Problem 19 - Prealgebra and Introductory Algebra

Question

On the number line, which number is: 6 units to the right of \(-3 ?\)

Step-by-Step Solution

Answer

The number which is 6 units to the right of \(-3\) on the number line is \(3\).

Step 1: Identify the starting point

The starting point on the number line is given as \(-3\)

Step 2: Determine the direction of movement

The movement should be made to the 'right' as directed. Remember, moving to the right on the number line is equivalent to adding values.

Step 3: Move the specified units

The exercise specifies that the movement should be of 6 units. So, adding 6 to the starting point value we get \(-3+6=3\)

Key Concepts

Adding Integers

Understanding how to add integers is an essential skill in math. When you add integers, you are essentially combining values to reach a new total. On a number line, moving to the right indicates adding positive values. To connect this to our exercise, we started at \(-3\). This is our initial integer. The exercise asks us to move 6 units to the right. Thus, we are adding 6 to \(-3\).

• Starting Integer: \(-3\)
• Units to Move Right (Add): 6
• Calculate: \(-3 + 6 = 3\)

The direction and number of units are crucial cues. Moving to the right always leads to adding positive integers, whereas to the left means adding negative integers. Always check the sign of the integers being added and consider direction for precise calculations.

Coordinate System

A coordinate system, particularly the number line, is an effective way to visualize mathematical operations involving integers. A number line is a straight horizontal line with numbers placed at strategic intervals. It helps in understanding the concept of positioning and direction when adding or subtracting integers.In our exercise, we used the number line to find a number 6 units to the right of \(-3\). The initial position on the number line was \(-3\), a point situated left of 0, indicating a negative value. By counting 6 units to the right, we pass through different integer points until reaching 3, our final position.

• Start at \(-3\)
• Move right for positive addition
• End at 3

The number line not only reflects spatial reasoning but also aids in easy calculation of addition and subtraction of integers by emphasizing direction and distance.

Elementary Math Problem Solving

Solving elementary math problems involves a clear understanding of basic arithmetic operations and their representation on a number line. Using step-by-step logic effectively breaks down problems into manageable parts, making them easier to solve.For this exercise, we started by identifying the initial position: \(-3\). Understanding the direction (right) and the number of units (6) formed the strategy. We then calculated the result by adding, helping avoid common pitfalls like incorrect direction or calculation.

• Start with a known value
• Follow the directed movement (right for addition)
• Perform calculations step by step: \(-3 + 6 = 3\)

Simple steps not only make problem-solving more manageable but also foster a deeper understanding, providing foundational skills crucial for more complex mathematical concepts and applications in the future.