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Chapter 1: Problem 58

Select the lesser of the two given numbers. $$ 4,|-3| $$

Short Answer

Expert verified
The lesser number is 3.

Step by step solution

01

Understand Absolute Value

The absolute value of a number is its distance from zero on a number line, regardless of direction. For any negative number, its absolute value will be positive.
02

Calculate the Absolute Value

Find the absolute value of \(-3\). This can be written as \(|-3|= 3\).
03

Compare the Numbers

After calculating the absolute value, compare the two numbers. Now, the comparison is between \(4\) and \(3\).
04

Select the Lesser Number

Among \(4\) and \(3\), the lesser number is \(3\).

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Key Concepts

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

absolute value
Absolute value is an important concept when comparing numbers, especially when dealing with negatives. The absolute value of a number is its distance from zero on the number line, regardless of direction. For instance, the absolute value of both 3 and -3 is 3. We denote absolute value with two vertical bars. So, \(-3\) becomes \(|-3| = 3\).

It's like asking how far a number is from zero without worrying about which side of zero it is on. This concept helps to simplify comparisons by focusing only on size and ignoring direction or sign.
number comparison
Number comparison involves evaluating which of two numbers is larger or smaller. Once we understand absolute value, it becomes easier to compare numbers. Take the given numbers, which involve \(4\) and \(|-3|\).

We must simplify them both to their absolute values first if needed. In our example, since \(|-3| = 3|\), we then compare 4 and 3 directly.

When comparing two numbers \(a\) and \(b\), if \(a > b\), then \(a\) is greater; if \(a < b\), then \(a\) is smaller. Using \(<\) and \(>\) symbols helps in visualizing comparisons conveniently.
lesser number selection
Selecting the lesser number means identifying which number is smaller in size. After simplifying the absolute values and comparing the numbers, the final step is to select the smallest.

For example, in comparing 4 and 3, we find that 3 is the lesser number because \(3 < 4\). This is a crucial step, as it finalizes the answer to which number is less in the pair given.

Remember: Selecting the lesser number is straightforward once you've done comparisons correctly and understood absolute value.

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Most popular questions from this chapter

Among entertainment expenditures, the average annual spending per U.S. household on fees and admissions was \(\$ 526\) in 2001 . This amount decreased \(\$ 32\) by 2003 and then increased \(\$ 112\) by \(2006 .\) What was the average household expenditure for fees and admissions in \(2006 ?\)

The operation of division is used in divisibility tests. A divisibility test allows us to determine whether a given number is divisible (without remainder) by another number. An integer is divisible by 3 if the sum of its digits is divisible by \(3,\) and not otherwise. Show that (a) \(4,799,232\) is divisible by 3 and (b) \(2,443,871\) is not divisible by 3

Translate each phrase into a mathematical expression. Use \(x\) as the variable. Combine like terms when possible. Six times a number added to \(-4,\) subtracted from twice the sum of three times the number and 4 (Hint: Twice means two times.)

Simplify each expression. $$ 16-5 m-4 m-2+2 m $$

Write a numerical expression for each phrase and simplify. Three-fourths of the sum of \(-8\) and 12
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