Question

Evaluate each expression. $$ 8-4 \cdot 2 $$

Short answer

0

Step-by-step solution

- Identify the Order of Operations

To evaluate the expression, follow the order of operations: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). This is often abbreviated as PEMDAS.

- Perform the Multiplication

According to PEMDAS, perform the multiplication before the subtraction. Multiply 4 by 2 to get 8. The expression now reads: 8 - 8

- Perform the Subtraction

Subtract 8 from 8. 8 - 8 = 0

Key concepts

PEMDAS

When evaluating mathematical expressions, it's essential to follow the order of operations. This order is remembered easily with the acronym PEMDAS, standing for:

• P - Parentheses: Solve anything inside parentheses first.
• E - Exponents: Next, calculate any exponents.
• M - Multiplication and D - Division: Perform these operations from left to right.
• A - Addition and S - Subtraction: Finally, perform these operations from left to right.

In our example, \( 8 - 4 \times 2 \), you see multiplication and subtraction. According to PEMDAS, you must handle the multiplication first.

Multiplication

In the order of operations, multiplication comes before addition and subtraction. In the expression \( 8 - 4 \times 2 \), multiplication must be done first. Multiply the numbers: \( 4 \times 2 = 8 \). Now, the expression is simplified to: \( 8 - 8 \). Remember, always look to complete multiplication (and division) before moving on to addition and subtraction.

Subtraction

After completing multiplication, the next step is subtraction. The simplified expression from our earlier step was \( 8 - 8 \). Perform the subtraction: \( 8 - 8 = 0 \). It's crucial to follow the order of operations correctly so that the solution is accurate. Skipping steps or doing operations out of order can lead to mistakes.

Evaluate Expressions

Evaluating expressions means finding the value of the expression by following mathematical rules, specifically the order of operations. Let's put it all together for our expression \( 8 - 4 \times 2 \):

• Step 1: Identify the operations (multiplication and subtraction).
• Step 2: Follow PEMDAS, starting with multiplication. Calculate \( 4 \times 2 \) to get \( 8 \).
• Step 3: Substitute the product back into the expression, resulting in \( 8 - 8 \).
• Step 4: Perform the subtraction to get \( 0 \).

By understanding and following these steps, you can accurately evaluate any expression, ensuring accurate results.