Problem 53 - Basic College Mathematics

Question

Use \(<\) or \(>\) for \(\square\) to write a true sentence. $$ 0 \square 23 $$

Step-by-Step Solution

Answer

0 < 23.

Step 1 - Understand the symbols

Identify the meaning of the symbols. The symbols '>' and '<' are used to compare two values. '>' means greater than, and '<' means less than.

Step 2 - Analyze the given numbers

Compare the two numbers provided in the exercise. In this case, the numbers are 0 and 23.

Step 3 - Determine the relation

Decide whether 0 is greater than or less than 23. Since 0 is less than 23, the correct symbol to use is '<'.

Step 4 - Write the true sentence

Replace the square with the correct symbol to form a true sentence: 0 < 23.

Key Concepts

inequality symbols

In mathematics, we often need to compare numbers to see which one is larger or smaller. This is where inequality symbols come in handy. The two primary symbols used for basic comparisons are '<' and '>'.

• '<' means 'less than'.
• '>' means 'greater than'.

These symbols help us form statements that compare two values. For example, if we say '3 < 5', we mean that 3 is less than 5. Similarly, '7 > 2' means that 7 is greater than 2. By understanding these symbols, we can accurately express numerical relationships.

number comparison

Comparing numbers is a fundamental skill in mathematics. It allows us to understand the size of different values relative to each other. To compare two numbers, we look at their sizes and use the appropriate inequality symbol.
For instance, consider the numbers 10 and 4. Since 10 is larger than 4, we use the '>' symbol to write '10 > 4'. On the other hand, if we have the numbers 1 and 8, since 1 is smaller than 8, we use the '<' symbol to write '1 < 8'.
By practicing number comparison, you will become more comfortable with identifying the relationships between different values.

true sentence formation

Forming true sentences using inequality symbols is straightforward once you understand the symbols and comparison process. To create a true sentence:

• Choose the two numbers you need to compare.
• Decide which number is larger or smaller.
• Use the correct inequality symbol to express this relationship.

Let's take an example from the given exercise: Consider 0 and 23. Since 0 is less than 23, we use the '<' symbol. Thus, the true sentence is '0 < 23'.
Practicing these steps will help you quickly and accurately form true sentences in various mathematical problems.