Problem 34 Order the integers in each set f... [FREE SOLUTION]

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Chapter 2: Problem 34

Order the integers in each set from least to greatest. $$\\{5,0,-8\\}$)$$

Short Answer

Expert verified

The set ordered from least to greatest is: $-8, 0, 5$.

Step by step solution

Identify the Integers

The first step involves identifying and listing the integers present in the set. These integers are: 5, 0, and -8.

Compare the Integers

To order the integers, we need to compare them. Recall that on a number line, negative numbers come before positive numbers. Therefore, -8 is less than both 0 and 5. Next, 0 is less than 5.

Arrange in Ascending Order

Using the comparisons made, arrange the numbers from the smallest to the largest. The ordered set is: $-8, 0, 5$.

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Key Concepts

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

Integer Comparison

Comparing integers is an essential skill in mathematics, particularly when you need to arrange numbers in a specific order. Integers include negative numbers, zero, and positive numbers. When comparing these, it helps to think about their position on a number line.

Negative numbers are less than positive numbers.
Among negative numbers, those with a smaller absolute value are greater. For example, $-2$ is greater than $-8$.
Zero is the pivot point around which negative and positive numbers revolve. It is less than any positive number but greater than any negative number.

By understanding these basic facts, you can quickly identify which integers are greater or lesser relative to each other. Always remember that a smaller number, whether positive or negative, lies to the left of a greater number on the number line.

Number Line

The number line is a visual tool that helps in understanding the positioning and relationship between numbers, including integers. On a number line:

Numbers increase as you move to the right.
Numbers decrease as you move to the left.
Every number has a distinct position that visually represents its value.
Negative numbers are placed to the left of zero, while positive numbers are placed to the right.

Visualizing integers on a number line can simplify the process of comparing and ordering them. For instance, in the set \{5,0,-8\}, when plotted, $-8$ comes first, then $0$, and finally $5$. This visual arrangement makes it evident which numbers come before others, aiding in systematic integer ordering.

Ascending Order

Ordering numbers in ascending order means arranging them from the smallest to the largest. This method is particularly useful when you need to organize or analyze data logically.

Start by comparing each number to determine which is smallest.
Place the smallest number first, then proceed to the next smallest, and continue in this manner.
If using a number line, simply read from left to right to determine the order.

In the given exercise, the integers $-8, 0,$ and $5$ were ordered as such: $-8$ is the smallest, followed by $0$, and $5$ is the largest. Familiarity with the concept of ascending order can help you effortlessly organize and compare various sets of numbers in your mathematical journey.

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91影视

Order the integers in each set from least to greatest. $$\\{5,0,-8\\}$)$$

Short Answer

Step by step solution

Identify the Integers

Compare the Integers

Arrange in Ascending Order

Key Concepts

Integer Comparison

Number Line

Ascending Order

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