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Chapter 1: Problem 76

Fill in the blank with the inequality symbol \(<\) or \(>\). $$5 \square 7$$

Short Answer

Expert verified
5 < 7

Step by step solution

01

Understand the numbers

Identify the two numbers in the inequality. Here, the numbers are 5 and 7.
02

Numerical comparison

Determine which number is smaller and which number is larger. Compare 5 and 7.
03

Choose the correct inequality symbol

Since 5 is smaller than 7, use the inequality symbol that denotes 'less than' (\textless). So, the correct inequality is \(5 \textless 7\).
04

Fill in the blank

Place the chosen inequality symbol in the blank to complete the inequality: \(5 \textless 7\).

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Key Concepts

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

Numerical Comparison
When working with inequalities, we often start with numerical comparison. This means we need to recognize and understand the values of the numbers involved. Let鈥檚 take the numbers 5 and 7 from our exercise. The idea is to determine which number is larger and which is smaller. Numerical comparison provides the foundation for understanding how to arrange numbers in order and how to properly use inequality symbols. For example, comparing 5 and 7 is straightforward because we recognize that 5 is less than 7.

To practice numerical comparison:
  • Line the numbers up.
  • Think about their order on a number line.
  • Recognize which number appears first (this is the smaller number).
In this case, 5 appears before 7, telling us that 5 is smaller than 7.
Inequality Symbols
After comparing the numbers, we use inequality symbols to express the relationship between them. The main inequality symbols we use are:
  • \textless (less than)
  • \textgreater (greater than)
These symbols show whether one number is smaller or larger than another.

Remember these tips to help keep inequality symbols straight:
  • The \textless symbol looks like an arrow pointing to the left, indicating that the number on the left is smaller.
  • The \textgreater symbol looks like an arrow pointing to the right, indicating that the number on the right is smaller.
In our example, since 5 is less than 7, we use the \textless symbol. So, we write this as: \( 5 \textless 7 \).
Comparing Numbers
To become comfortable with comparing numbers, practice identifying which number is larger or smaller. Using visual tools like number lines or practicing with real-life objects can help. Here鈥檚 how you might proceed:

First:
  • Choose two numbers to compare.
  • Place them in numerical order using a number line if needed.
Next:
  • Decide which number comes first (this one is smaller).
  • Use the correct inequality symbol (\textless or \textgreater) to show the relationship.
For our exercise, we compare 5 and 7. We see that 5 comes before 7 on the number line, helping us understand that 5 is less than 7. Therefore, we use the less than symbol to write: \( 5 \textless 7 \). Practicing these steps routinely can help solidify your understanding of how to compare numbers and use inequality symbols correctly.

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