Problem 50 - Algebra A Combined Function

Question

Add. See Examples 1 through 12,18, and 19. $$ 8+(-2)+7 $$

Step-by-Step Solution

Answer

13

Step 1: Identify Numbers and Operators

The given expression is \(8 + (-2) + 7\). It involves adding three numbers: 8, \(-2\), and 7.

Step 2: Simplify the Expression

Start by simplifying the expression step by step. First, add the first two numbers: \(8 + (-2)\). Adding \(-2\) is the same as subtracting 2 from 8, so \(8 + (-2) = 6\).

Step 3: Add the Result to the Next Number

Take the result from Step 2, which is 6, and add it to the next number in the expression, 7. So, calculate \(6 + 7\).

Step 4: Final Calculation

Complete the addition from Step 3: \(6 + 7 = 13\). This is the final result of the expression.

Key Concepts

Arithmetic Operations

Arithmetic operations are fundamental mathematical processes where numbers are computed in various ways, such as addition, subtraction, multiplication, and division. In the given exercise, we are focusing on addition, which is the process of finding the total or sum by combining numbers.

When performing arithmetic operations, it is crucial to understand:

• The operation signs: plus (+) for addition, minus (-) for subtraction.
• The numbers being operated on are called 'operands.'

Start with the leftmost numbers and proceed to the right, following the operation indicated by the operation sign. Combining this systematically allows us to solve expressions involving several numbers, as demonstrated in the original solution.

Negative Numbers

Negative numbers are values less than zero, represented with a minus sign (-). Understanding how to work with them is essential in arithmetic operations.

When adding a negative number, think of it as subtracting its absolute value. For instance, adding (-2) is the same as subtracting 2. This is why in the exercise, when we calculate \(8 + (-2)\), it simplifies to \(8 - 2 = 6\).

Important things to remember with negative numbers include:

• Adding a negative number decreases the overall value.
• Subtracting a negative number increases it.
• Negative times negative equals positive.

Properly handling negative numbers ensures accuracy in solving expressions like those in the exercise.

Order of Operations

The order of operations is a set of rules used to determine the sequence in which different operations are performed in a mathematical expression. Knowing this order is crucial to ensure that calculations are done correctly.

For simple addition expressions like the given problem, we are primarily focusing on left-to-right operations. Thus, the operations are executed in the order they appear. However, in more complex expressions involving various operations, follow the standard PEMDAS/BODMAS rules:

• Parentheses/Brackets
• Exponents/Orders
• Multiplication and Division (left to right)
• Addition and Subtraction (left to right)

This set of rules keeps calculations systematic and ensures consistency in results, as illustrated in the orderly steps of the provided solution.