Problem 19 Fill in the blank with $<$ ... [FREE SOLUTION]

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Prealgebra

Julie Miller, Molly O鈥橬eill, Nancy Hyde

$Math Studyset 91影视 Explanations$ Math

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Chapter 2: Problem 19

Fill in the blank with $<$ or $>$ to make a true statement. $$-8 \square-9$$

Short Answer

Expert verified

-8 > -9

Step by step solution

Understand the numbers

Identify the given numbers in the problem. The two numbers are -8 and -9.

Compare magnitudes

Compare the absolute values of the numbers. Here, | -8 | = 8 and | -9 | = 9. Note that 8 is less than 9.

Determine the order of negative numbers

Remember that among negative numbers, a number with a smaller magnitude is greater. Since -8 has a smaller magnitude than -9, -8 is greater than -9.

Fill in the blank

Based on the comparison, fill in the blank with the correct inequality symbol: declare that -8 > -9.

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Key Concepts

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

Comparing Negative Numbers

When you compare negative numbers, it can seem tricky at first. But it's just a matter of understanding how they work. Imagine negative numbers on a number line: they are below zero. The further left you go on the number line, the smaller the number.

If you compare -8 and -9, which one is closer to zero? It's -8! This means -8 is greater than -9 because -8 is closer to zero. Remember this quick tip: A negative number is larger if it is closer to zero, even if it looks smaller.

Absolute Value

Absolute value is a useful concept for comparing numbers. The absolute value of a number is its distance from zero on a number line, without considering direction.

For example, the absolute value of -8 is 8, written as $|-8| = 8$. Similarly, $|-9| = 9$.

Absolute values ignore the minus sign, making everything positive. This helps to determine how 'big' a number is. You can compare the absolute values to understand the relative sizes of negative numbers.
In our example:

$|-8| = 8$
$|-9| = 9$

This shows us that 9 is bigger than 8, but when comparing negative numbers, this means that -8 is greater than -9.

Mathematical Inequalities

Inequalities are expressions that show the relationship between two values where they are not strictly equal. Understanding how to read and use inequalities is crucial in math.

Common inequality symbols include:

$<$ which means less than
$>$ which means greater than

For example: $3 > -2$ means 3 is greater than -2. However, with negative numbers: $-8 > -9$

This is true because -8 is closer to zero than -9, making it larger.
To summarize: when working with inequalities and negative numbers, if a number has a smaller negative value, it is actually larger.

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91影视

Fill in the blank with \(<\) or \(>\) to make a true statement. $$-8 \square-9$$

Short Answer

Step by step solution

Understand the numbers

Compare magnitudes

Determine the order of negative numbers

Fill in the blank

Key Concepts

Comparing Negative Numbers

Absolute Value

Mathematical Inequalities

One App. One Place for Learning.

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