Problem 19 - College Algebra with Corequisite Support

Question

For the following exercises, simplify the given expression. \(6+2 \times 2-1\)

Step-by-Step Solution

Answer

The simplified expression is 9.

Step 1: Identify the Order of Operations

To simplify the expression, first identify the order of operations. According to the PEMDAS/BODMAS rule, you should handle 1) Parentheses/Brackets, 2) Exponents/Orders, 3) Multiplication and Division (from left to right), and 4) Addition and Subtraction (from left to right). In this expression, we have multiplication, addition, and subtraction.

Step 2: Perform Multiplication

Identify and perform the multiplication in the expression first. We have '2 times 2', so evaluate this as: \[ 2 \times 2 = 4 \]This simplifies the expression to:\[ 6 + 4 - 1 \]

Step 3: Perform Addition

Next, perform the addition operation. Add the results: \[ 6 + 4 = 10 \]This simplifies the expression to:\[ 10 - 1 \]

Step 4: Perform Subtraction

Finally, perform the subtraction:\[ 10 - 1 = 9 \]Now, the entire expression has been simplified.

Key Concepts

PEMDAS

PEMDAS is an acronym that helps us remember the order in which to perform mathematical operations. It stands for:

• Parentheses
• Exponents
• Multiplication and Division
• Addition and Subtraction

Notice that multiplication and division are on the same level, as are addition and subtraction. This means you perform them from left to right as they appear in the expression. Suppose you see the expression: \(8 + 3 imes 2 - 1\).First, perform the multiplication, then addition, and finally subtraction following this sequence. PEMDAS ensures that we end up with the correct results because skipping this order could lead us astray. Think of it as a traffic light for numbers, making sure everything flows smoothly.

simplifying expressions

Simplifying expressions means breaking down a mathematical expression into its simplest form. By following the order of operations, you can combine or reduce terms to make it easier to understand or solve. In the example \(6 + 2 \times 2 - 1\), you start by focusing on each operation in turn. Multiplication comes first, simplifying \(2 \times 2\) to 4. The expression then becomes \(6 + 4 - 1\). This is much easier to solve now. By dealing with the more complex parts first, you reduce the equation gradually until there's nothing left to calculate. It's just like cleaning up a room: tackle the big messes first, like laundry or toys, and then organize smaller things like books and papers.

mathematical operations

Mathematical operations include addition, subtraction, multiplication, and division. These are the basic actions that allow us to manipulate numbers in various ways. - **Addition (\(+\))** adds quantities together.- **Subtraction (\(-\))** takes one quantity away from another.- **Multiplication (\(\times\))** is repeated addition.- **Division (\(\div\))** is repeated subtraction or the opposite of multiplication.In our exercise, we use these operations to change the expression step by step. In \(6 + 2 \times 2 - 1\), you start with multiplication because it has a higher priority. After simplifying \(2 \times 2\) to 4, you add 6 and 4 to get 10, then subtract 1 to get the final result. Understanding these operations helps see the calculation's bigger picture by breaking it into simpler parts.