Problem 93 - Elementary Algebra Within Reach

Question

Plot the numbers on the real number line. $$\frac{3}{2}, 1,-1$$

Step-by-Step Solution

Answer

On the number line, from left to right, it goes \(-1\), \(0\), \(1\), and \(\frac{3}{2}\).

Step 1: Plotting Positive Numbers

Starting from the origin (0), move right on the number line to plot \(1\) and \(\frac{3}{2}\). Remember, \(\frac{3}{2}\) is greater than \(1\) and it will be placed to the right of \(1\).

Step 2: Plotting Negative Numbers

Starting from the origin (0), move left on the number line to plot \(-1\). Negative numbers will always be placed to the left of the origin in a number line.

Step 3: Observing the Number Placement

Observe the entire range of your numbers on the number line. From left to right, it will be \(-1\), \(0\), \(1\), and \(\frac{3}{2}\).

Key Concepts

Plotting Numbers

When you're learning to plot numbers on the real number line, think of it as placing markers on a straight path. Imagine a long ruler, where every point or marker is a number. The center of this line is called the "origin," represented by 0.

Here's a simple guide to how you start plotting:

• First, identify each number you need to plot. In your exercise, these were \(\frac{3}{2}\), \(1\), and \(-1\).
• Next, decide where each number will go on the number line compared to the origin.
• Ensure that numbers increase as you move to the right and decrease as you move left.

To make plotting easier and more accurate, visualize or draw equal spaces representing each 'integer'. Place your numbers at the right incremental spots based on their value.

Positive Numbers

Positive numbers are numbers greater than zero and are placed on the right side of the origin in the real number line. Consider them as the steps forward from zero. They increase as you move further away from the origin.

Here's how to plot them:

• Start at the origin (0).
• Count your steps towards the right to find space for each positive number.
• For example, plot \(1\) by moving one full unit to the right. To plot \(\frac{3}{2}\) (which is the same as 1.5), go one and a half units to the right.

It's vital to recognize that numbers like \(\frac{3}{2}\) require you to think about fractions as parts of a whole number. This understanding helps in plotting more precise positions.

Negative Numbers

Negative numbers are fascinating! They're the ones you plot by moving to the left of the origin on the real number line. Think of these as stepping backwards or below zero. Each step left represents a reduction in value.

Here's the step-by-step on plotting them:

• Start again at the origin (0).
• Move in the opposite direction from positive numbers, to the left.
• For instance, plotting \(-1\) means moving one unit left from zero.

Remember, the more you move left, the smaller in value the numbers become. It's like climbing down a ladder with each negative number representing a step further down. Get comfortable with negative numbers, as they often appear in math both on their own and as solutions to equations.