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Chapter 5: Problem 7

Insert either \(<\) or \(>\) in the shaded area between the integers to make the statement true. \(-13\square 2\)

Short Answer

Expert verified
-13 < 2

Step by step solution

01

Understand the Integers

Here we have two integers, -13 and 2. The number -13 is negative and the number 2 is positive.
02

Compare the Integers

We know from predefined mathematical rules that any negative number is always smaller than any positive number.
03

Fill the Shaded Area

After comparing, it is clear that -13 is smaller than 2. Hence, we fill the blank with '<' symbol which denotes that the value on the left is less than the value on the right.

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Key Concepts

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

Understanding Negative Numbers
Negative numbers are those that are less than zero. They are represented with a minus (-) sign. Think of them as being in debt or below the ground level. Negative numbers still hold importance and follow mathematical rules like other numbers.

Here are some important points about negative numbers:
  • They always represent a decrease, downfall, or reversal of a usual quantity.
  • The further left you go on the number line, the smaller the negative number becomes.
  • For example, -3 is greater than -7, because -3 is located to the right of -7 on the number line.
  • Every negative number is always less than zero and less than any positive number.
Remember that understanding negative numbers helps in evaluating expressions, solving equations, and comparing values.
Exploring Positive Numbers
Positive numbers are greater than zero. They are the numbers we often encounter in daily life, such as when counting objects or measuring distances. They don鈥檛 need a plus (+) sign, but it can be used for clarity.

Some key features of positive numbers include:
  • They represent an increase or gain.
  • They are always located to the right of zero on a number line.
  • Larger positive numbers indicate higher values.
  • Positive numbers are greater than zero and always greater than any negative number.
Keep these features in mind as you work with integers, as they help in contextually understanding the world around us!
Decoding Mathematical Symbols
Mathematical symbols are visual representations that help us express relationships between numbers. Two common symbols used in integer comparison are the greater than (>) and less than (<) symbols.

Here's a breakdown:
  • The symbol < means "less than." It denotes that the number on the left is smaller than the number on the right.
  • The symbol > means "greater than." It indicates that the number on the left is larger than the number on the right.
  • To remember which way the symbols point, think of the open side as wanting to "eat" the larger number.
Using these symbols makes mathematical communication clear and concise. In the example -13 < 2, the less than symbol correctly shows that -13 is smaller than 2. Practice regularly to get familiar with these conventions!

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Most popular questions from this chapter

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