Problem 87 - Elementary Algebra

Question

For exercises \(85-108\), write \(>\) or \(<\) between the numbers to make a true statement. $$ -12 \quad 5 $$

Step-by-Step Solution

Answer

-12 < 5

Step 1: Identify the numbers

Examine the two numbers given in the exercise: The first number is \(-12\). The second number is \(5\).

Step 2: Understand the number line

Recall that on a number line, numbers to the left are smaller than numbers to the right. Negative numbers are always to the left of positive numbers.

Step 3: Compare the numbers

Since \(-12\) is a negative number and \(5\) is a positive number, \(-12\) is to the left of \(5\) on the number line. Therefore, \(-12\) is less than \(5\).

Step 4: Write the correct symbol

Since \(-12\) is less than \(5\), write \(-12 < 5\) to make a true statement.

Key Concepts

number line

Understanding a number line is crucial for comparing numbers. A number line is a visual representation where numbers are placed in a straight line. Moving right means the numbers increase, while moving left means the numbers decrease. Negative numbers are always located to the left of zero, and positive numbers are to the right. If you have two numbers, the one on the left is always smaller. This rule holds true whether you are comparing negative numbers, positive numbers, or a mix of both.

negative numbers

Negative numbers are any numbers less than zero and are represented with a minus sign (-). Examples include -1, -5, -12, and -100. On the number line, negative numbers are always to the left of zero, indicating they are smaller than zero. The further left a negative number is, the smaller its value. For example, -12 is smaller than -5 because -12 is farther to the left.

positive numbers

Positive numbers are any numbers greater than zero and do not have a minus sign. Some examples are 1, 5, 12, and 100. These numbers appear to the right of zero on the number line. The further right a number is located, the larger its value. Comparing positive numbers is straightforward because you just look at which number is further to the right; for example, 12 is larger than 5 because it is further to the right on the number line.

greater than and less than symbols

The symbols > (greater than) and < (less than) help us compare two numbers. To use these symbols, remember the open end of the symbol always points towards the larger number. When comparing -12 and 5, you notice -12 is a negative number and 5 is a positive number. Since negative numbers are always less than positive numbers, write -12 < 5 to make a true statement. Here are some tips:

• If the left number is smaller, use < (e.g., -12 < 5).
• If the left number is greater, use > (e.g., 5 > -12).