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Chapter 2: Problem 11

Fill in the blanks. The symbol \(<\) means _____. The symbol \(>\) means Answer _____

Short Answer

Expert verified
The symbol \( < \) means 'is less than,' and the symbol \(>\) means 'is greater than.'

Step by step solution

01

Understand the Less Than Symbol

Firstly, understand the meaning of the symbol \( < \). In mathematics, when we compare two numbers, the symbol \( < \) is used to denote that the number on the left side is smaller than the number on the right. For example, \(3 < 5\) - here the number 3 is smaller than 5.
02

Understand the Greater Than Symbol

Now consider the symbol \( > \). Similarly, this symbol is used when the number on the left side is greater than the number on the right. For example, \(5 > 3\) - in this case, the number 5 is greater than 3.

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Key Concepts

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

Understanding 'Less Than'
The concept of "less than" is fundamental in mathematics. When we see the symbol \(<\), it indicates a comparison between two numeric values. If a number on the left of the \(<\) sign is said to be "less than" the number on the right, this means the first number is smaller or lower in value.

For example, take the expression \(2 < 8\). Here, 2 is obviously smaller than 8.
  • "Less than" essentially means fewer in number or quantity.
  • In a practical example, if you have 2 apples, and your friend has 8 apples, your number of apples is less than your friend's.
The "less than" symbol effectively communicates a concise relationship between numbers, helping to compare different quantities or values efficiently.
Understanding 'Greater Than'
The "greater than" concept is another crucial element of math. When we encounter the symbol \(>\), it denotes that the quantity on the left is larger than the one on the right. This simple comparison helps us understand which number holds more value.

For instance, in the expression \(10 > 7\), the number 10 is greater than 7.
  • "Greater than" implies that something is larger or more abundant in quantity.
  • Take for example, if you have 10 candies, and your sibling has 7, your collection is more than theirs.
Mistakes often occur when misreading the direction of the symbol. Remember, the "mouth鈥� of the symbol always "eats" the larger number.
Comparison of Numbers
Comparing numbers is a basic math operation that helps us understand the relationship between different quantities. We often use these comparisons to make decisions and understand contexts in daily life.

When comparing two numbers:
  • The \(<\) symbol is used when the first number is smaller.
  • The \(>\) symbol is used when the first number is bigger.
For example, let's compare 4 and 6.
Since 4 is less than 6, the expression \(4 < 6\) is accurate. Conversely, for 6 and 4, you would use \(6 > 4\), meaning 6 is greater.

Understanding these symbols and their meanings helps lay the foundation for more complex mathematical concepts, such as equations and inequalities.

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