Problem 17 Replace the question mark by \(&... [FREE SOLUTION]

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Chapter 0: Problem 17

Replace the question mark by \(<,>,\) or \(=\), whichever is correct. \(-1 ?-2\)

Short Answer

Expert verified

-1 > -2

Step by step solution

Understand the problem

Determine whether \( -1 \) is greater than, less than, or equal to \( -2 \).

Number line consideration

Consider the positions of \( -1 \) and \( -2 \) on a number line. Numbers to the right are greater, and numbers to the left are smaller.

Compare the positions

\(-1\) is to the right of \(-2\) on the number line.

Conclusion

Since \(-1\) is to the right of \(-2\), \(-1 > -2\).

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Key Concepts

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

number line

A number line is a straight horizontal line used to represent numbers. It typically has zero in the middle with positive numbers to the right and negative numbers to the left.

For example:

To the right of 0: 1, 2, 3, ...
To the left of 0: -1, -2, -3, ...

This layout helps in visualizing and comparing integers easily.

In our problem, locating -1 and -2 on the number line shows that -1 is to the right of -2.
Therefore, -1 is greater than -2.

greater than and less than

The symbols < and > are used to compare integers.

- The symbol < means 'less than'. For example, -3 < -1 means -3 is less than -1.
- The symbol > means 'greater than'. For example, -1 > -2 means -1 is greater than -2.

In our problem, because -1 is to the right of -2 on the number line, we conclude that -1 > -2.

Understanding these symbols helps in comparing numbers accurately.

negative numbers

Negative numbers are numbers less than zero. They are found to the left of zero on the number line.

Some examples include: -1, -2, -3, etc.

The value of a negative number decreases as you move further left from zero. For example, -3 is less than -1 because it is further to the left.

In our exercise, we compared -1 and -2. Knowing that -2 is further left, we infer that -2 is less than -1. Hence, -1 > -2.

integer comparison

Comparing integers means determining which of two integers is greater, or if they are equal.

Using the number line is a useful strategy. Numbers to the right are always greater than numbers to the left.

Another crucial aspect is understanding the position of zero. Positive numbers are greater than zero, and negative numbers are less than zero.

In our case, by comparing -1 and -2, we see -1 is to the right of -2. Thus, -1 is greater than -2. This skill is essential for solving similar problems accurately.

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91影视

Replace the question mark by \(<,>,\) or \(=\), whichever is correct. \(-1 ?-2\)

Short Answer

Step by step solution

Understand the problem

Number line consideration

Compare the positions

Conclusion

Key Concepts

number line

greater than and less than

negative numbers

integer comparison

One App. One Place for Learning.

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