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Chapter 1: Problem 73

Use \(<\) or \(>\) for \(\square\) to write a true sentence. Draw the number line if necessary. $$ 34 \square 12 $$

Short Answer

Expert verified
34 > 12.

Step by step solution

01

- Understand the Problem

The task asks for the appropriate inequality symbol (< or >) to complete the sentence so that it is true: \(34 \square 12\). We need to determine the relationship between the numbers 34 and 12.
02

- Determine the Relationship

Compare the two numbers. Notice that 34 is greater than 12. In mathematical terms, 34 > 12.
03

- Draw the Number Line (Optional)

If visualizing helps, draw a number line. Place 12 and 34 on the number line. Since 34 is to the right of 12 on the number line, it further confirms that 34 is greater than 12.
04

- Write the Correct Inequality

Based on the comparison, use the 'greater than' symbol to complete the sentence correctly: \(34 > 12\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Number Comparison
To solve inequalities like the example given, we begin with number comparison. Number comparison involves determining which of two numbers is larger or smaller. It is fundamental to many areas of mathematics and everyday problem-solving.
For example, when comparing 34 and 12, you need to decide if 34 is greater than, less than, or equal to 12. Assessing their values, we find that 34 is greater than 12. This process involves:
  • Identifying both numbers
  • Analyzing their values
  • Deciding their relative sizes in comparison to each other
Understanding number comparison is a key skill, as it leads to correct usage of symbols like < and >.
Number Line
The number line is a powerful visual aid for comparing numbers. It is a simple straight line where each point corresponds to a number.
Here's how to use a number line for our example:
  • First, draw a horizontal line.
  • Mark points on this line, spacing them evenly to represent different numbers.
  • Locate and label the numbers you are comparing 鈥� in this case, 12 and 34.
You will see that 34 is to the right of 12 on the number line. This visualization helps confirm that 34 is greater than 12. The number line shows not just the value comparison but also the magnitude difference between the numbers.
Greater Than Symbol
In mathematics, we use different symbols to represent relationships between numbers. The 'greater than' symbol (>) is used to show that one number is larger than another.
For example, in the statement 34 > 12:
  • The symbol > points to the smaller number (12).
  • It opens towards the larger number (34).
  • This format clearly communicates that 34 is greater than 12
Remembering this simple rule can help you accurately solve many inequalities. Always make sure the opening of the symbol faces the larger number to represent a 'greater than' relationship.

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