Problem 4 - Algebra 1

Question

Complete the statement using \(>\) or \(<\). \(-3 \underline{?}-5\)

Step-by-Step Solution

Answer

-3 > -5

Step 1: Understand the comparison

First understand that we are trying to compare two numbers: -3 and -5. The question asks whether -3 is greater than or less than -5.

Step 2: Compare the numbers

On the number line, numbers to the right are greater than numbers to the left. Negative numbers are to the left of zero on the number line. The closer a negative number is to zero, the greater it is. Thus, -3 is to the right of -5, making -3 greater than -5.

Step 3: Fill in the blank

Now that we have identified -3 is greater than -5, we can fill the blank with the appropriate symbol, which is '>'. So the completed statement is -3 > -5.

Key Concepts

Understanding Negative Numbers

Negative numbers are numbers that are less than zero. They are typically written with a minus sign in front of them. When counting backwards from zero, the first number is -1, then -2, and so on. Each step to the left on a number line increases the negative value.

Negative numbers are used in various real-world situations, such as temperatures below freezing and debts in financial accounts. With negative numbers, the larger the numeral after the minus sign, the smaller its value. For instance, -3 is greater than -5 because it is less far from zero. This is an important concept to grasp as it can initially feel counterintuitive.

Navigating the Number Line

The number line is a visual representation that helps us understand the order and magnitude of numbers. It is a straight line where each number belongs to a specific point linked with its real value (positive or negative).

• The number line extends infinitely in both directions.
• Positive numbers are placed to the right of zero, while negative numbers are to the left.
• The further right a number is, the larger its value; conversely, numbers further left are smaller.

When comparing numbers, the number to the right of the other is always greater. This simple rule aids in understanding statements such as -3 > -5, where -3 is positioned to the right of -5 on the number line.

Comparing Numbers Effectively

Comparing numbers involves determining which of two numbers is greater or smaller. This process is crucial in mathematics and everyday decision-making. With positive numbers, it is straightforward: 5 is greater than 3 because 5 is further from zero in the positive direction.

However, with negative numbers, the concepts require careful understanding.

• Numbers that are closer to zero are larger than those further away.
• For instance, -2 is greater than -7 because -2 is closer to zero.
• The symbol '>' means "greater than," while '<' means "less than".

This knowledge is vital and applying it allows us to solve problems like determining if -3 is greater than -5, ultimately filling the blank with the correct symbol.