Question

Problem Solving with Integers The temperature was \(-7^{\circ} \mathrm{F}\) in the afternoon. That night, the temperature dropped by \(5^{\circ} \mathrm{F}\). What was the nighttime temperature?

Short answer

Answer: The nighttime temperature was -12°F.

Step-by-step solution

Identify the given temperatures

We know that the temperature in the afternoon is \(-7^{\circ}\mathrm{F}\) and the drop in temperature during the night is \(5^{\circ}\mathrm{F}\).

Set up the subtraction

Since the temperature dropped, we need subtract the drop in temperature from the afternoon temperature which means we have: \((-7^{\circ}\mathrm{F}) - (5^{\circ}\mathrm{F})\)

Consider subtraction as addition of the opposite

To subtract a positive integer from a negative integer, we can think of subtraction as adding the opposite, so we get: \((-7^{\circ}\mathrm{F}) + (-5^{\circ}\mathrm{F})\)

Add the negative integers

Now, simply add the negative integers together: \((-7) + (-5) = -12\)

Write the final temperature as Fahrenheit

Now that we have found the sum (-12) we can write it with the temperature unit: \(-12^{\circ}\mathrm{F}\) So the nighttime temperature was \(-12^{\circ}\mathrm{F}\).