Problem 68 - Beginning and Intermediate Algebra

Question

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

Step-by-Step Solution

Answer

The lesser number is 3.

Step 1 - Identify the Numbers

Identify the two numbers given in the problem. The numbers are 4 and |-3|.

Step 2 - Evaluate the Absolute Value

Calculate the absolute value of -3. The absolute value of -3 is 3, so |-3| becomes 3.

Step 3 - Compare the Numbers

Compare the numbers 4 and 3. To do this, determine which of the two numbers is smaller.

Step 4 - Select the Lesser Number

The lesser number between 4 and 3 is 3.

Key Concepts

Absolute Value

Absolute value is a key concept in mathematics, especially useful in number comparison. The absolute value of a number is its distance from zero on a number line. This distance is always non-negative. For instance, the absolute value of both -3 and 3 is 3. We write the absolute value of a number using vertical bars: \(|-3| = 3\).

Essentially, when we consider absolute value, we disregard any negative sign. This helps us deal with numbers that might appear negative in computations but should be considered positive for distance or magnitude purposes.

Think of it like this: Absolute value measures how 'big' a number is without worrying about its sign. This is important when comparing numbers to determine which is lesser or greater.

Number Comparison

Comparing numbers means determining if one number is smaller, larger, or equal to another number. This is done through direct observation or calculation.

For example, when comparing the numbers 4 and \(|-3|\), it is crucial first to compute the absolute value of -3. As determined earlier, \(|-3| = 3\). Therefore, the problem reduces to comparing 4 and 3.

Since 3 is smaller than 4, we select 3 as the lesser number. Number comparison often involves:

• Identifying the given numbers
• Applying any necessary mathematical operations (like absolute value calculation)
• Direct comparison to see which one is smaller, larger, or if they are equal

This step-by-step approach ensures clarity and accuracy in results.

Basic Arithmetic

Basic arithmetic is fundamental in mathematics, involving simple operations like addition, subtraction, multiplication, and division. These operations form the bedrock of more complex mathematical concepts.

However, for problems like determining the lesser number, basic arithmetic sometimes involves pre-adjustment steps, like absolute value calculation.

Let's apply these principles to the exercise at hand:

• Identify the numbers: 4 and \(|-3|\)
• Calculate \(|-3|\): This gives us 3
• Compare the numbers: 3 and 4
• Select the lesser number: 3

This systematic approach uses simple arithmetic and logical comparison to arrive at the correct answer. Thus, mastering basic arithmetic is akin to mastering the building blocks of mathematics.