Problem 21 - Algebra A Combined Function

Question

Simplify each expression. $$ 5+6 \cdot 2 $$

Step-by-Step Solution

Answer

The simplified expression is 17.

Step 1: Apply Order of Operations

In mathematical expressions, we follow the Order of Operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)). Here, we need to perform multiplication before addition.

Step 2: Perform Multiplication

Identify the multiplication in the expression. Multiply 6 by 2, which equals 12. Replace the multiplication part of the expression with 12, simplifying it to:\[ 5 + 12 \]

Step 3: Perform Addition

Add the remaining numbers together. Add 5 to 12, which equals 17.\[ 5 + 12 = 17 \]

Key Concepts

PEMDAS

To simplify mathematical expressions accurately, we follow a set of rules known as the order of operations. These rules ensure that regardless of who looks at a problem, everyone comes to the same solution. The acronym PEMDAS helps us remember the correct order:

• P: Parentheses
• E: Exponents
• M and D: Multiplication and Division (from left to right)
• A and S: Addition and Subtraction (from left to right)

Whenever you simplify expressions, remember to first handle operations inside parentheses and then move to exponents, continuing with multiplication and division, and finishing with addition and subtraction.
For example, in the expression \(5 + 6 \cdot 2\), we multiply first because multiplication comes before addition. This application of PEMDAS ensures clarity and consistency in mathematics.

simplifying expressions

Simplifying expressions involves breaking down a mathematical expression into its simplest form. It's like reducing a fraction to its lowest terms. This process makes the expression easier to interpret and use in further calculations.
Start by identifying any operations or terms that can be immediately combined or reduced, such as arithmetic operations or algebraic terms. When simplifying expressions, apply the order of operations step-by-step.
For instance, in the expression \(5 + 6 \cdot 2\), we first calculate \(6 \times 2 = 12\), breaking the expression down to \(5 + 12\). At this point, it becomes simple to compute \(5 + 12\) to reach a final result of 17. By systematically following these steps, we make sure the expression is as straightforward as possible.

mathematical operations

Mathematical operations are the foundation of arithmetic and algebra, including addition, subtraction, multiplication, and division. Each operation has its own rules and can dramatically change the value and form of an expression.
Let's take a deeper look at these operations.

• Addition: Combining numbers to get a total. For example, \(5 + 3\) results in 8.
• Subtraction: Finding the difference between numbers. \(8 - 3\) leads to 5.
• Multiplication: Repeated addition of a number. \(5 \times 2\) is the same as \(5 + 5\), which equals 10.
• Division: Splitting into equal parts or groups. \(10 \div 2\) results in 5.

By mastering these operations, we can effectively work through complex expressions. In our example of \(5 + 6 \cdot 2\), we perform multiplication first, then proceed with addition. This careful order helps in achieving the correct and intended result.