Problem 23 - Elementary Algebra

Question

For exercises 1-80, evaluate. $$ (20-6) \div 2+1 $$

Step-by-Step Solution

Answer

8

Step 1 - Parentheses First

Evaluate the expression inside the parentheses. \(20 - 6 = 14\)

Step 2 - Division

Next, divide the result by 2. \(14 \div 2 = 7\)

Step 3 - Addition

Finally, add 1 to the result from the division. \(7 + 1 = 8\)

Key Concepts

Parentheses

In mathematical expressions, parentheses are used to indicate which operations should be performed first. This is also known as 'bracketing' or 'grouping'. The general rule is: **always perform the calculations inside the parentheses before anything else**.

Let’s look at our exercise: \((20-6) \div 2 + 1\).

In this case, we first evaluate the expression within the parentheses: \(20 - 6 = 14\).

Why is this important?

• Parentheses ensure that calculations are executed in the intended order.
• They help clarify complex expressions.

This makes it essential to identify and solve the operations within parentheses before moving on to the other arithmetic operations.

Division

After evaluating any expressions within parentheses, the next step is division. According to the order of operations (PEMDAS/BODMAS rules), **division** and **multiplication** come after parentheses and exponents, but before addition and subtraction.

In our exercise, after solving the expression inside the parentheses \(20-6 = 14\), we proceed to the division step: \(14 \div 2 = 7\).

Why is division important in the order of operations?

• It breaks down the problem step-by-step.
• Ensures accurate redistribution of quantities.

This clarification means we handle division immediately after parentheses (if it's present), ensuring we follow the proper operation sequence and get the correct result.

Addition

The final step in our order of operations is addition. This step comes after we have completed any calculations inside parentheses, then any multiplications or divisions.

In our exercise, after solving the division \(14 \div 2 = 7\), we move on to the addition: \(7 + 1 = 8\).

Addition is considered a fundamental arithmetic operation that combines quantities:

• It allows the combination of values.
• Simplifies expressing total amounts.

Following the order of operations, addition is one of the last steps, ensuring all preceding operations are accurately performed before summing up quantities.