Problem 61 - Algebra 1: Concepts and Skills

Question

Evaluate the expression. \(5+8-3\)

Step-by-Step Solution

Answer

The evaluated expression is \(10\).

Step 1: Identify the operations

Look at the expression \(5+8-3\). You can identify two operations here: addition and subtraction. In this case, the operations are just executed from left to right.

Step 2: Perform the addition

Start by adding \(5+8\) which results in \(13\). The expression then reads as \(13-3\).

Step 3: Perform the subtraction

Next, subtract \(3\) from \(13\). This results in the final answer \(10\).

Key Concepts

Basic Arithmetic

Understanding basic arithmetic is essential for evaluating simple expressions such as 5+8-3. Basic arithmetic includes the fundamental operations of addition, subtraction, multiplication, and division. When we work with numbers, these operations are the building blocks for more complex mathematical concepts.

To begin with, recognize the numbers and symbols involved in the expression. Here, for instance, the numbers are 5, 8, and 3, and the symbols + and - represent addition and subtraction, respectively. Grasping this foundation allows us to proceed with evaluating the expression step by step, ensuring accuracy in the final result.

Addition and Subtraction

Addition and subtraction are two of the four basic operations in arithmetic. Addition combines numbers to increase their total value, while subtraction removes value from a number, reducing its quantity.

Practical Tip

When facing a problem that includes both addition and subtraction, like 5+8-3, start by identifying which operation occurs first. If they occur in sequence without any grouping symbols such as parentheses, they are typically performed from left to right. In our example, after adding 5 and 8 to get 13 (5+8=13), you would subtract 3 from 13 to reach the final answer (13-3=10). These fundamental skills allow us to manipulate numbers to solve real-world problems.

Order of Operations

The order of operations is a collection of rules that clarify which procedures to perform first in a given mathematical expression. In our problem, 5+8-3, it might seem that there's no need for these rules because the operations appear straightforward. However, more complex expressions require a clear order of operations to avoid ambiguity and to achieve consistency in results.

The acronym PEMDAS can help remember the order: Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). Since our example does not contain parentheses, exponents, or any multiplication or division, we simplify by performing addition first and then subtraction. Remembering these rules ensures that all arithmetic problems are solved correctly.