Problem 35 a. Which is greater, 5 or \(7 ?\... [FREE SOLUTION]

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Prealgebra

Julie Miller, Molly O鈥橬eill, Nancy Hyde

$Math Studyset 91影视 Explanations$ Math

1 Edition

Chapter 2: Problem 35

a. Which is greater, 5 or $7 ?$ b. Which is greater, $|5|$ or $|7| ?$

Short Answer

Expert verified

7 is greater than 5, and $|7|$ is greater than $|5|$.

Step by step solution

Understand the Absolute Value

Absolute value represents the distance of a number from zero on the number line, regardless of direction. Thus, $|x|$ will always be a non-negative number.

Compare 5 and 7

Since 7 is greater than 5 in a normal comparison, the value of 7 is greater.

Evaluate the Absolute Values

Calculate the absolute values: $|5| = 5|$ and $|7| = 7|$.

Compare Absolute Values

Since $|7| = 7$ and $|5| = 5$, 7 is greater than 5 even considering their absolute values.

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Key Concepts

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

Absolute Value

The concept of absolute value is fundamental in mathematics. It shows how far a number is from zero on a number line. Absolute value ignores negative signs.

For instance, $|-3| = 3$ and $|3| = 3$. Both values are 3 because they stand 3 units away from zero. Remember, absolute value is always non-negative.

This means that no matter the sign of the number, we only look at its distance from zero without considering the sign. This property makes absolute values essential in comparing magnitudes of numbers, regardless of their direction.

Number Line

A number line is a visual representation of numbers laid out in order along a straight line.

Zero is typically placed at the center as the reference point. Positive numbers are placed to the right of zero, and negative numbers to the left.

When comparing numbers using a number line, their position relative to zero and each other is crucial. For example, on a number line: -7, -3, 0, 2, 5 are placed sequentially from left to right. This visual aid helps in understanding the positioning and magnitude of numbers readily.

Comparing 5 and 7: 7 is further right, so it is greater.
Comparing -5 and -2: -2 is further right, so it is greater.

Comparison of Numbers

Comparing numbers involves evaluating which number is larger or smaller. This process is straightforward with positive numbers, but absolute values make it just as easy for negative numbers.

For example: $|-5|\text{ vs. }|-7|$. Since $|-5| = 5$ and $|-7| = 7$, we ignore the signs and simply compare: 7 is greater than 5.

Follow these steps for smooth comparison:

Identify the numbers to compare.
If dealing with absolute values, find the distance from zero ignoring the sign.
Place them on a number line, if needed, to visualize.
Determine which number is further to the right; that is the larger number.

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91影视

a. Which is greater, 5 or \(7 ?\) b. Which is greater, \(|5|\) or \(|7| ?\)

Short Answer

Step by step solution

Understand the Absolute Value

Compare 5 and 7

Evaluate the Absolute Values

Compare Absolute Values

Key Concepts

Absolute Value

Number Line

Comparison of Numbers

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