Problem 43 - Prealgebra and Introductory Algebra

Question

Write the given numbers in order from smallest to largest. $$-10,4,12,-5,-7$$

Step-by-Step Solution

Answer

The numbers in order from smallest to largest are: \( -10, -7, -5, 4, 12 \).

Step 1: Identify the negative numbers

From the given list \( -10,4,12,-5,-7 \) , we can see that \( -10, -5, \) and \( -7 \) are negative numbers.

Step 2: Order the negative numbers

On a number line, negative numbers are to the left of zero and thus smaller than positive numbers. Hence, among our negative numbers, \( -10 \) is the smallest, followed by \( -7 \) and then \( -5 \).

Step 3: Identify the positive numbers

From the given list \( -10,4,12,-5,-7 \), \( 4 \) and \( 12 \) are positive numbers.

Step 4: Order the positive numbers

Positive numbers are larger than negative numbers. Within our two positive numbers, \( 4 \) is smaller, followed by \( 12 \).

Step 5: Combine the ordered negative and positive numbers

Write down the ordered negative numbers first, followed by the ordered positive numbers. The result is the ordered list of the original numbers from smallest to largest: \( -10, -7, -5, 4, 12 \).

Key Concepts

Negative Numbers

Understanding negative numbers is essential in the world of mathematics. These are numbers less than zero, represented by a minus sign, like ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline -3 or ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline -9. They represent a value of 'less than nothing' and are used to denote a deficit, like a temperature below freezing or a bank account in overdraft.

Positive Numbers

In contrast to negative numbers, positive numbers are those greater than zero and do not have a minus sign in front of them. Examples include 2, 8, or 27. These numbers are commonly used to represent measures such as distance, temperature above zero, or money in a savings account. Understanding both positive and negative numbers helps us describe and quantify a wide range of real-world phenomena.

Number Line

A number line is a visual representation of numbers laid out in a straight line, where each point corresponds to a number. Usually, zero is in the middle, with positive numbers extending indefinitely to the right and negative numbers to the left. This helps to visualize the relative position of numbers and is particularly helpful when learning to comprehend negative and positive values and their relationships to each other.

Comparing Integers

Understand the Relationship

In the context of integers, which include both positive and negative whole numbers, comparing them involves understanding their placement and value relative to each other on the number line. The further right a number is, the greater its value; conversely, numbers to the left represent smaller values.

Ordering Integers

To compare and order integers, like in the given exercise ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline -10, -7, -5, 4, 12, observe their positions on the number line. This visual approach can simplify determining which integers are smaller or larger than others, aiding in their organization from smallest to largest or vice versa.