Question

What is the range of the set \(\\{3,8,2,-6,0,-2,7\\}$$?\)

Short answer

The range is 14.

Step-by-step solution

- Identify the smallest number

Look at the set \(\text{\{3, 8, 2, -6, 0, -2, 7\}}\) and identify the smallest number. The smallest number in this set is \(-6\).

- Identify the largest number

Next, identify the largest number in the set. The largest number in this set is \(8\).

- Calculate the range

Subtract the smallest number from the largest number to find the range. \[8 - (-6) = 8 + 6 = 14\]

Key concepts

Set Theory

Set theory deals with the collection of objects, known as elements, and is fundamental in understanding concepts in mathematics. In our exercise, the set is \(\text{\{3, 8, 2, -6, 0, -2, 7\}}\)

• A set is typically enclosed within curly brackets \({...}\).
• Elements in a set are unique and order does not matter.
• Elements can be numbers, letters, or other objects.

Understanding that the given numbers form a set helps in analyzing and performing operations such as identifying minimum and maximum values.

Minimum and Maximum Values

Finding the minimum and maximum values in a set is crucial to calculating its range.
First, let's define each:

• Minimum value: The smallest element in the set.
• Maximum value: The largest element in the set.

In our given set \(\text{\{3, 8, 2, -6, 0, -2, 7\}}\), we identify:

• Minimum value: \(-6\)
• Maximum value: \(8\)

These values are critical for the next step, where we calculate the range. Always ensure every number in the set is considered, as missing one could lead to incorrect results.

Subtraction in Math

Subtraction is one of the basic arithmetic operations and is essential for finding the range. The operation is performed as follows:

• Identify the minuend (the number from which another number is to be subtracted).
• Identify the subtrahend (the number to be subtracted).

For our range calculation:

• Minuend (maximum value): \(8\)
• Subtrahend (minimum value): \(-6\)

Perform the subtraction: \(8 - (-6)\). Remember that subtracting a negative number is equivalent to adding its positive counterpart. Hence, \(8 - (-6) = 8 + 6 = 14\). Understanding subtraction's role helps ensure accurate range calculation.