Problem 11 - Algebra 1: Concepts and Skills

Question

Write the numbers in increasing order. \(2,-3,-8,1,-2\)

Step-by-Step Solution

Answer

The numbers in increasing order are \(-8, -3, -2, 1, 2\).

Step 1: Identify the Numbers

Firstly, take a look at the list of numbers. The numbers given are \(2, -3, -8, 1, -2\).

Step 2: Identify The Lowest Number

Next, identify the lowest (or most negative) number in the list. Here, the lowest number is \(-8\). This is the first number in your sorted list.

Step 3: Identify The Next Lowest Number

Then, identify the next lowest number. In this case, it is \(-3\). Add this to your list.

Step 4: Move to The Next Number

Following the same process, identify the next lowest number, which is \(-2\). Proceed by adding this number to your list.

Step 5: Continue in the Same Manner

Continue the same process with the remaining numbers. The next number in the sequence, which is \(1\), is added to your list.

Step 6: Finalize Your List

The final number to be added to your list is \(2\). Hence, the list in increasing order is given by \(-8, -3, -2, 1, 2\).

Key Concepts

Negative Numbers

Negative numbers are numbers found to the left of zero on the number line. They have a less-than-zero value and are often indicated with a minus sign (−).
When dealing with negative numbers, it is crucial to understand that the more negative a number is, the smaller its value. For instance,

• -8 is smaller than -3 because it is further to the left on the number line.
• -3 is smaller than -2, as it is still further left.

Recognizing these properties helps in effectively comparing and ordering negative numbers.

Increasing Order

To arrange numbers in increasing order means to list them from the smallest to the largest. It involves ordering from the least negative to the most positive values.
When organizing a mix of positive and negative numbers, one begins by identifying the most negative number as the smallest, moving towards the least negative (or highest number if dealing with positives). In the example,

• -8 is the smallest number, then -3, followed by -2.
• Next is the least negative but still positive numbers, such as 1 and finally 2.

Ordering numbers in increasing order makes comparisons straightforward and is fundamental in many math applications.

Integer Comparison

Integer comparison is the process of determining the relative size of numbers. This involves looking at both positive and negative values and placing them in order.
When comparing integers:

• Negative values are always considered smaller than positive values.
• Among the negative numbers, a number with a larger absolute value is actually smaller.
• Among positive numbers, a larger number is greater.

In the list provided, -8 is smaller than all others because it is the most negative. Understanding integer comparison is key to organizing lists of both positive and negative numbers accurately.