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Chapter 1: Problem 54

Select the lesser of the two given numbers. $$ -8,-13 $$

Short Answer

Expert verified
-13 is the lesser number.

Step by step solution

01

Identify the Given Numbers

The two given numbers are -8 and -13.
02

Understand Negative Numbers

In the context of negative numbers, a number with a greater negative value is actually smaller. Essentially, the further left a number is on the number line, the smaller it is.
03

Compare the Numbers

Compare -8 and -13. Since -13 is further to the left on the number line than -8, it is the smaller number.
04

Select the Lesser Number

From the comparison, -13 is determined to be the lesser number of the two.

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Key Concepts

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

Comparing Negative Numbers
Negative numbers are fascinating because they work differently from positive numbers. When comparing negative numbers, remember this key idea: the more negative a number is, the smaller it actually is.
For example, think of -8 and -13. Even though 13 is greater than 8, when you add the negative sign, the logic flips.
-8 is closer to zero than -13, which means -8 is a larger number than -13. Always remember: the 'more negative' a number, the 'smaller' it is in value.
Number Line
The number line is a useful tool to visualize the positions of numbers, especially negatives.
Picture a horizontal line with numbers increasing to the right and decreasing to the left. Zero sits comfortably in the middle. Moving leftward, you go into negative territory: -1, -2, -3, and further left you reach -8 and -13.
Here鈥檚 the trick: the further left you go, the smaller the number. So on a typical number line:
  • -8 is placed to the right of -13.
  • -13 is further left than -8.
This helps confirm that -13 is smaller than -8.
Greater Negative Value
Understanding 'greater negative value' might seem a bit tricky at first. In simple terms, the 'greater negative' a number, the smaller it is.
When we say -13 has a 'greater negative value' than -8, it means -13 is more negative, and therefore, smaller.
Let's break it down again:
  • -8 is less negative compared to -13.
  • Thus, -8 is larger than -13.
Always keep this in mind for negative numbers: more negative means the number is further from zero on the left, making it smaller.

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Most popular questions from this chapter

Solve each problem. In \(1998,\) undergraduate college students had an average (mean) credit card balance of 1879. The average balance increased \(\$ 869\) by 2000 , then dropped \(\$ 579\) by \(2004,\) and then increased \(\$ 1004\) by \(2008 .\) What was the average credit card balance of undergraduate college students in \(2008 ?\)

Write a numerical expression for each phrase and simplify. See Examples 7 and \(8 .\) The product of \(-3\) and the difference between 3 and \(-7\)

Find each difference. $$ -\frac{3}{4}-\frac{5}{8} $$

Decide whether each statement is true or false. \(|13-8| \leq|7-4|\)

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 4 if its last two digits form a number divisible by \(4,\) and not otherwise. Show that (a) \(6,221,464\) is divisible by 4 and \((b) 2,876,335\) is not divisible by 4
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