Question

Complete the sentence. The absolute value of \(-4\) is _______________

Short answer

Answer: The absolute value of -4 is 4.

Step-by-step solution

Identify the number with a negative sign

In this case, the given number is \(-4\).

Understand the concept of absolute value

To obtain the absolute value, you need to find the distance of the given number from 0 on the number line, which is always non-negative.

Calculate the absolute value

Since the distance between \(-4\) and 0 on the number line is 4, the absolute value of \(-4\) is 4. The complete sentence is: The absolute value of \(-4\) is 4.

Key concepts

Negative Numbers

When we discuss negative numbers, we are referring to numbers that are less than zero. These numbers are typically denoted with a minus sign in front, such as (-4). Negative numbers are crucial in prealgebra because they help us understand concepts such as debt, temperature below zero, or depth below sea level.

Negative numbers can be confusing, but they follow the same rules as positive numbers for addition, subtraction, multiplication, and division, just in the opposite direction on the number line. For example, subtracting a negative number is the same as adding its positive counterpart. Remember that when you multiply or divide two negative numbers, the result will always be positive.

Number Line

The number line is a visual representation of numbers laid out in a straight path. Each point on the line corresponds to a number, and the line extends infinitely in both the positive and negative directions. At the center of the number line is zero, which serves as the starting point to measure distance between numbers.

To find the absolute value of a negative number on the number line, you measure how many units it is away from zero. Regardless of the direction, distance is always a non-negative number. That's why the absolute value of (-4) is simply 4 – it's 4 units away from zero on the number line.

Prealgebra

Prealgebra serves as the foundation for all mathematical studies. It encompasses basic arithmetic, the introduction to variables and simple equations, and, importantly, the understanding of core concepts such as the absolute value. In prealgebra, absolute value represents the idea of 'distance' or 'magnitude' of a number without regard to its sign.

This means that whether you're working with negative numbers or positive numbers, the absolute value will always give you a non-negative result. If a student can grasp this prealgebra concept, it will make learning higher level math, such as algebra and beyond, much more accessible.