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Chapter 1: Problem 53

Select the lesser of the two given numbers. $$ -11,-3 $$

Short Answer

Expert verified
-11

Step by step solution

01

Identify the given numbers

The given numbers are -11 and -3.
02

Understand negative numbers

In negative numbers, the number with the larger absolute value is actually lesser. For example, -11 is less than -3, because -11 is further to the left on the number line.
03

Compare the numbers

Compare -11 and -3. Since -11 has a larger absolute value, it is less than -3.
04

Select the lesser number

The lesser number between -11 and -3 is -11.

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Key Concepts

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

Absolute Value
Understanding the concept of absolute value can make comparing negative numbers much easier. The absolute value of a number is its distance from zero on the number line, regardless of its direction. For example, both -3 and 3 have an absolute value of 3 because each is 3 units away from zero.

When we compare numbers using absolute value, we often disregard the sign and focus on the magnitude. However, it鈥檚 important to remember that the absolute value does not convey the direction, so -11 and 11 are considered equal in terms of absolute value, but they are quite different in real value.
Number Line
A number line is a straight line where numbers are placed at equal intervals. It extends infinitely in both directions: positive to the right and negative to the left. This visual tool is extremely useful when comparing quantities.

To compare negative numbers using a number line, you can simply locate both numbers and see which is further to the left. For instance, -11 is placed further to the left than -3 on the number line. This shows that -11 is less than -3 because the left side represents smaller values.

Remember the rule: as you move left on the number line, the numbers get smaller. Conversely, as you move right, the numbers get larger.
Negative Numbers
Negative numbers represent values less than zero and are usually denoted with a minus sign (-) in front. They are crucial for describing values like temperatures below freezing, debts, or elevations below sea level.

Comparing negative numbers can sometimes be tricky because the number with the larger absolute value is actually lesser. For example, between -11 and -3, -11 is less than -3 even though 11 is greater than 3.

To sum up:
  • Negative numbers are to the left of zero on the number line.
  • The further left the number is, the smaller its value.
  • Negative numbers have applications in various real-world contexts.

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Most popular questions from this chapter

Solve each problem. 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 \(2006 ?\)

Solve each problem. Bruce Buit also enjoys playing Triominoes. On five successive turns, his scores were \(-13,15,-12,24,\) and \(14 .\) What was his total score for the five turns?

Decide whether each statement is true or false. \(-|-5| \geq-|-9|\)

Find each difference. $$ -6-(-2) $$

Perform each indicated operation. $$ (9-3)-15 $$
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