Problem 10 - Elementary Algebra

Question

For the following problems, use the order of operations to find each value. $$2+3(6)$$

Step-by-Step Solution

Answer

Answer: The value of the expression is 20.

Step 1: Identify the operations and their order

In the given expression, we only have two operations, addition and multiplication: 2 + 3(6). As per the order of operations, we need to perform multiplication first and then addition.

Step 2: Perform multiplication

Start by performing the multiplication inside the parenthesis: 3 * 6 = 18. Our expression now becomes: 2 + 18.

Step 3: Perform addition

Now, perform the addition operation: 2 + 18 = 20.

Step 4: Write the final answer

The final value of the expression is 20.

Key Concepts

Addition

Addition is one of the most basic operations in mathematics. It involves combining two or more numbers to get a total or sum. In our given expression, after performing the multiplication, we proceed with addition.
Following the order of operations, the expression becomes 2 + 18.
This step involves simply combining these numbers together to reach a total of 20.

• **Addition combines numbers.**
• Perform after other higher precedence operations (like multiplication).
• Used to find the sum or total value of numbers.

Remember, addition plays a crucial role in solving expressions, especially when followed by operations like multiplication in an expression.

Multiplication

Multiplication is another fundamental operation that represents repeated addition. In the expression 2 + 3(6), multiplication needs to be done first according to the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).

• **Multiplication is performed before addition.**
• It simplifies expressions and reduces them into single terms.
• In our problem, 3 * 6 results in 18.

By multiplying first, we ensure that the overall value in complex calculations is accurate. It's critical to recognize and commence with multiplication where required.

Mathematical Expression

A mathematical expression is a combination of numbers and operations arranged according to mathematical rules. The goal is often to simplify or solve these expressions while adhering to the order of operations.
In our exercise, the expression was 2 + 3(6). To solve this:

• **Recognize the operations involved.**
• Identify the correct order to perform these operations.
• Simplify step-by-step to reach the final value.

Understanding how to decompose a mathematical expression correctly ensures accurate and logical problem-solving. It simplifies complex problems by breaking them down into manageable operations.