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Chapter 1: Problem 77

Fill in the blank with the inequality symbol \(<\) or \(>\). $$3 \square 7$$

Short Answer

Expert verified
3 < 7

Step by step solution

01

Understand the Inequality Symbols

The inequality symbol '<' means 'less than,' and the symbol '>' means 'greater than.'
02

Compare the Numbers

Compare the numbers 3 and 7. Determine if 3 is less than 7 or greater than 7.
03

Fill in the Blank

Since 3 is less than 7, the correct inequality symbol is '<'.

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Key Concepts

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

Inequality Symbols
In mathematics, inequality symbols are used to compare two values or expressions. The most commonly used inequality symbols are:

  • < (less than)
  • > (greater than)
These symbols help us understand and express how numbers relate to each other. For instance, using these symbols, you can easily denote that one number is either smaller or larger than another.

It鈥檚 essential to become comfortable with these symbols because they are foundational in math. You'll encounter them in various contexts, including algebra, calculus, and beyond. Improving your understanding of these symbols can simplify many math problems.
Comparing Numbers
When you're comparing numbers, you're essentially determining their relative size to one another. Here are some simple steps to do this effectively:

  • Start by looking at the digits from left to right.
  • If the numbers have different digits in the first place, the number with the larger digit is greater.
  • If the first digits are the same, move to the next digit, and repeat until you find a difference.

For example, comparing 3 and 7 involves looking at the first digit in each number. Since 3 is immediately smaller than 7, we determine that 3 is less than 7.

Simple comparisons like these form the groundwork for understanding more complex mathematical concepts.
Less Than
The 'less than' symbol (<) is used to show that one number is smaller than another. This symbol points to the smaller number.

For instance, in the inequality 3 < 7, the open end of the symbol points towards the larger number (7), and the pointed end aims at the smaller number (3). This visual cue can help you remember which way the sign should face.

Learning to correctly place the 'less than' symbol is important for accurately expressing inequalities in math.
Greater Than
The 'greater than' symbol (>) shows that one number is larger than another. The open end of this symbol faces the larger number.

For example, when looking at 8 > 5, the open end is towards the larger number (8), and the pointed end is towards the smaller number (5).

This concept is essentially the opposite of the 'less than' symbol and is just as important for comparing numbers. Practicing with the 'greater than' symbol will make you more confident in solving inequality problems.

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