Problem 18 - Algebra 1

Question

Use a number line to find the sum. $$-5+8+(-2)$$

Step-by-Step Solution

Answer

The sum of -5, 8, and -2 is 1.

Step 1: Identify the starting point

Start at the number -5 on the number line because it is the first number in the expression.

Step 2: Move to the right

The next number is 8, which is positive. So, move 8 steps to the right from the starting point (-5). This brings us to the number 3 on the number line.

Step 3: Move to the left

The last number in the expression is -2, which is negative. From the number 3 on the number line, move 2 steps to the left. This brings us to the final number 1 on the number line.

Key Concepts

Number Line

A number line is a straight, horizontal line that represents numbers in increasing order, heading right, and decreasing order, heading left. It's a valuable tool in math that helps visualize the addition and subtraction of integers. By plotting numbers on this line, we can easily grasp how each step adds or subtracts from the total. When you perform the operation \(-5 + 8 + (-2)\), each component number is represented as a specific movement:

• Moving right adds a positive value.
• Moving left subtracts a value.

Incorporating a number line allows students to physically trace math operations, providing clarity while solving integer addition problems.

Positive and Negative Numbers

Understanding positive and negative numbers is crucial for integer operations. Positive numbers are greater than zero and appear right of zero on the number line, while negative numbers are less than zero and appear to the left.When you add a positive number, you shift to the right along the line, making the number larger. Conversely, when adding a negative number, you're moving left, effectively subtracting and making the number smaller. This concept is essential when calculating expressions, such as \(-5 + 8 + (-2)\). Here,

• \(-5\) starts you left of zero.
• Addition of \(8\) moves you right.
• Adding \(-2\) shifts you back left.

Grasping these movements clarifies how total values are affected by different integer operations.

Arithmetic Operations

Arithmetic operations on integers involve basic mathematical functions like addition, subtraction, multiplication, and division. In this context, we'll focus on addition. By using a number line, these operations can be easily understood and visualized.When adding integers, like in the expression \(-5 + 8 + (-2)\), keep in mind:

• Each positive number adds to the total and directs you right on the number line.
• Each negative number reduces the total and directs you left.

Arithmetic operations with integers often challenge learners, but breaking them down into visual steps simplifies understanding. It shows how moving right or left affects the final result.

Step-by-Step Problem Solving

Breaking down a math problem step-by-step ensures understanding and accuracy in solving it. The strategy involves visualizing each part and monitoring changes along the way.For the expression \(-5 + 8 + (-2)\):

• Start at \(-5\) on the number line.
• Move right by \(8\) steps to reach \(3\).
• Conclude by moving left \(2\) steps to arrive at \(1\).

Each step in this structured process clarifies how the number line visualizes the arithmetic, connects each operation, and leads you to the correct answer.