Problem 38 - Prealgebra

Question

Graph the solution of each equation on a number line. $$\frac{n}{12}=3$$

Step-by-Step Solution

Answer

The solution is \( n = 36 \), which is shown as a point at 36 on a number line.

Step 1: Understand the Equation

We are given the equation \( \frac{n}{12} = 3 \). This equation states that a number \( n \) divided by 12 equals 3.

Step 2: Solve for the Variable

To solve for \( n \), multiply both sides of the equation by 12 to isolate \( n \). The equation becomes \( n = 3 \times 12 \).

Step 3: Calculate the Value of \( n \)

Perform the multiplication on the right side of the equation: \( 3 \times 12 = 36 \). Thus, \( n = 36 \).

Step 4: Graph the Solution on a Number Line

On a number line, mark a point at 36. This represents the solution to the equation where \( n = 36 \). The number line should clearly highlight the integer 36, perhaps with an arrow or dot.

Key Concepts

Number Line

A number line is a simple yet powerful tool for visualizing numerical relationships. It's essentially a straight line on which numbers are placed at intervals. Each point on a number line corresponds to a real number. When solving equations, number lines help to make the solutions visible and tangible, offering a clear way to see where numbers fall in relation to one another.

Imagine the line as a ruler, with each tick marking an integer. Negative numbers are to the left of zero, while positive numbers are to the right. To graph a solution, like the number 36, you simply find this point on the line and mark it. You can use a dot, circle, or arrow to indicate this specific value. Number lines are especially beneficial for prealgebra students because they provide a straightforward, visual way to understand how numbers relate to equations.

Graphing Solutions

Graphing solutions on a number line is like creating a map of the answer to an equation. In the equation \( \frac{n}{12} = 3 \), once we solve for \( n \) and find \( n = 36 \), this number can be plotted on a number line.

To effectively graph this:

• Start by drawing a horizontal line and equally spacing numbers on it, ensuring your line includes the number 36.
• You should then place a significant mark at 36, such as a dot or small circle.
• This mark illustrates that 36 is the specific value of \( n \) for our equation.

Graphing on a number line confirms your solution's accuracy visually, making it an essential step in problem-solving, especially at introductory levels of mathematics.

Prealgebra Concepts

Prealgebra is an introductory level of algebra where foundational mathematical skills are developed. In prealgebra, students learn to work with equations, like solving \( \frac{n}{12} = 3 \), which involves understanding variables and operations to isolate unknowns.

Key prealgebra concepts entail:

• Understanding variables as symbols (like \( n \)) that represent unknown numbers.
• Learning operations such as addition, subtraction, multiplication, and division to manipulate and solve for variables.
• Applying properties like the distributive property, which helps in solving more complex expressions later.

Grasping these ideas allows students to confidently tackle basic algebra problems. These skills form the underpinning of all future mathematics study, demonstrating their importance in a student's educational journey.