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Chapter 10: Problem 27

Use either \(<\) or \(>\) for \(\square\) to write a true sentence. $$ -8 \square 8 $$

Short Answer

Expert verified
-8 < 8

Step by step solution

01

Understand the Inequality Symbols

Remember that the symbol \( < \) means 'less than' and the symbol \( > \) means 'greater than'.
02

Compare the Numbers

Compare \(-8\) and \(+8\). A negative number is always less than a positive number.
03

Choose the Correct Symbol

Since \(-8\) is less than \(8\), the correct inequality symbol to use is \( < \).

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Key Concepts

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

greater than symbol
The symbol \( > \) is called the 'greater than' symbol. It indicates that the number on the left side is bigger than the number on the right side. For example, if we write \( 5 > 2 \), it means 5 is greater than 2.
Using the 'greater than' symbol helps us quickly understand and communicate which number is larger when comparing two values.

Key points to remember about the greater than symbol:
  • The open part of the symbol faces the larger number.
  • It鈥檚 used to compare numbers, quantities, and even expressions.
  • Remembering that the symbol points to the smaller number can be a helpful trick.
When you encounter an inequality problem, always take a moment to recall what the symbols mean to avoid any confusion.
less than symbol
The \( < \) symbol is known as the 'less than' symbol. It shows that the number on the left side is smaller than the number on the right side. For example, in the comparison \( 3 < 7 \), 3 is less than 7.
This symbol is essential for understanding inequalities and makes it straightforward to see which number is smaller.

Important notes on the less than symbol:
  • The open part of the symbol points towards the larger number.
  • It鈥檚 used widely in mathematics to compare not just numbers but also variables and expressions.
  • Associating the pointed end with the smaller number can simplify understanding.
Always be sure to write the less than symbol correctly, especially when solving inequality problems, to prevent misinterpretations.
comparing numbers
Comparing numbers is a fundamental skill in mathematics. It involves determining the relationship between two numbers, which is often done using inequality symbols like \( < \) and \( > \).
When comparing numbers, consider the following:
  • Negative numbers are always smaller than positive numbers.
  • You can use a number line to visualize and compare numbers easily.
  • Understand the context of the numbers: whether they are whole numbers, fractions, or decimals.

In the example problem, comparing \(-8\) and \(8\), it is clear that \(-8\) is less than \(8\). Hence, the correct symbol to use is \( < \), forming the inequality \( -8 < 8 \).Practicing such comparisons helps in building strong foundational math skills.

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Most popular questions from this chapter

Subtract and simplify. \(\frac{11}{90}-\frac{11}{120}\)

Multiply. \(\left(-\frac{5}{6}\right)\left(\frac{1}{8}\right)\left(-\frac{3}{7}\right)\left(-\frac{1}{7}\right)\)

Simplify. $$ 14-2(-6)+7 $$

Subtract and simplify. \(6 \frac{1}{2}-2 \frac{3}{10}\)

Divide. $$ -\frac{5}{9} \div\left(-\frac{5}{6}\right) $$
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