Question

Evaluate each expression. \((3+3) \times(2+2)\)

Short answer

24

Step-by-step solution

Simplify Inside the Parentheses

First, simplify the expressions inside the parentheses. Evaluate \((3 + 3)\) and \((2 + 2)\).

Calculate Each Parentheses Individually

Calculate the sum inside each parentheses: \(3 + 3 = 6\) and \(2 + 2 = 4\).

Multiply the Results

Finally, multiply the results of the sums from the parentheses: \(6 \times 4 = 24\).

Key concepts

Simplifying Expressions

Simplifying expressions is a fundamental concept in mathematics.
It means making the expression easier to work with.
This involves combining like terms and performing arithmetic operations to arrive at a simpler form.
In our exercise, we start with the expression \( (3+3) \times (2+2) \).

Let's understand this more:

• Combine like terms: When simplifying expressions, combine any terms that are similar.
• Follow the order of operations: Always follow the correct sequence to ensure the expression is simplified correctly.

By following these steps, we make the complicated expression into something more manageable.
This prepares us for the next steps in solving the problem.

Parentheses

Parentheses are used in mathematical expressions to indicate the operations that should be performed first.
Whenever you see parentheses, you need to solve the expression inside them before moving on to other operations.
This is also known as the 'order of operations' rule.
In the given exercise, we have the expression \( (3+3) \times (2+2) \).

Here's a more detailed explanation:

• Step 1: Look inside the parentheses: Identify the expressions inside the parentheses.
• Step 2: Solve the inner expressions first: Perform the arithmetic operation inside the parentheses.
• Step 3: Replace parentheses with results: Insert the simplified values back into the main expression.

Following these steps ensures that we adhere to the correct order of operations.
It makes solving the expression clearer and more structured.

Multiplication

Multiplication is one of the basic arithmetic operations.
When dealing with expressions involving multiplication after simplifying other operations, it's essential to perform it accurately.
From our previous steps: \( (3+3) \times (2+2) \) becomes \( 6 \times 4 \).

To multiply correctly:

• Identify the numbers being multiplied: Ensure you have simplified the expression fully before multiplying.
• Perform the multiplication: Multiply the two numbers to get the final result.
• Double-check your work: Ensure that the multiplication was performed correctly.

In our exercise, multiplying 6 and 4 gives us 24.
This completes the expression with the final simplified result.
Mastering multiplication is essential for handling more complicated mathematical problems efficiently.