Problem 35 - Beginning and Intermediate Algebra

Question

Find each sum. $$ 4+[13+(-5)] $$

Step-by-Step Solution

Answer

The sum is 12

Step 1: Evaluate the expression inside the brackets

First, solve the expression inside the brackets:

Step 2: Simplify inside the brackets

Inside the brackets, we have

Step 3: Apply the evaluated value to the remaining equation

Now, we substitute the result from Step 2 back into the equation:

Step 4: Perform the final addition

Lastly, perform the addition to find the sum:

Key Concepts

arithmetic operations

Understanding arithmetic operations is essential for beginning algebra. These operations include addition, subtraction, multiplication, and division. They form the foundation of most mathematical calculations.
When adding numbers, pay attention to their signs (positive or negative). For instance, adding a negative number is equivalent to subtracting its positive counterpart. For example, adding -5 is the same as subtracting 5.
In the exercise given, the primary arithmetic operation is addition. We start with the inner expression: \(13 + (-5)\). Here, we add a negative number to a positive one. In mathematical terms, this becomes: \[13 - 5 = 8 \].

evaluating expressions

Evaluating expressions involves performing operations in the correct order and simplifying them step-by-step. The order of operations is crucial. You should follow the PEMDAS rule: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
Let's take our exercise as an example: \(4 + [13 + (-5)]\). According to the PEMDAS rule, we first solve the expression inside the brackets: \(13 + (-5)\), simplifying that to 8. Once we have simplified this part, it looks like \[4 + 8\].
By following these rules, we can accurately evaluate and understand complex expressions step-by-step.

simplifying expressions

Simplifying expressions means reducing them to their simplest form, where no further arithmetic operations can be performed. This process usually makes the expressions easier to understand and work with.
In our example, after evaluating \(13 + (-5)\) inside the brackets to get 8, we substitute this back into the main expression. Our equation now looks simpler: \[4 + 8\]. By performing the final addition, we get the sum: 12.
The goal of simplifying is to break down complex problems into more manageable parts. By doing this, we can clearly see the final result with minimal effort.