- Define the high temperature \(H = 8\) and the low temperature \(L = -3\).
- Recall the average formula for two numbers: \(\frac{H + L}{2}\).
- Substitute the values into the formula to get \(\frac{-3 + 8}{2}\), which is \((-3 + 8) \div 2\).
- Select the matching option, which is \(\boxed{\text{b}}\).
Explanation
- Analysis of Temperature Data
To find the average of the high and low temperatures, we first represent the given temperatures as numerical values. The high temperature on Friday was \(8\) degrees above zero, which we represent as \(H = 8\). The low temperature was \(3\) degrees below zero, which we represent as \(L = -3\). We are asked to identify the expression that correctly calculates the average of these two temperatures.
- Formulating the Average Expression
The formula for the average of two numbers \(x\) and \(y\) is \(\frac{x + y}{2}\). Applying this formula to our temperatures \(H\) and \(L\), the average is given by:
\[ \text{Average} = \frac{H + L}{2} = \frac{8 + (-3)}{2} \]
Using the commutative property of addition, this can also be written as:
\[ \text{Average} = \frac{-3 + 8}{2} \]
This is equivalent to the expression \((-3 + 8) \div 2\).
- Comparison with Given Options and Conclusion
Comparing our derived expression \((-3 + 8) \div 2\) with the given options:
A\((-3 + 8) \div (-2)\)
B\((-3 + 8) \div 2\)
C\(-(3 + 8) \div 2\)
D\([(-3 + (-8))] \div 2\)
We can see that option 'b' matches our calculated expression exactly. Therefore, the correct expression for the average of the high and low temperatures is \((-3 + 8) \div 2\).
Examples
Understanding how to calculate averages is essential in many practical situations. For example, meteorologists use daily highs and lows to determine the mean daily temperature, which helps in climate tracking and agricultural planning. Similarly, if you want to determine your average test score from two exams, you would sum the scores and divide by two, using the same mathematical principles used to find the average of temperatures.