Question

Write a list indicating the numbers in the set of integers. Express each amount as a positive or negative integer. Mount Everest is the tallest mountain in the world. Its peak is \(29,035\) feet above sea level.

Short answer

Question: Express the height of Mount Everest as an integer. Answer: The height of Mount Everest is a positive integer, which is 29,035.

Step-by-step solution

(Step 1: Understanding Integers)

(An integer is a whole number (not a fraction or decimal) and can be positive, negative, or zero. Positive integers are numbers greater than zero, negative integers are numbers less than zero, and zero is an integer itself.)

(Step 2: Identify the given information)

(In this case, we are given the height of Mount Everest, which is \(29,035\) feet above sea level.)

(Step 3: Express the height as a positive integer)

(Since Mount Everest is above sea level, its height is considered a positive value. Therefore, its height can be expressed as the positive integer \(29,035\).)

Key concepts

Positive and Negative Numbers

Positive and negative numbers are fundamental elements in understanding integers. Integers encompass all whole numbers, including zero, along with their positive and negative counterparts. Positive numbers are above zero and often represent quantities or measures more than a neutral point. Think of them as representing gains or elevations, much like Mount Everest's height is a positive integer due to its towering stature above sea level.
Negative numbers, on the other hand, are less than zero, typically reflecting losses, depths, or reductions. For instance, they could illustrate debts, valleys, or temperatures below freezing. When working with positive and negative numbers, it's crucial to know:

• Addition and subtraction involving negatives requires careful attention to signs.
• Negatives can flip the direction of comparison; for example, \( -5 < 0 \), though 5 is greater than 0."
• Multiplying or dividing two negative numbers yields a positive result, while a positive and a negative product remains negative."

Whole Numbers

Whole numbers are the non-fractional integers that are zero or any positive number. This means they are endless and include 0, 1, 2, 3, continuing infinitely upwards. Whole numbers are extremely useful for counting and quantifying everyday objects like apples in a basket or even steps taken in a walk.
While they appear straightforward, whole numbers form the basis for understanding more complex mathematical concepts. They lack any fractional or decimal component, which simplifies arithmetic operations such as addition and multiplication. Here are some quick points about whole numbers:

• Zero, though not positive, is a whole number and acts as the starting point or neutral element.
• Whole numbers do not include any negative figures by definition.
• They are crucial for simple computations and often precede the introduction of more advanced topics involving fractions or decimals.

Educational Math Concepts

Learning math is all about building blocks of knowledge, where each new concept relies on understanding the one before it. Understanding integers, positive and negative numbers, and whole numbers are foundational educational math concepts. They underpin everything from simple calculations to more advanced mathematical theories.
Here's why comprehending these concepts is vital:

• The ability to handle positive and negative numbers is essential for real-world problem-solving — from balancing budgets to analyzing temperatures.
• Mastery of whole numbers aids in grasping arithmetic, providing a stepping stone to tackling fractions and decimals.
• These concepts are widely applicable across numerous fields, including physics for tracking velocity and height differences, and economics for profit and loss analysis.

By solidifying your understanding of these educational math concepts, you equip yourself with the tools to approach more complicated topics effectively.