Question

Which is the same as \(3(9-5)\) ? A. \(12-8\) B. \(27+15\) C. \(27-15\) D. \(12+8\)

Short answer

The same as \(3(9-5)\) is Option C: \(27 - 15\).

Step-by-step solution

- Simplify inside the Parentheses

Start by simplifying the expression inside the parentheses: \(9 - 5 = 4\)

- Multiply by the Factor Outside the Parentheses

Now, multiply the result by the factor outside the parentheses: \(3 \times 4 = 12\)

- Compare with the Given Options

We need to find the option that results in 12. Let's evaluate each one:A. \(12 - 8 = 4\)B. \(27 + 15 = 42\)C. \(27 - 15 = 12\)D. \(12 + 8 = 20\)Option C is \(12\), which matches our result.

Key concepts

Order of Operations

Understanding the **order of operations** is crucial when simplifying algebraic expressions. In mathematics, operations must be performed in a specific order to ensure the correct result.
The order can be remembered by the acronym **PEMDAS**, which stands for:

- **P**arentheses: Solve expressions inside parentheses first.
- **E**xponents: Then solve exponents.
- **M**ultiplication and **D**ivision: Perform from left to right.
- **A**ddition and **S**ubtraction: Finally, perform from left to right.

Applying this to our example, we first handle the operation inside the parentheses: \(9 - 5\). Then we multiply by the factor outside: \(3 \times 4\). Correctly following these steps helps avoid mistakes and ensures accuracy.

Multiplication

Multiplication is one of the fundamental operations in algebra. In our problem, after simplifying the expression within the parentheses, we need to multiply the result by the number outside the parentheses.
Here's what happens in our example:

1. First, we simplified the expression inside the parentheses: \(9-5=4\).
2. Next, we multiplied the result by 3: \(3 \times 4 = 12\).

Remember, multiplication can impact the entire equation. Always perform it as indicated by the order of operations. In algebraic expressions, multiplication often follows parentheses.

Parentheses

Parentheses are used in algebra to group parts of an expression that should be evaluated first. Whatever is within the parentheses must be simplified before any other operations are performed.

In our given example, we have parentheses around \(9-5\). By simplifying what's inside the parentheses first, we get \(4\). Only after this step, we proceed to multiplication, which in this case is \(3 \times 4\).

Using parentheses correctly allows for more complex expressions and helps avoid ambiguity. It’s essential to always start by addressing the operations inside the parentheses before moving on to the rest of the expression.