Problem 63 - Beginning and Intermediate Algebra

Question

Select the lesser of the two given numbers. -11,-4

Step-by-Step Solution

Answer

-11

Step 1 - Understand the Problem

The goal is to find the lesser (or smaller) of the two given numbers: -11 and -4.

Step 2 - Identify the Numbers on the Number Line

Place both numbers, -11 and -4, on a number line. Remember that numbers further to the left are smaller.

Step 3 - Compare the Numbers

Compare -11 and -4 based on their position on the number line. Since -11 is further to the left than -4, -11 is the smaller number.

Step 4 - Write the Answer

Based on the comparison, the lesser of the two numbers -11 and -4 is -11.

Key Concepts

Number Line

The number line is a visual representation of numbers along a straight horizontal line.
On the number line, smaller numbers are positioned to the left, and larger numbers are positioned to the right.
For example, negative numbers are on the left side of zero, and positive numbers are on the right.
Let's look at the numbers from the exercise: -11 and -4.
If you place them on a number line, -11 will be to the left of -4 because -11 is smaller.
Using a number line makes it easier to visually compare the size of the numbers.
Think of it as a ruler where each mark represents a number. The further left you go, the smaller the number becomes.

Negative Numbers

Negative numbers are values less than zero, represented with a minus sign (-).
On the number line, they are always to the left of zero.
Negative numbers can sometimes be confusing because a 'larger' negative number has a smaller value than a 'smaller' negative number.
For instance, -11 is less than -4.
The further a negative number is from zero, the smaller its value.
Think of negative numbers in terms of debt.
If you owe 11 dollars, your debt (-11) is more significant than owing 4 dollars (-4).
Understanding this concept is crucial for comparing negative numbers correctly.

Ordering Numbers

Ordering numbers means arranging them from smallest to largest or vice versa.
When ordering numbers, including negative numbers, a number line can be very helpful.
Start from the far left and move to the right to list numbers from smallest to largest.
To order -11 and -4, you'd place -11 first because it's further left on the number line, then -4.
Here's a quick tip:
The smaller a negative number is (the further left it is), the lesser its value.
So, -11 comes before -4 in an ordered list.
This skill is essential for solving many math problems and understanding the relationships between different numbers.