Problem 9 - Algebra 1

Question

Graph the numbers on a number line. Then write the numbers in increasing order. $$2,3,-4$$

Step-by-Step Solution

Answer

The numbers in increasing order are \(-4, 2, 3\).

Step 1: Graph the numbers

The numbers in the list are \(2,3,-4\). Draw a number line and mark these three numbers. Negative numbers are to the left of zero on the number line and positive numbers are to the right. So, start from the center of the line with zero, mark -4 to the left of zero, and 2 and 3 to the right.

Step 2: Order the numbers

The numbers are now graphed, and their positions indicate their relative values. The most left number is the smallest while the most right one is the biggest. In this case, from left to right, we have \(-4, 2, 3\). So, the order of these numbers in increasing form is \(-4, 2, 3\).

Key Concepts

Negative Numbers

Negative numbers are numbers less than zero. They are typically represented with a minus sign in front, like \(-4\).
These numbers are found on the left side of zero on a number line. Zero itself is neither positive nor negative.
When you visualize a number line, think of it as a horizontal line with zero at the center.

• All numbers to the left of zero are negative.
• The further left you go, the smaller the numbers become.

Negative numbers are often used to represent situations where something is being taken away or where values have dropped below a baseline. For example, temperatures below freezing or financial debt can be shown with negative numbers.
Understanding their position on a number line is crucial for comparing them to positive numbers.

Positive Numbers

Positive numbers are greater than zero and are found to the right of zero on the number line. In the exercise, numbers like \(2\) and \(3\) are positive.
Generally, positive numbers don't carry any signs, but you can sometimes add a plus sign to make it explicit, such as \(+2\).

• All numbers to the right of zero are positive.
• As you move farther right on the number line, numbers increase.

Positive numbers are commonly used in daily life to indicate values that are above zero, such as profits, savings, or elevations above sea level.
They are generally easier to work with because they align with our intuitive sense of going "up" or "more".

Increasing Order

Increasing order is a way to arrange numbers from the smallest to the largest. Imagine moving from the left to the right on a number line.
When numbers are arranged in increasing order, they follow their position on the number line starting from the far left.

• This means negative numbers will be listed first.
• Followed by positive numbers in ascending value.

In the exercise example, the numbers \(-4, 2, 3\) are ordered from smallest to largest. Increasing order helps in making data easy to analyze.
It's especially useful in mathematical calculations and data analysis because it reduces confusion and organizes information systematically.