Problem 76 - Elementary Algebra

Question

Find the sums for the the following problems. \([14+(-8)]+(-2)\)

Step-by-Step Solution

Answer

Answer: The sum of the given numbers is \(4\).

Step 1: Addition within the brackets

We first need to add the numbers within the brackets, i.e., \(14 + (-8)\). To do this, we can think of it as \(14 - 8\). So, the addition within the brackets will be \(14 - 8 = 6\).

Step 2: Add the result to the remaining number

Now that we have the sum of the numbers within the brackets, we need to add it to the remaining number, which is \(-2\). So, we need to find the sum of \(6 + (-2)\). We can think of this as \(6 - 2\). Therefore, the sum will be \(6 - 2 = 4\). So, the sum for the given problem is \(4\).

Key Concepts

Order of Operations

When solving mathematical expressions, it's crucial to follow the order of operations, often remembered by the acronym PEMDAS. This stands for Parentheses, Exponents, Multiplication and Division (left to right), and Addition and Subtraction (left to right). In our exercise, we first deal with the operations inside the parentheses. The expression

• \([14 + (-8)] + (-2)\)

shows that we should perform the operation inside the brackets first. This ensures that we are respecting the natural hierarchy of operations, which helps prevent mistakes and ensures consistency in mathematical calculations.
Understanding and applying the order of operations is foundational in mathematics and vital for successfully tackling complex algebraic expressions.

Integer Arithmetic

Integer arithmetic involves operations with whole numbers, including positive, negative, and zero. In the given problem, we are adding negative and positive integers.

• First, we analyze \(14 + (-8)\).
• This can be thought of as a subtraction problem: \(14 - 8 = 6\).

Next, we take

• \(6 + (-2)\).
• Similarly, this is like \(6 - 2\), which gives us \(4\).

When adding integers:

• If the signs are the same, add the absolute values.
• If the signs are different, subtract the smaller absolute value from the larger, and keep the sign of the number with the larger absolute value.

Mastering these rules is essential for performing accurate calculations with integers in algebra.

Basic Algebra

Basic algebra includes understanding how to manipulate and solve expressions and equations using variables and numbers. In our example, we worked with a simple numeric expression:

• \([14+(-8)]+(-2)\)

to practice fundamental algebraic skills. Basic algebra provides a foundation for more complex topics, helping you solve problems by understanding relationships between numbers and how they can be simplified or rearranged. This process:

• Starts with identifying operations and their order.
• Continues by simplifying the expression step by step, respecting the structure provided by parentheses and signs.
• Finally, arrives at a solution by carefully following arithmetic rules.

Strengthening these skills makes it easier to handle higher-level math and everyday problem-solving by applying logical and structured thinking.