Problem 47 - Elementary Algebra

Question

Fill in the blank with \(<,=,\) or \(\geqslant\). -500 _____ 200

Step-by-Step Solution

Answer

-500 is less than 200; use <.

Step 1: Understand the Problem

We need to compare two numbers and determine the relationship between them using comparison symbols: less than ( < ), equal to ( = ), or greater than or equal to ( ≥ ).

Step 2: Identify the Numbers

In this problem, the two numbers given are -500 and 200 .

Step 3: Comparing the Numbers

To find the relationship, determine which number is smaller. Since negatve numbers like -500 are always smaller than positive numbers like 200 , we conclude -500 < 200 .

Step 4: Select the Correct Symbol

Based on our comparison, we select the less than symbol ( < ) to fill in the blank: -500 < 200 .

Key Concepts

Comparing Numbers

When comparing numbers, we evaluate their values to understand the relationship between them. The primary symbols used for comparison are:

• < : less than
• = : equal to
• \( \geqslant \) : greater than or equal to

To determine which symbol to use, start by examining each number separately. If one number is further to the left on the number line, it is smaller. For example, with the numbers -500 and 200:- -500 is located to the left of 200.- This shows that -500 is less than 200.Therefore, the relationship between -500 and 200 is symbolized by -500 < 200.

Negative Numbers

Negative numbers represent values less than zero. They are shown with a minus (-) sign in front. A key idea about negative numbers is that the farther left they are on the number line, the smaller their value. Here's how to understand negative numbers better:

• Negative numbers are less than zero, e.g., -1, -20, -500.
• Closer negative numbers to zero are larger than those further away, e.g., -1 is greater than -20.

In comparison problems, such as -500 and 200, remember: - Negative numbers are always smaller than positive numbers. So in this case, -500 < 200.

Number Relationships

Understanding number relationships involves knowing how numbers relate to each other in terms of size or value. This is crucial in determining the correct comparison symbol. Key points to consider include:

• Positive numbers are always greater than zero and any negative number.
• Two numbers of the same value are equal, symbolized by =.
• The concept of 'greater than or equal to' (\( \geqslant \)) combines both greater than and equal to. However, negatives are neither greater nor equal compared to any positive number unless both numbers are zero.

In the exercise, the relationship is built on the fact that -500 is a negative number and 200 is positive, leading us to correctly use -500 < 200.