Question

Complete the sentence. The absolute value of 21 is ________________

Short answer

Answer: The absolute value of 21 is 21.

Step-by-step solution

Locate the number on the number line

First, find the numerical value of 21 on the number line. Since 21 is a positive number, it is located to the right of 0.

Determine the distance from 0

Next, determine the distance from 21 to 0 on the number line. As 21 is a positive number, the absolute value will be the same as the numerical value (since the distance is measured without the sign).

Write the absolute value

Finally, the absolute value of 21 is 21. So the completed sentence would be: "The absolute value of 21 is 21."

Key concepts

Understanding the Number Line

Imagine the number line as a long, straight path. On this path, each point represents a unique number. At the very center, you'll find zero, the origin. As you move to the right, numbers increase in value, becoming positive. Moving left from zero, the numbers decrease, becoming negative.

For instance, if we were looking to locate the number 21, we'd walk 21 steps to the right of zero. This is because 21 is a positive number. In the exercise, finding 21 on the number line is crucial to understand its relative position and its absolute value. The number line is not just a math tool; it's a visual representation that helps us picture where numbers sit in relation to one another, crucial for calculations and understanding numerical concepts.

The absolute value, in essence, is the distance a number is from zero on this line, regardless of direction. That's why when we depict the absolute value on a number line, we ignore the left or right directions and simply count the steps needed to reach zero.

Grasping Numerical Value

Every number possesses a numerical value, which is a way to express its magnitude without considering its sign. The numerical value is what we would use to count or measure something. In math problems, particularly when dealing with absolute values, focusing solely on the numerical value without its positive or negative indicator is a common practice.

When you strip a number of its sign, what remains is the numerical value. For the number 21, our numerical value is simply 21. It's a representation of 'how much' or 'how many,' which in the context of our exercise, is all that matters when computing the absolute value. It's crucial to equate the absolute value to the numerical value and not confuse it with the general concept of the number that has a positive or negative association.

Interpreting Positive Numbers

Positive numbers are the familiar figures we use in everyday life. They sit on the right side of the zero on the number line and are used to denote values greater than nothing. From counting apples to measuring distances, positive numbers are the go-to.

In the context of our absolute value exercise, recognizing that 21 is a positive number helps us simplify the process. Since absolute value measures how far a number is from zero, and since positive numbers are already located to the right of zero, their absolute value coincides with their numerical value. This means that for positive numbers, the steps to determine absolute value are uncomplicated. We simply reaffirm their numerical value, which in the example of 21, both the positive number and its absolute value are the same: 21.