations as you encounter them from left to right.
• Addition and Subtraction: Finally, handle these operations from left to right.

The idea is to navigate expressions one step at a time, ensuring each operation is tackled in the correct sequence. This prevents errors and ensures consistent results, which is the essence of using PEMDAS.

Arithmetic Operations

Arithmetic operations are the building blocks of mathematics. They include addition, subtraction, multiplication, and division. Understanding these operations allows us to solve expressions like the one given easily.

• Addition: Combining two or more numbers to find their total.
• Subtraction: Taking away a number from another to determine the difference.
• Multiplication: Repeated addition of a number, essentially scaling one number by another.
• Division: Splitting a number into equal parts or groups.

These operations work together, often following the PEMDAS rule, to help us simplify and solve mathematical expressions.

Division and Multiplication

In the order of operations, division and multiplication are handled at the same level. This means in a mathematical expression, you perform them as they appear from left to right. They both work as scaling operations. For instance, in our example:
1. Division: Start with 9 divided by 3, which equals 3.
2. Multiplication: Take that result and multiply it by another number (in our case, 3), resulting in 9.

• Always perform division and multiplication before addition and subtraction, unless parentheses dictate otherwise.
• If both operations appear, handle them sequentially as they appear.

This order ensures an accurate solving process and prevents mistakes often made when bypassed.

Addition and Subtraction

Like multiplication and division, addition and subtraction share the same level in PEMDAS. They are often the last operations to perform when tackling an expression, processed from left to right. In our example, once multiplication was completed, we moved to addition:
1. Addition: Added 5 to the result of multiplication, getting 14.
2. Subtracted 8 from this sum, finally arriving at 6.

• After addressing parentheses, exponents, and division or multiplication, handle addition and subtraction.
• Proceed in the order they appear from left to right, as this maintains consistency in the procedure.

By following these steps, addition and subtraction wrap up the calculation process smoothly, giving us the correct answer.