Question

Evaluate the expression. \(5+2+(-3)\)

Short answer

The evaluated expression is 4.

Step-by-step solution

Understanding Expressions

An expression is a string of numbers, variables and operations. Here we do not have any variables but only three numbers and the operations addition and negative sign, which turns the number it precedes into a negative number. The expression \(5+2+(-3)\) means that we have to add 5, 2 and -3 (which is the same as subtracting 3).

Adding Positive Numbers

First add the positive numbers: \(5 + 2 = 7\).

Adding Negative Number

Next, add the negative number: \(7 + (-3) = 4\).

Key concepts

Expressions in Algebra

In algebra, expressions are the building blocks that represent numbers, variables (symbols that stand for numbers), and operations. They can be as simple as a single number or as complex as a combination of multiple operations and variables. An expression like 5+2+(-3) might look simple, yet it wonderfully illustrates the essential concepts in algebra: combining positive and negative numbers through basic operations to produce a new value.

When evaluating such an expression, the order of operations—often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction)—plays a significant role. However, in our straightforward example, we only have addition, so we can proceed from left to right. Understanding this concept ensures that students can tackle more intricate algebraic expressions by breaking them down into manageable parts.

Adding Positive and Negative Numbers

The process of adding numbers with different signs is a fundamental skill in algebra. Adding a positive number is straightforward, as it increases the value of the expression. On the other hand, adding a negative number—like (-3) in our example—is equivalent to subtracting that number's absolute value. This can be visualized on a number line where positive numbers move to the right and negative numbers move to the left.

Thus, when we have 7 + (-3), we start at 7 and move three places to the left, landing on 4. Keeping track of these movements helps students internalize how combining positive and negative values work, enabling them to handle more complex calculations confidently.

Basic Algebraic Operations

Algebra relies heavily on four basic operations: addition, subtraction, multiplication, and division. Each operation follows specific rules and has a distinct effect on numbers. Our exercise involves addition, an operation that combines values to produce a sum. It's associative and commutative, meaning numbers can be added in any order, and the sum remains the same.

When faced with a mix of positive and negative numbers, understanding how these rules apply simplifies the evaluation process. For instance, in our example, starting by adding the positive numbers and then including the negative number simplifies to a single step: moving along the number line to find the final value. Grasping these operations paves the way for students to delve into more advanced algebraic concepts.