Problem 38 - Algebra 1

Question

Evaluate the expression. $$ 4+(-3)-(-5) $$

Step-by-Step Solution

Answer

The result of the expression \(4 + (-3) - (-5)\) is \(6\).

Step 1: Evaluate The Addition Operation

Start by handling the addition operation \(4 + (-3)\). Adding the negative equivalent is the same as subtracting, so this can also be seen as \(4 - 3\), which gives us \(1\).

Step 2: Evaluate The Subtraction Operation

Then, subtract the negative 5 from the result of the first operation, which is 1. Subtracting a negative is the same as adding, so this can also be seen as \(1 + 5\), which gives us \(6\).

Key Concepts

Integer Operations

Integer operations are essential in the realm of arithmetic and algebra, allowing us to work with both positive and negative whole numbers. The operations involve addition, subtraction, multiplication, and division. Let's take a closer look at why these operations are important:

• They help in solving real-world problems, such as calculating debt or changes in temperature.
• Understanding integer operations is fundamental for grasping more advanced algebraic concepts.
• They form the basis for incoming math topics like solving equations and inequalities.

While addition and subtraction of integers are foundational, multiplication and division also follow specific rules with signs. When multiplying or dividing: - Two positive numbers or two negative numbers always yield a positive result. - A positive and a negative number together produce a negative result. Approaching these operations with a solid understanding of the rules and their real-life analogies can make computational tasks straightforward and intuitive.

Addition and Subtraction of Integers

Adding and subtracting integers involves understanding how to deal with both positive and negative numbers effectively. When you're adding integers:

• If numbers bear the same sign, you add their absolute values and keep the common sign.
• If they have different signs, subtract the smaller absolute value from the larger one, retaining the sign of the larger absolute value.

Subtraction can be thought of as reversing the sign of the number being subtracted and then following the rules of addition. For example:- Given expression is \(4 + (-3) - (-5)\).- **Step 1:** Calculate \(4 + (-3)\). This is the same as \(4 - 3\), giving \(1\).- **Step 2:** Compute \(1 - (-5)\). The subtraction of a negative is equal to addition, so it becomes \(1 + 5\), resulting in \(6\).Practicing these basic operations can build a gaming-changing foundation for future math skills.

Evaluating Expressions

Evaluating expressions is a crucial skill in algebra, as it involves simplifying or calculating the value of expressions in their numerical form. It includes the following steps:- **Identify the operations**: Look for addition, subtraction, multiplication, or division signs.- **Apply order of operations**: Remember the PEMDAS/BODMAS rule, which stands for Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).- **Work through the expression**: Perform each operation carefully and sequentially.Let's consider the expression \(4 + (-3) - (-5)\):1. **First**, begin with \(4 + (-3)\). This equals \(1\) when calculated, as negative 3 acts as a subtraction factor.2. **Next**, tackle \(1 - (-5)\). Here, the subtraction of a negative number flips to addition, producing \(1 + 5\), which equals \(6\).By carefully following these steps, the evaluation of expressions becomes manageable and clear, enhancing problem-solving skills across various math challenges.