Question

Simplify. $$|14|$$

Short answer

Answer: The simplified expression of $$|14|$$ is $$14$$.

Step-by-step solution

Interpret the absolute value

The given expression is $$|14|$$, which asks for the absolute value of 14. The absolute value of a number represents how far it is from 0 on the number line.

Find the absolute value

Since 14 is already a positive number, its distance from 0 on the number line is the number itself. Therefore, $$|14|=14$$.

Provide the simplified expression

The simplified expression is $$14$$.

Key concepts

Simplifying Expressions

When it comes to mathematical concepts, simplifying expressions is a fundamental skill. Think of simplification as tidying up a room so that you can easily find everything you need. In mathematics, simplifying an expression means to rewrite it in a more concise and easier-to-comprehend format without changing its value or meaning.
For instance, when you encounter an absolute value expression such as \(|14|\), your goal is to simplify it by finding the number's distance from zero on a number line, regardless of direction. Simplification in this case requires you to evaluate the absolute value. If the number inside the absolute value sign is positive, the simplification is straightforward—it's already in its simplest form, which is the number itself. This process involves very few steps, making it an excellent starting point for mastering the broader concept of expression simplification.

Why Simplify Expressions?

• To solve equations and inequalities more easily.
• To understand the underlying structure of mathematical problems.
• To communicate solutions clearly and effectively.

By regularly practicing simplification, you'll build a strong foundation for more complex algebraic operations.

Positive Numbers

Positive numbers are all the numbers greater than zero. They are an integral part of the number system and represent quantities that exist in reality, like the number of apples in a basket or the miles traveled by a car.
Think of positive numbers as your friends in the number world—they are the building blocks for measuring, counting, and describing things that have value or quantity. In the context of absolute value, a positive number inside the absolute value symbol, such as \(14\) in \(|14|\), will remain positive. This is because the absolute value of a number is always non-negative, as it represents the distance from zero. Distance is inherently a positive quantity, as there's no such thing as negative distance in the physical world.

Characteristics of Positive Numbers

• They are to the right of zero on the number line.
• They play a crucial role in real-life scenarios like banking and science.
• When you multiply or add two positive numbers, the result is always positive.

Engaging with positive numbers helps in understanding how different mathematical operations work and paves the way for grasping more advanced topics.

Number Line

The number line is an incredibly useful tool in understanding and visualizing the concept of numbers and their relationships to each other. It is a straight line with numbers placed at intervals, where each point corresponds to a number. The number line extends indefinitely in both the positive and negative directions, showing that numbers themselves are infinite.
At the heart of the number line is the number zero, which acts as the central reference point. To the right of zero, you have positive numbers, like +1, +2, and so on, reflecting greater quantities. On the other hand, to the left, you find negative numbers, like -1, -2, which represent lesser quantities or deficits.

Uses of the Number Line

• It helps in performing operations like addition and subtraction visually.
• It is essential in understanding the concept of absolute value as the distance from zero.
• It aids in comparing and ordering numbers.

For an expression like \(|14|\), if you were to plot the number 14 on the number line, you'd find it to the right of zero. The absolute value reflects this distance without considering direction, emphasizing the non-negative aspect of numbers on the line. Understanding the number line is a step towards grappling with more complex concepts such as real numbers, integers, and coordinate systems.