Problem 99 Fill in the blank with \(<,=\... [FREE SOLUTION]

91影视

Elementary Algebra

John Redden

$Math Studyset 91影视 Explanations$ Math

2011 Edition

Chapter 1: Problem 99

Fill in the blank with $<,=$, or $>$. -100 _____ $-(-(-50))$

Short Answer

Expert verified

-100 < -(-(-50))

Step by step solution

Simplify the expression

First, we simplify the expression $-(-(-50))$. The negative sign negates the number it is applied to. So, apply the first negative to $-50$ which becomes $50$. Then, apply the next negative to $50$, which becomes $-50$. So, $-(-(-50)) = -50$.

Compare the numbers

Now, we compare $-100$ with $-50$. We know that on the number line, $-100$ is to the left of $-50$. Hence, $-100 < -50$.

Final Step: Fill in the blank

Since $-100$ is less than $-50$, we fill in the blank with $<$. Therefore, $-100 < -(-(-50))$.

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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 simply numbers with a minus sign in front of them. They represent values less than zero. Negative numbers can initially seem tricky, but they're essential in everyday life for things like temperature, debt, and elevation.
When working with multiple negatives, remember that two negatives make a positive. For example:

The negative of (-50) makes it positive: 50.
The negative of a positive number: (-50) remains negative.

This flipping process is key to simplifying expressions like (-(-(-50))).
Essential points:

Negative of a negative flips to positive.
Negative applied again flips back to negative.

The Number Line and Its Value

A number line is a visual tool that helps us understand the position of numbers. It has zero in the middle, positive numbers to the right, and negative numbers to the left.
On the number line:

Navigating left means moving towards smaller values.
Navigating right means moving towards larger values.

This visual aid can help us easily compare numbers鈥攚hether they're positive or negative. For instance, in our problem, (-100) is to the left of (-50) on the number line, signifying that (-100) is indeed smaller.

Comparison of Numbers

Comparing numbers is about determining which number is bigger or smaller. This is evident on a number line and in practical calculations.
Key ideas when comparing numbers:

Numbers further right are larger.
In negative numbers, a smaller absolute value means a larger number (e.g., (-50) is greater than (-100) because it's closer to zero).

The symbols (<, =, >) are used to denote inequality (less than, equal to, greater than). Therefore, understanding how to place these symbols correctly is essential. By knowing where numbers fall on a number line, you can accurately decide their relationship.

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91影视

Fill in the blank with \(<,=\), or \(>\). -100 _____ \(-(-(-50))\)

Short Answer

Step by step solution

Simplify the expression

Compare the numbers

Final Step: Fill in the blank

Key Concepts

Understanding Negative Numbers

The Number Line and Its Value

Comparison of Numbers

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