Problem 113 - Elementary and Intermediate Algebra

Question

True or false: \(-4>-5 ?\)

Step-by-Step Solution

Answer

True, -4 is greater than -5.

Step 1: Understanding the Statement

The exercise asks us to determine if the statement "-4 is greater than -5" is true or false. To do this, we need to compare the integers on the number line.

Step 2: Identify the Numbers on the Number Line

On the number line, numbers to the right are greater than numbers to the left. -4 is located to the right of -5, meaning -4 is greater than -5.

Step 3: Conclusion

Since -4 is to the right of -5 on the number line, we conclude that -4 is indeed greater than -5.

Key Concepts

Number Line

A number line is a visual representation of numbers laid out in a straight line, helping us understand their relative positions and values. This tool is particularly useful when comparing integers or performing basic arithmetic operations. On a standard horizontal number line:

• Positive numbers are placed to the right of zero.
• Negative numbers are placed to the left of zero.
• The farther right a number is, the greater its value.

This way, you can quickly see which numbers are larger or smaller by looking at their positions: numbers to the right are always larger than those to the left.
Visualizing numbers with a number line can be a powerful way to grasp many math concepts, making it easier to understand and solve problems such as comparing integers.

Negative Numbers

Negative numbers are values less than zero. They appear on the number line to the left of zero. These numbers can be tricky because they operate differently from positive numbers in some respects. When dealing with negative numbers, it's important to remember:

• The lower the absolute value, the larger the actual number (e.g., -3 is larger than -5).
• Negative numbers decrease in value as they move leftward.
• Adding a negative number is like subtracting its absolute value from a positive number.

By understanding these characteristics, working with negative numbers becomes less confusing. For example, when comparing -4 and -5, even though they are both negative, -4 is considered greater because it's less far to the left on the number line.

Greater Than Comparison

'Greater than' comparison helps us determine which of two numbers holds a higher value. In comparing integers, especially involving negative numbers, a useful approach is to visualize their positions on a number line.

• If one number is further to the right on the line than another, it's greater.
• This rule holds true whether the numbers are positive or negative.

For example, when determining whether \(-4 > -5\), we check their placement on the number line. Since -4 is to the right of -5, it's indeed greater. Understanding this concept eliminates confusion and provides clarity in mathematical problems, ensuring accurate comparison results every time.