Problem 30 - Elementary and Intermediate Algebra

Question

Simplify. $$ 3-4 \cdot 2 $$

Step-by-Step Solution

Answer

-5

Step 1: Understand the Order of Operations

According to the order of operations (PEMDAS/BODMAS), multiplication and division are performed before addition and subtraction. So first, identify and perform any multiplication or division in the equation.

Step 2: Perform the Multiplication

Identify the multiplication in the equation, which is ewline \(4 \times 2\). Calculate the result: \(4 \times 2 = 8\).

Step 3: Substitute Back into the Equation

Replace the multiplication part in the original equation with its result. The equation now becomes ewline \(3 - 8\).

Step 4: Perform the Subtraction

Finally, perform the subtraction: \(3 - 8 = -5\).

Key Concepts

PEMDAS

PEMDAS is a helpful acronym that stands for: Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction. This order tells you which operations to perform first in a math equation.

When simplifying, always begin with:

• Parentheses first (do any calculations inside parentheses).
• Then handle Exponents (like squared or cubed numbers).
• Next come Multiplication and Division, done from left to right.
• Lastly, deal with Addition and Subtraction, also from left to right.

Understanding PEMDAS ensures you solve equations correctly and avoid errors.

Multiplication and Division

In the PEMDAS order, Multiplication and Division come after Parentheses and Exponents, but before Addition and Subtraction.

Here's what to remember:

• First, look left to right and perform any Multiplication or Division as you find them in the equation.
• It's crucial to do these first because they can significantly change the outcome if performed out of order.

For example, in the equation from the exercise, you have to solve the multiplication part first:
ewline \(4 \times 2\)
Once you have the result of that multiplication, you can move to the next step.

Addition and Subtraction

Once all Parentheses, Exponents, Multiplication, and Division are handled, move on to Addition and Subtraction. Just like Multiplication and Division, these operations are performed from left to right.

Remember:

• Addition and Subtraction are the last operations you perform.
• Doing these steps in this order ensures your final answer is correct.

Looking at the exercise example:
ewline After doing the multiplication (4 × 2 = 8), replace it in the equation:
ewline \(3 - 8\)
Finally, perform the subtraction:

\(3 - 8 = -5\)
And that gives you the simplified form of the equation!