The temperature dropped $-4^{\circ} F$ on Monday, $-5^{\circ} F$ on Tuesday, and $-3^{\circ} F$ on Wednesday. Which equation correctly shows how to find the average drop in temperature for all three days?
$\begin{array}{l}
(-4)+(-5)+(-3)=12 \\
12 \div-3=-4
\end{array}$
$\begin{array}{l}
(-4)+(-5)+(-3)=12 \\
12 \div 3=4
\end{array}$
$\begin{array}{l}
(-4)+(-5)+(-3)=-12 \\
-12 \div 3=-4
\end{array}$
Answer (2)
Calculate the sum of the temperature drops: ( − 4 ) + ( − 5 ) + ( − 3 ) = − 12 .
Divide the sum by the number of days to find the average: 3 − 12 = − 4 .
The equation that correctly shows the average temperature drop is: ( − 4 ) + ( − 5 ) + ( − 3 ) = − 12 − 12 ÷ 3 = − 4 .
The average temperature drop is − 4 .
Explanation
Understanding the Problem The problem asks us to find the correct equation that shows how to calculate the average temperature drop over three days. We are given the temperature drops for Monday, Tuesday, and Wednesday. To find the average, we need to add the temperature drops for each day and then divide by the number of days.
Calculating the Sum of Temperature Drops First, we need to calculate the sum of the temperature drops. The temperature dropped − 4 ∘ F on Monday, − 5 ∘ F on Tuesday, and − 3 ∘ F on Wednesday. So, the sum is: ( − 4 ) + ( − 5 ) + ( − 3 ) = − 12
Calculating the Average Temperature Drop Next, we need to divide the sum by the number of days, which is 3. So, the average temperature drop is: 3 − 12 = − 4
Identifying the Correct Equation Now, we compare our calculations with the given options to find the correct equation. The correct equation should show the sum of the temperature drops as -12 and the average temperature drop as -4. The third option matches our calculations:
( − 4 ) + ( − 5 ) + ( − 3 ) = − 12 − 12 ÷ 3 = − 4
Final Answer Therefore, the correct equation that shows how to find the average drop in temperature for all three days is:
( − 4 ) + ( − 5 ) + ( − 3 ) = − 12 − 12 ÷ 3 = − 4
Examples
Understanding averages is useful in many real-life situations. For example, if you want to track your spending over a week, you can calculate the average daily spending to see if you are staying within your budget. Similarly, if you are monitoring the temperature changes in your city, calculating the average temperature drop can help you understand the overall trend and prepare accordingly. This concept is also used in sports to calculate batting averages or points per game, providing a summary of a player's performance.
To find the average temperature drop over three days, we calculate the total drop as -12°F by summing the drops of -4°F, -5°F, and -3°F. Dividing this total by 3 gives an average drop of -4°F. The correct equation that reflects this calculation is: ( − 4 ) + ( − 5 ) + ( − 3 ) = − 12 and − 12 ÷ 3 = − 4 .
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